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New and Noteworthy of the American Mathematical Society Piecewise-smooth Dynamical Lie Sphere Geometry An Introduction to Bayesian Volume 54, Number 9 2ND October 2007 Systems With Applications to EDITION Scientifi c Computing Theory and Applications Submanifolds Ten Lectures on Subjective Computing M. di Bernardo , University of Bristol, UK; University T. E. Cecil , College of the E. Somersalo , Helsinki University of Technology, of Naples Federico II, Italy; C. Budd , University of Holy Cross, Worcester, MA, USA Helsinki, Finland; D. Calvetti , Case Western Reserve Bath, UK; A. Champneys , University of Bristol, UK; This book provides a modern treatment of Lie’s University, Cleveland, OH, USA P. Kowalczyk , University of Bristol, UK; University of geometry of spheres, its applications and the study This book has been written for undergraduate and Exeter, UK of Euclidean space. It begins with Lie’s construction graduate students in various areas of mathematics This book presents a coherent framework for of the space of spheres, including the fundamental and its applications. It is for students who are understanding the dynamics of piecewise-smooth notions of oriented contact, parabolic pencils of willing to get acquainted with Bayesian approach to

and hybrid systems. An informal introduction spheres and Lie sphere transformation. The link with computational science but not necessarily to go expounds the ubiquity of such models via Euclidean submanifold theory is established via the through the full immersion into the statistical numerous. The results are presented in an informal Legendre map. This provides a powerful framework analysis. It has also been written for researchers style, and illustrated with many examples. The book for the study of submanifolds, especially those working in areas where mathematical and statistical The Character is aimed at a wide audience of applied mathemati- characterized by restrictions on their curvature modeling are of central importance, such as biology cians, engineers and scientists at the beginning spheres. and engineering. Table for E postgraduate level. Almost no mathematical This new edition contains revised sections on taut 8 background is assumed other than basic calculus submanifolds, compact proper Dupin submanifolds, 2007. Approx. 215 p. (Surveys and Tutorials in the and algebra. reducible Dupin submanifolds, Lie frames and frame Applied Mathematical Sciences, Volume 2) page 1122 reductions. Completely new material on isopara- Softcover 2007. Approx. 510 p. 234 illus. (Applied Mathemat- metric hyperspaces in spheres, Dupin hyperspaces ISBN 978-0-387-73393-7  $39.95 ical Sciences, Volume 163) Hardcover with three and four principle curvatures is also ISBN 978-1-84628-039-9  $99.00 included. An Introduction to Manifolds Paul Halmos: L. W. Tu , Tufts University, Medford, MA, USA The Riemann Hypothesis 2nd ed. 2008. Approx. 305 p. 14 illus. (Universitext) In His Own Words Softcover This book introduces the fundamental theory of A Resource for the Affi cionado and Virtuoso ISBN 978-0-387-74655-5  approx. $49.95 manifolds in a readable but rigorous manner. In Part page 1136 Alike I the theory of diff erential forms on Rn is presented P. Borwein , S. Choi , B. Rooney , Simon Fraser Semiparallel as a natural bridge between calculus and the theory University, Burnaby, BC, Canada; A. Weirathmueller , Submanifolds in of manifolds. Once this intuitive foundation is laid, University of Western Ontario, London, ON, Canada manifolds are defi ned in Part II, and several San Diego Meeting Space Forms examples considered. In Parts III and IV tangent This book presents the Riemann Hypothesis, spaces are introduced, along with Lie groups and connected problems, and a taste of the body of Ü. Lumiste , University of page 1225 Lie algebras. Throughout, the author emphasizes theory developed towards its solution. It is targeted Tartu, Estonia the connection between tangent spaces and the at the educated non-expert. Almost all the material This book off ers a familiar methods of linear approximation from is accessible to any senior mathematics student, comprehensive survey to calculus. With this background in place, calculus on and much is accessible to anyone with some date of the theory of manifolds is studied, and important topological university mathematics. The appendices include a semiparallel submani- invariants, such as the de Rham cohomology, are selection of original papers that encompass the folds. Introduced in 1985, semiparallel submani- computed. most important milestones in the evolution of folds have emerged as an important area of Assuming only a year of real analysis and a semester research within diff erential geometry and topology.

theory connected to the Riemann Hypothesis. The Volume 54, Number 9, Pages 1113–1272, October 2007 of abstract algebra at the undergraduate level, and appendices also include some authoritative Lumiste begins with the necessary background on: with all necessary point-set topology summarized expository papers. These are the “expert witnesses” symmetric and semisymmetric Riemannian in an appendix, this book introduces manifolds at a whose insight into this fi eld is both invaluable and manifolds, smooth manifolds in space forms, and level suitable for advanced undergraduates and irreplaceable. parallel submanifolds. Semiparallel submanifolds beginning graduate students. are introduced in Chapter 4, where characteriza- 2007. Approx. 590 p. 25 illus. (CMS Books in tions of their class and several subclasses are given. 2007. Approx. 390 p. 104 illus. (Universitext) Mathematics) Hardcover In later chapters Lumiste introduces the concept of Softcover ISBN 978-0-387-72125-5  approx. $79.95 main symmetric orbit and presents all known ISBN 978-0-387-48098-5  approx. $49.95 results concerning umbilic-like main symmetric orbits. Semiparallel Submanifolds in Space Forms will appeal to both researchers and graduate students.

2008. Approx. 325 p. Hardcover ISBN 978-0-387-49911-6  approx. $79.95

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D-Modules, Perverse Sheaves, and Representation Theory Additional forthcoming titles in the CORNERSTONES series: RYOSHI HOTTA, Wako, Japan; KIYOSHI TAKEUCHI, Tsukuba University, Japan; TOSHIYUKI TANISAKI, Osaka City University, Japan Distributions Translated by KIYOSHI TAKEUCHI, Tsukuba University, Japan Theory and Applications The key to D-modules, Perverse Sheaves, and Representation Theory is the authors’ essential algebraic-analytic approach JOHANNES J. DUISTERMAAT; JOHAN A.C. KOLK, to the theory, which connects D-Modules to representation theory and other areas of mathematics. Signifi cant concepts both Universiteit Utrecht, The Netherlands and topics that have emerged over the last few decades are presented, including a treatment of the theory of holonomic This text is a concise, application-oriented D-modules, perverse sheaves, the all-important Riemann-Hilbert correspondence, Hodge modules, and the solution to introduction to the theory of distributions. It presents Kazhdan-Lusztig polynomials using D-module theory. To further aid the reader, and to make the work as self-contained distributions as a natural method of analysis from both as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. a mathematical and physical point of view. Methods are developed to justify many formal calculations that 2007/XII, 404 PP., 66 ILLUS./HARDCOVER/ISBN 9780817643638/$89.95/PROGRESS IN MATHEMATICS, VOL. 236 do not make sense in the classical framework. The discussion emphasizes applications to the general Dynamical Systems Integrable Systems in study of linear partial differential equations. The subject in this textbook is motivated by many with Applications using Celestial Mechanics examples, exercises, hints and solutions that guide Mathematica® DIARMUID Ó’MATHÚNA, Dublin Institute for Advanced the student along a path requiring only a minimal Studies, Dublin, Ireland STEPHEN LYNCH, Manchester Metropolitan University, UK mathematical background. This work focuses on the two integrable systems of On the author’s Maple edition: 2008/APPROX. 350 PP., 25 ILLUS./HARDCOVER relevance to celestial mechanics, both of which date ISBN 9780817646721/$59.95 TENT. “The book will be useful for all kinds of dynamical back to the 18th century. Under discussion are the CORNERSTONES systems courses…. 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Currents, continuous 2008/APPROX. 240 PP./HARDCOVER 2007/APPROX. 530 PP., 211 ILLUS./SOFTCOVER linear functionals on spaces of differential forms, ISBN 9780817640965/$89.95 TENT. ISBN 9780817644826/$59.95 are a natural language in which to formulate types PROGRESS IN MATHEMATICAL PHYSICS, VOL. 51 of extremal problems arising in geometry, and can Recently released in softcover: be used to study generalized versions of the Plateau Forthcoming in the CORNERSTONES problem and related questions in geometric analysis. series: Mathematical Analysis The text provides considerable background for the Linear and Metric Structures and Partial Diff erential Equations student and discusses techniques that are applicable Continuity Second Edition to complex geometry, partial differential equations, harmonic analysis, differential geometry, and many MARIANO GIAQUINTA, Scuola Normale Superiore, Pisa, EMMANUELE DIBENEDETTO, Vanderbilt University, Italy; GIUSEPPE MODICA, Università degli Studi di Firenze, Nashville, TN, USA other parts of mathematics. Italy “This book certainly can be recommended as an 2008/APPROX. 380 PP., 10 ILLUS./HARDCOVER This self-contained work on linear and metric introduction to PDEs in mathematical faculties and ISBN 9780817646769/$69.95 TENT. structures focuses on studying continuity and its technical universities.” CORNERSTONES applications to fi nite- and infi nite-dimensional spaces. —APPLICATIONS OF MATHEMATICS The authors provide motivation for the study of linear Also by Steven G. Krantz: (Review of the First Edition) and metric structures with examples, observations, Geometric Function Theory exercises, and illustrations. The book may be used in Large parts of this revised second edition have been the classroom setting or for self-study by advanced streamlined and rewritten to incorporate years of Explorations in Complex Analysis undergraduate and graduate students and as a valuable classroom feedback, correct errors, and improve “… the topics are presented with an explanation reference for researchers in mathematics, physics, clarity. Most of the necessary background material has of their interaction with other important parts of and engineering. been incorporated into the complements and certain mathematics. The presentations of the topics are clear nonessential topics have been given reduced attention and the text makes [for] very good reading; basic ideas 2007/XVIII, 470 PP., 128 ILLUS./SOFTCOVER to improve the fl ow of presentation. 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CALL: 1-800-777-4643 • FAX: (201) 348-4505 • E-MAIL: [email protected] • www.birkhauser.com Please mention promotion #013304 when ordering. Prices are valid in the Americas only and are subject to change without notice. For price and ordering information outside the Americas, please contact Birkhäuser Verlag AG by E-mail: [email protected] 013304x Notices of the American Mathematical Society October 2007 1150 Communications

1146 WHAT IS...a Woodin Cardinal? John R. Steel

1153 NSF Proposal Preparation: The View of an Ex-Program Officer Joseph Brennan 1150 1136 1158 Interview with Congressman Jerry McNerney

1161 Bass Receives National Medal of Science Features Allyn Jackson

Commentary 1122 The Character Table for E8 David Vogan 1117 Opinion: Two Landmarks, Two Heroes The recent machine calculation of the characters of the Allyn Jackson Lie group of type E8 was a mathematical and computa- tional achievement receiving widespread public atten- 1118 Letters to the Editor tion. The author, one of the particpants in the project, 1150 Bourbaki, A Secret Society explains why the result was significant and tells the of Mathematicians story of how it was done. and The Artist and the Mathematician—A Book Review 1136 Paul Halmos: In His Own Words Reviewed by Michael Atiyah John Ewing Paul Halmos (1916-2006) wrote widely about doing, teaching, and communicating mathematics. This collection of excerpts presents some of his best writing. Notices Departments of the American Mathematical Society About the Cover...... 1177 Mathematics People ...... 1164 EDITOR: Andy Magid SIAM Prizes Awarded, Prizes of the London Mathematical Society, Royal ASSOCIATE EDITORS: Society of Canada Elections, News from the IMA. Daniel Biss, Susanne C. Brenner, Bill Casselman (Graphics Editor), Robert J. Daverman, Susan Mathematics Opportunities...... 1166 Friedlander, Robion Kirby, Steven G. Krantz, Lisette de Pillis, Peter Sarnak, Mark Saul, John NSF Postdoctoral Research Fellowships, AMS Epsilon Fund, AMS-AAAS Swallow, Lisa Traynor Mass Media Summer Fellowships, Enhancing the Mathematical Sciences SENIOR WRITER and DEPUTY EDITOR: Workforce in the Twenty-First Century, Joint DMS/NIGMS Initiative in Allyn Jackson Mathematical Biology, News from PIMS, Teach for America Accepting MANAGING EDITOR: Sandra Frost Applications for the 2008 Corps, Call for Nominations for ICMI Awards, CONTRIBUTING WRITER: Elaine Kehoe Clay Research Fellow Nominations, Call for Nominations for André PRODUCTION ASSISTANT: Muriel Toupin Aisenstadt Mathematics Prize, AWM Essay Contest. PRODUCTION: Kyle Antonevich, Stephen Moye, Erin Murphy, Lori Nero, Karen Ouellette, Donna Salter, Inside the AMS...... 1170 Deborah Smith, Peter Sykes AMS Department Chairs Workshop, Undergraduate Research ADVERTISING SALES: Anne Newcomb Conference Proceedings Available, Deaths of AMS Members.

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Opinions expressed in signed Notices articles are those of the authors and do not necessarily reflect opinions of the editors or policies of the American Mathematical Society. Opinion

before Perelman’s story became front-page news? I am Two Landmarks, Two guessing few. Being highlighted by the Clay Mathematics Institute as one of its seven Millennium Prize Problems Heroes raised the conjecture’s profile a bit. But the Poincaré Conjecture is not a statement that is easily explained to The experts have weighed in, the dust has settled, and we those without mathematical background. Fermat’s Last can all now celebrate the proof of the Poincaré Conjecture. Theorem, of course, can be understood by schoolchil- And if you also raised a cheer for the proof of Thurston’s dren and thus attracted the efforts of legions of amateur Geometrization Conjecture, not many would try to shush mathematicians—and continues to attract them, despite you. Wiles’s proof. And who can blame them? Who can be 100 More than three years were needed for the experts to percent certain that there is not a really simple proof that work carefully through the papers of Grigory Perelman. has yet to be discovered? During this time the conviction gradually mounted that One interesting similarity between the two results is his work does indeed validate the vision of Richard Hamil- that Perelman and Wiles both worked in isolation. Wiles ton for attacking the conjectures. The climax came at the confided in his Princeton colleague Nicholas Katz; it International Congress of Mathematicians in Madrid in seems likely Perelman confided in no one at all. But the August 2006, when experts stated publicly that Perelman unveiling of their respective results could not have been had proved Poincaré (a bit more caution was expressed more different. Wiles revealed his proof before a cheering about Geometrization, but no doubts were voiced). crowd of his number theory colleagues, who had gathered The saga of Perelman and his work catapulted math- at the Newton Institute in Cambridge, one of the world’s ematics into headlines in a way not seen since Andrew major mathematics centers. By contrast, Perelman, hav- Wiles’s proof of Fermat’s Last Theorem in the mid-1990s. ing become increasingly isolated from the mathematical As with Fermat, the intense media blitz was followed community, posted his preprints on the arXiv, let a few by a period of silence during which books were written. selected people know they were there, and then waited Two have appeared recently: The Poincaré Conjecture: for the world to respond. Wiles attended the Berlin ICM In Search of the Shape of the Universe, by Donal O’Shea in 1998 and collected his “special award” from the In- (Walker, March 2007), and Poincaré’s Prize: The Hundred- ternational Mathematical Union to thunderous applause Year Quest to Solve One of Math’s Greatest Problems, by from the audience gathered at the opening ceremonies. George Szpiro (Dutton, June 2007). Perelman not only chose to skip the Madrid Congress in Fermat’s Last Theorem and the Poincaré Conjecture 2006, where he was to be awarded the Fields Medal, but are similar in that they both inspired a great deal of he refused to accept the honor altogether. mathematical development. Many special cases were es- These two landmark results are very different, but tablished: for example, FLT was proved for large classes of they both show how mathematics proceeds: It starts with exponents, and the Poincaré Conjecture was established a tantalizing question or a flash of insight compelling for many special types of manifolds. Despite these simi- enough to spark the search for the why. This basic human larities, as mathematical statements, FLT and Poincaré are desire for understanding is one reason Wiles and Perel- quite different. FLT is a somewhat isolated statement that man became heroes to the general public—and to many does not by itself have important implications that could mathematicians as well. be explored. By contrast, the Poincaré Conjecture cap- tures a deep truth about the nature of three-dimensional —Allyn Jackson shapes. The importance of Poincaré was reinforced when it was shown to be a particular case of Thurston’s sweeping Geometrization Conjecture, which has enormous impli- cations in topology and geometry. For years many papers have appeared with careful caveats about how far the results could be pushed given the current status of the Geometrization Conjecture. Probably few papers have begun, “Assuming Fermat’s Last Theorem, we prove…” Much more comparable to Geometrization is the deep conjecture that connected FLT to modern number theory, namely, the Taniyama-Shimura Conjecture, the center- piece of Wiles’s proof of FLT. Another big difference between FLT and Poincaré is their fame outside of mathematics. How many among the general public had heard of the Poincaré Conjecture

October 2007 Notices of the AMS 1117 Letters to the Editor

Review of Shadows of Reality Although I did not give the compli- Will then referees be responsible for cated algorithms, in the text and my the errors in papers? Fried’s opinion Thanks for so detailed a review of diagrams I clearly state that one does seems to be that they are responsible my book, Shadows of Reality [April not project all the hypercubic cells already now, without payment: “…it is 2007 issue]. But there are misrep- to the plane (or space) of projection, my experience that over 50% of papers resentation of arguments, mine and but that there is a gate or test that (yes, tough topics, but …) have very others. each vertex must pass before they are serious …errors. This reflects poorly Phillips says that I go too far with projected. In one, but only one, of the on referees. Why referees and not the influence of Jouffret on Picasso two de Bruijn algorithms it is possible authors?” I don’t see a clear answer and says that even Henderson is more to call this test a “strip” or a “slice”, to that question in what follows there. cautious. Her book on the subject was or refer to a “cut and project method”. I was always told and was convinced from her Ph.D. thesis in 1979, when as But to point to this test slice and say when actively editing journals that the a young graduate student she had no that my exposition if fundamentally authors not the referees are ultimate- choice but to offer a (single) caveat in flawed is again to misrepresent what ly responsible for errors. (Of course her long book. In lectures and many de Bruijn has done. He has seen that the referee should do her/his best to subsequent writings, Henderson is quasicrystals are projections of reg- notice them.) This seems to be sup- far more forceful. To imply that she ular higher-dimensional cubic cells. ported by the following stanza in R. P. is wishy-washy on the proposition is Quasicrystals are quixotic because Boas’s humorous but seriously meant to misrepresent her life’s work. It is of the irrational angle at which this (“Let me make it clear to you/This is true that I have taken her argument projection occurs. It is an almost what we’ll never do”) Retroactive Edi- further by giving other, more detailed unimaginable feat of mathematical torial Policy (Amer. Math. Monthly 89 examples from the Jouffret. Do I offer visualization from de Bruijn; don’t (1982), p. 32; the other three stanzas no proof, as Phillips contends? I show take this away from him because you are also worth reading): “We often that Picasso had the means, motive, are “disappointed” in me. note that authors, even those whose and opportunity. Also true, I looked It is the last chapter that has made work is strong, They sometimes go for and could not find the letter in some mathematicians so mad. In this too far and say a thing or two that’s which Picasso says he did copy from chapter I reject slices in favor of wrong. You needn’t worry very much the Jouffret, but written confessions projections as a model for spacetime about a stray mistake: If you can fool are not the only form of proof. I invite physics. Even the title of my book says the referee, what difference does it readers to look at the comparisons as much. I agree that to be furious make? But not in my journal.” and decide for themselves. at squares while being in love with One more short note about dead- Phillips likewise misrepresents triangles, does make one sound like a lines for referees. There is almost Minkowski in his reading of Minkows- nut. On the other hand, to accurately nothing so annoying for (active) ki that I quote. Minkowski says report on what physicists say and do editors and editorial staff than a (rearranging his words a bit) that is responsible journalism, and if they referee from whom, notwithstanding to project from spacetime to three say that space + time is best modeled reminders, one does not hear for dimensions “cast[s] only a very com- as a projection of spacetime, then months and months, while the au- plicated projection”. But we can not that is responsible journalism. Did I thors keep asking “What happened take that statement to mean that unfairly characterize their work? Or to my paper?” There may also be a Minkowski is rejecting “projection”. do I bring up something that oth- slight chance of priority problems: I argue that Minkowski states that ers have missed! That is the proper while priority can be established from these complications are exactly the subject of criticism. submission dates, people tend to distortions of special relativity. It is —Tony Robbin quote where they first saw the re- not fair to change Minkowski’s mean- New York City sult. Editors-in-chiefs and managing ing just to hammer me; Minkowski [email protected] editors are usually patient when the did not intend to dismiss projection referee informs them approximately here. (Received April 20, 2007) how much more time they need but I have programmed both of the de not if they get only silence. Bruijn methods for generating fool- Referees Also referees should say (write) as proof quasicrystals, as well as written soon as possible if they can not or programs for assembling quasicrystal In his Opinion on “Should journals would not referee the paper (e.g., for blocks. It took almost a year out of compensate referees?” (Notices 54 lack of time and certainly if it is “far my life; it is not easy for an artist to (2007), no. 5, p. 589) Michael Fried from topics in which the prospective learn enough linear algebra to do this. seems to answer that question by Yes. referee publishes papers”). Judging

1118 Notices of the AMS Volume 54, Number 9 Letters to the Editor from the reports we finally got, many and an expansion on Aczel’s top- in as far as there is added content or editors (including me) got the impres- ic are on my website math.uci.edu/ value. sion that many referees (apparently ~mfried/proplist-ams.html, item The economics of learned soci- not Fried and his # 1 correspondent) # 4. eties and journal publishing work were tardy not because they did a thor- Refereeing is a hard task, and too rather differently in Europe from in ough job but because they delayed so few do it well. I suggest, if there the USA—more than can be covered long starting it. were incentives, more mathemati- in this letter but perhaps worthy of cians would feel it worth developing further debate in your pages. —János Aczél the high skills that go with quick, University of Waterloo, Emeritus —Kenneth Falconer quality refereeing. [email protected] University of St. Andrews —Michael Fried [email protected] (Received May 4, 2007) University of California, Irvine (Received June 20, 2007) [email protected] Reply to Aczel (Received July 2, 2007) Librarians like Online Notices Aczel raises an issue of received I applaud Notices’ move to com- wisdom: That it’s not the referee’s re- Journal Pricing sponsibility to vouch for the accuracy plete online issues, mentioned in of an author’s paper. He suggests I I was pleased to read the recent ar- the June/July “Letter from the Editor”. didn’t make a case for this responsi- ticle “Jumping Ship: Topology Board We librarians like online versions that bility though I did say at least 50% Resigns” [May 2007 issue] in the AMS contain everything found in the paper of the papers I referee have serious Notices, particularly the coverage of versions…and more, of course. errors. our launch of the LMS-owned Journal In the past, I have had difficulties Finding referees for new, not- of Topology with a detailed account with pictures missing from the online yet-assimilated tools is one tough of recent history. The London Math- version of articles, and I hope that no problem. It requires interdisciplinary ematical Society is delighted to be longer happens now. refereeing expertise and editors who launching this new journal in a very —Martha Tucker, Librarian follow the analysis. Or else, it is rife important and exciting area of mathe- University of Washington for abuse. matics. We are very fortunate to have [email protected] An example from my early expe- an excellent and world-renowned edi- rience will help me address Aczel’s torial board and the support of our (Received June 26, 2007) concerns. publishers, Oxford University Press, My first Annals paper solved a prob- in this venture. The signs are already AK-47 Memories lem posed by Ax and Kochen. Prior to encouraging, with substantial interest my result, someone well-connected from all parts of the world. I read the “Letter from the Editor” in to the area “proved” there could be I note your comments on the pric- the June/July 2007 Notices of the AMS no such theorem as mine. ing of the new journal. The Society with great interest. My paper had five referees. Four has worked hard to keep the price low. In Fall 1968, I was drafted during called my office at Stony Brook, with But in order to maintain its activities my first term in graduate school, so the same technical questions. A fifth in support of mathematics nationally in January 1969 when Andy Magid be- revealed himself years later. I did and internationally we must operate gan collecting the Notices, my parents get a fair hearing from a rare fair in a businesslike way, and it is essen- were forwarding mine to me at Fort editor—Armand Borel—to whom I tial that we work to a model for the Dix, New Jersey, where I had been lobbied for my paper during a two new journal that at least breaks even sent for basic training. year postdoctoral at IAS. in a reasonable period and does not If I had had any idea that the My experience: Editors dominate disadvantage the Society financially Notices were capable of stopping an in this process over referees. in the long term. AK-47 round, you can be sure I would Aczel also complains about tardy The Society fully recognises the im- have started saving them, too. I cer- referees. portance of the dissemination of tainly would have brought old issues Correspondent # 5 in my article mathematical knowledge and the with me to Vietnam, where I served as asked, “Why do mathematicians ref- threats of rising prices of journals an infantryman near the Cambodian eree without compensation?” He and falling library budgets. In pur- border from June 1969 to June 1970. wondered, among the possibilities suing its objectives of increasing its My mathematical background paid off in Vietnam. I was trained as a rifle- if it was “a fair trade for having their support for mathematical activities, man, but when I got to my company in papers refereed?” the Council of the Society will contin- the field, I was put in the (somewhat) In my experience as an author, ue to seek to expand its activities in safer mortar platoon to do the vector you may not even get that. Jus- publishing but its policy is that the addition for firing and adjusting the tification for this, responses from prices of its journals should not rise fire of the 81mm mortar. For 37 years others who wrote me directly, in real terms (against inflation) except

October 2007 Notices of the AMS 1119 Letters to the Editor

I’ve felt this change of assignment may very well have saved my life. Fortunately, I never stopped, or even slowed down, an AK-47 round. I returned to graduate school in 1971, and came to Georgia Tech in 1976. —Fred Andrew Georgia Institute of Technology [email protected]

(Received June 27, 2007)

Paper Notices Will Be Read More

While reading the editorial in the No- tices of the AMS (June/July, 2007), I had the following thoughts. I feel the Notices would not be read as much if we all had to download it. Individuals are innately lazy. I have a colleague who subscribes to the Notices, but is too lazy to open the wrapper; his issues are stacked in pristine condition with the cellophane still intact to keep the dust out. Will such individuals find downloading less of an effort? Even if every reader downloaded the issue it would not be cost effective in time and paper. Who downloads on two sides? Just as those who use digital cameras say they will get the pictures to you immediately, either they never arrive or they arrive much later than those developed from film. Perhaps the anticipation of a paper copy each month in the mail is best; it arrives bound and easy to handle. All that is required is to slit open the cellophane. Then the Notices can be read in the office, at home, or on the bus. Be bold: be conservative. —Agnes M. Herzberg Queen’s University [email protected]

(Received July 11, 2007)

1120 Notices of the AMS Volume 54, Number 9 APPLIED MATH TITLES from

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Your donations support: Learn about giving opportunities and estate planning • Career paths of young mathematicians www.ams.org/giving-to-ams • Recognition of important work Contact the AMS • Public awareness and appreciation of Development Office mathematics 1.800.321.4267 • Inspiration of young scholars (U.S. and Canada) or (Epsilon Fund) 1.401.455.4000 (worldwide) • International outreach 08/04 email: [email protected] The Character Table for E8 David Vogan

n January 8, 2007, just before 9 in What’s E8? the morning, a computer finished writ- A Lie group is a group endowed with the structure ing to disk about sixty gigabytes of of a smooth manifold, in such a way that group files containing the Kazhdan-Lusztig multiplication and inversion are smooth maps. Opolynomials for the split real group Every finite group is a Lie group: the manifold G of type E8. Values at 1 of these polynomials structure is just the zero-dimensional discrete are coefficients in characters of irreducible repre- structure. For that reason the study of Lie groups sentations of G; so all irreducible characters were is necessarily more complicated than the study written down. The biggest coefficient appearing of finite groups. But it’s not unreasonable to was 11,808,808, in the polynomial concentrate on connected Lie groups. If you do that, a miracle happens: connected Lie groups are 152q22 + 3472q21 + 38791q20 + 293021q19 less complicated than finite groups. The reason is that a connected Lie group is almost completely +1370892q18 + 4067059q17 + 7964012q16 determined by its Lie algebra. The Lie algebra is the tangent space to the group manifold at the identity 15 14 13 +11159003q + 11808808q + 9859915q element, endowed with a nonassociative product called the Lie bracket. Since the Lie algebra is a +6778956q12 + 3964369q11 + 2015441q10 finite-dimensional vector space, it can be studied using linear algebra ideas. A typical method is to +906567q9 + 363611q8 + 129820q7 look at one element X of the Lie algebra, and to +41239q6 + 11426q5 + 2677q4 regard “Lie bracket with X” as a linear transfor- mation from the Lie algebra to itself. This linear +492q3 + 61q2 + 3q. transformation has eigenvalues and eigenvectors, and those invariants can be used to describe the Its value at 1 is 60,779,787. structure of the Lie algebra. This calculation is part of a larger project Just as finite groups are successive extensions called the atlas of Lie groups and repre- of nonabelian simple groups (and Z/pZ), connected sentations. In this article I’ll try to explain the Lie groups are successive extensions of connected atlas project, what Kazhdan-Lusztig polynomials simple Lie groups (and the additive group R). Many are, why one might care about them, and some- questions about general Lie groups can be reduced thing about the nature of this calculation and the to the case of connected simple Lie groups, and calculators. so to questions about simple Lie algebras over the real numbers. David Vogan is professor of mathematics at the Mas- Many algebra problems are easier over alge- sachusetts Institute of Technology. His email address is braically closed fields, so it’s natural to relate Lie [email protected]. Supported in part by NSF FRG grant algebras over R to Lie algebras over C. If k ⊂ K is 0554278. any field extension, an n-dimensional Lie algebra

1022 Notices of the AMS Volume 54, Number 9 gk over the small field k gives rise naturally to an well established as the “right” way to present the n-dimensional Lie algebra gK = gk ⊗k K over the theory, the older explicit constructions continue large field K. The algebra gk is called a k-form of to be a powerful tool. gK . We can study real Lie algebras by first studying What we are seeking is an understanding of complex Lie algebras, and then studying their real Lie groups and (infinite-dimensional) representa- forms. tions of this aesthetically inferior sort: one that Wilhelm Killing in 1887 was able to classify for the exceptional groups in particular may rely simple Lie algebras over the complex numbers. He on explicit calculations. Always our goal is to found four infinite families of classical Lie algebras find formulations of results that are as clean and An, Bn, Cn, and Dn; and five exceptional Lie algebras simple and general as possible; but we allow for G2, F4, E6, E7, and E8. Each of these complex Lie the possibility of verifying some results by long algebras has a finite number of real forms; the real computations. The calculation we have done for E8 forms were described completely by Élie Cartan in is certainly long. I will say a few words in the last the 1890s. section about the kind of clean and simple results In each case there are two distinguished real we are extracting from it. forms: the compact real form, for which the cor- A general warning about mathematical precision. responding Lie group is compact, and the split I have tried to make the mathematical statements real form. The term “split” refers to factorization convey accurately our level of understanding; but I of certain characteristic polynomials. The split have deliberately omitted or obscured many impor- form has the property that there is an open set tant details. (Here is an example. In equation (D) of Lie algebra elements X for which the linear below, I say that Harish-Chandra found a basis for transformation of Lie bracket with X has only real the solutions of a system of differential equations. eigenvalues. If one works with simple Lie algebras When certain eigenvalues for the system are zero, over other fields, there is always an analogue of Harish-Chandra did not find all the solutions. The the split form. The compact form is special to the ones that he found suffice for the expression real field. of irreducible characters: equation (E) remains The Lie groups attached to classical Lie algebras true.) Undoubtedly the number of unintentional are all related to classical linear algebra and ge- obscurities and omissions is equally large. For both ometry. A real Lie group of type Bn, for instance, categories, I apologize in advance. 2n+1 is the group of linear transformations of R The level of historical precision is perhaps even preserving a nondegenerate quadratic form. These lower. I have omitted reference to many mathe- groups were already known in Lie’s work, and in maticians whose work played a crucial role in the some sense they go back even to Euclid. developments reported here. For these omissions I The great surprise in Killing’s work was his will not attempt to give an illustrative example but discovery of the exceptional Lie algebras: five I will again apologize. simple Lie algebras (of dimensions 14, 52, 78, 133, and 248) having no straightforward connection to Unitary Representations and Their classical geometry. Work in the twentieth century on the classification of finite simple groups shows Disreputable Cousins that we should be delighted with such a short and A unitary representation of a topological group tractable list of exceptions. G is a continuous action of G by automorphisms The atlas project is aimed at understanding the of a Hilbert space (preserving the inner product). structure and representation theory of Lie groups. Another way to say this is that a unitary repre- Each member of the project has a slightly different sentation is a realization of G as symmetries of a idea about what “understanding” means. Certainly (possibly infinite-dimensional) Euclidean geometry. it should include a thorough understanding of the Because Hilbert spaces are the basic objects of exceptional groups. quantum mechanics, one can also say that a unitary There is an aesthetic in this subject according representation is a realization of G as symmetries to which the best proof is one not referring to of a quantum-mechanical system. A unitary repre- the Cartan-Killing classification. In practice, such a sentation is called irreducible if the Hilbert space proof may be difficult to find. One of the most fun- has exactly two closed G-stable subspaces. damental results is Cartan and Weyl’s description Because so many function spaces are closely of the finite-dimensional irreducible representa- related to Hilbert spaces, unitary representations tions of a connected Lie group. This theorem are a fundamental tool for understanding ac- was first proved in the 1930s using explicit con- tions of topological groups. To prepare this tool structions of representations of simple Lie groups, for use, we seek to understand arbitrary unitary given separately in each case of the classification. representations of arbitrary topological groups. Only twenty years later did Harish-Chandra give An arbitrary unitary representation can often a construction independent of the classification. be written as a direct integral of irreducible uni- Even today, when Harish-Chandra’s approach is tary representations. The notion of direct integral

October 2007 Notices of the AMS 1023 extends that of direct sum. If T is the unit circle, (The correct notion of equivalence—Harish- the Hilbert space L2(T) has a direct sum decom- Chandra’sinfinitesimal equivalence—isabitsubtle, 2 P inθ position L (T) = n∈Z C · e given by Fourier and involves unbounded operators. That causes series. The Hilbert space L2(R) has a direct integral difficulties with making precise statements in the 2 R ixξ decomposition L (R) = ξ∈R C · e dξ given by the rest of this section, but nothing insurmountable.) Fourier transform. Quasisimple representations turn out to be easier There is an extremely general theorem guaran- to describe than unitary representations. teeing existence of a direct integral decomposition What is the relation to the original problem into irreducible representations: it suffices that of describing unitary representations? A unitary the topological group have a countable dense representation is automatically quasisimple, so we subset. There are moderately general theorems want to understand when a quasisimple irreducible guaranteeing uniqueness of direct integral decom- representation is actually unitary. That is, we want positions. This uniqueness holds (for example) to know whether Vπ admits a G-invariant Hilbert for all algebraic Lie groups—subgroups of n × n space structure. This question can be broken into matrices defined by polynomial equations in the two parts: whether there is a G-invariant Hermitian matrix entries. We therefore seek to understand form, and whether this form is definite. We can irreducible unitary representations for algebraic therefore define Lie groups. Πh(G) = equivalence classes of irreducible Work begun by George Mackey and complet- quasisimple Hermitian representations of G, ed by Michel Duflo describes irreducible unitary representations of algebraic Lie groups by a very and get inclusions concrete and explicit reduction to the case of Πu(G) ⊂ Πh(G) ⊂ Πq(G). reductive algebraic groups. (These are essentially direct products of simple and abelian Lie groups.) The atlas goal of understanding the irreducible One of the goals of the atlas project is this: unitary representations of a reductive algebraic Lie group G can now be divided into three steps: to describe the set (G) of irreducible unitary Πu • representations of each reductive algebraic Lie describe Πq(G) (all representations); • group G. describe Πh(G) (hermitian representations) as a subset of (G); and Since we haven’t yet reached this goal, we want to Πq •describe (G) (unitary representations) as a identify steps that represent progress towards it. Πu subset of (G). Harish-Chandra in the 1950s, following a sugges- Πh tion of Chevalley, began to study the larger class of The first two steps of this program have been irreducible representations that are not necessarily addressed by Langlands and by Knapp-Zuckerman; unitary. A representation of a topological group there is an excellent account in Knapp’s book G means a continuous action of G on a complete Representation Theory of Semisimple Groups. Here locally convex topological vector space. We may is an approximate statement. write it as a group homomorphism “Theorem” 1 (Langlands, Knapp-Zuckerman). Suppose G is a reductive algebraic Lie group. Then π : G → Aut(Vπ ), the set Πq(G) of equivalence classes of irreducible with Vπ the vector space. We say that π is irreducible quasisimple representations of G is in natural if Vπ has exactly two closed invariant subspaces. bijection with a countable discrete collection of The study of irreducible representations in general complex algebraic varieties Xi (C). Each of these is complicated by the existence of invertible linear algebraic varieties is defined over R, and the subset operators on infinite-dimensional Banach spaces Πh(G) corresponds to the real points Xi (R). having no nontrivial closed invariant subspaces. Stated in this way, the “Theorem” is equally true Such operators define irreducible representations for reductive algebraic groups over arbitrary local of the group Z, but they have little to do with most fields. The quotation marks correspond to some problems of harmonic analysis. Harish-Chandra small and well-understood technical difficulties; for found a natural technical condition called quasisim- the experts, the magic words are “R-groups”. Each plicity on irreducible representations of reductive subset Πu(G) ∩ Xi (R) is defined by real algebraic Lie groups that excludes such pathological behav- inequalities; the difficulty is that we do not know a ior. (The condition is that all operators commuting simple description of those inequalities. with the representation are assumed to be scalar. In the case of unitary irreducible representations, Representations of Compact Lie Groups quasisimplicity is the theorem called Schur’s Lem- What is the nature of the information provided ma.) If G is any reductive algebraic Lie group, we by “Theorem” 1 above? The example of compact define Lie groups (which is a special case!) is helpful. I Πq(G) = equivalence classes of irreducible will go into some detail about that classical theory, quasisimple representations of G. seeking to formulate results in a way that carries

1024 Notices of the AMS Volume 54, Number 9 over to general reductive algebraic Lie groups. because the set P is very easy to compute and to An irreducible representation of a compact Lie manipulate. It is very unsatisfactory as a descrip- group is automatically quasisimple, Hermitian, and tion of the irreducible representations, because unitary; so those distinctions will not appear at all. it does not even explicitly describe the “natural Suppose K is a compact connected Lie group, bijection”. In order to do that, we need a bit more and T is a maximal torus in K (a maximal connected structure theory. Attached to each coroot α∨ there abelian subgroup). Necessarily T is isomorphic to is a root α ∈ Πu(T ); the set of all roots is written a product of ` circles, where ` is a nonnegative R(K, T ) ⊂ u(T ). integer called the rank of K. Π Any irreducible unitary representation of T must The roots are by definition the nontrivial repre- be one-dimensional. A one-dimensional unitary sentations of T appearing in the “adjoint action” representation (of any topological group G) is a of T on the complexified Lie algebra of K. Cor- ∨ continuous homomorphism from G to the group responding to the simple coroots S are simple U(1) of 1 × 1 unitary matrices, which is again roots just the circle group. Any homomorphism from S = {α1, . . . αm} ⊂ R(K, T ) ⊂ Πu(T ). (C) the circle to itself is given by raising to the mth Here is a description of the Cartan-Weyl bijection. power for some integer m. That is, Πu(circle) ' Z. Because T is a product of ` circles, it follows that Theorem 3 (Cartan and Weyl). In the setting of ` Theorem 2, an irreducible representation π of K u(T ) ' Z . In a coordinate-free way, we say that Π corresponds to a dominant weight µ ∈ P if and Πu(T ) is a lattice of rank `. The structure theory of compact Lie groups only if the following conditions are satisfied: a) the provides a finite collection R∨(K, T ) of nonzero weight µ appears in the restriction of π to T ; and b) ∨ for every simple root α ∈ S, the weight µ + α does Z-linear maps α : Πu(T ) → Z, called the coroots of T in K. The structure theory points also to not appear in the restriction of π to T . certain natural subsets of the coroots, called simple Theorem 3 is in some sense a complete descrip- coroots; we fix such a subset tion of the irreducible representations of K, but it is still not completely satisfactory. It does not say ∨ = { ∨ ∨ } S α1 , . . . αm . (A) how to calculate the dimension of a representation The simple coroots are linearly independent, so or its restriction to a compact subgroup of K. We they define a nonempty cone will address those questions (and generalizations ∨ ∨ ∨ for noncompact groups) in the next section. P = {µ ∈ Πu(T ) | α (µ) ≥ 0 (α ∈ S )}, (B) called the cone of dominant weights. Character Tables for Lie Groups It is a fundamental fact that everything about Much of the content of the Atlas of finite groups the structure of the compact Lie group K—and and representations consists of character tables. indeed of arbitrary reductive algebraic groups—is In this section I’ll recall what that means, how encoded by the lattice Πu(T ) and the finite set to extend the notion to Lie groups, and how it’s ∨ of Z-linear maps S . (To be precise, one needs possible to write character tables for reductive Lie also the simple roots S ⊂ Πu(T ), introduced in (C) groups in a finite form. below.) In the hands of Chevalley and Grothendieck Suppose π : G → Aut(Vπ ) is a representation and others, this fact led to the theory of reductive of a topological group on a finite-dimensional groups over arbitrary fields (or even commutative complex vector space Vπ . The character of π is a rings). For the atlas project, it means that the complex-valued function on G, defined by structure of reductive groups can be described in terms of strings of integers and so is perfectly Θπ (g) = tr π(g). suited to exact computer calculation. It’s very easy to see that Θπ is a class function on G Theorem 2 (Cartan and Weyl). Suppose K is a com- (that is, Θπ is constant on conjugacy classes in G). pact connected Lie group, and T is a maximal torus What is not quite so obvious, but still elementary, is in K. Pick a set S of simple coroots for T in K as in that irreducible (finite-dimensional) representations (A) above, and define dominant weights P as in (B). having the same character are equivalent. Then there is a natural bijection between dominant In the case of a finite group G of order N, the weights and irreducible representations of K eigenvalues of G are Nth roots of unity, so the values of characters of G are integer combinations P ↔ (K). Πu of the N complex numbers exp(2πmi/N) (for m In the language of the Langlands and Knapp- an integer between 0 and N − 1). It is therefore Zuckerman Theorem 1, P parametrizes the count- possible to write a character of G precisely: for able set of algebraic varieties Xi . Each Xi consists each conjugacy class in G, one can write the N of a single point, so Xi (C) = Xi (R). integers that are the coefficients of these roots This theorem is very satisfactory as a parame- of unity. (Fortunately it is possible in practice trization of the irreducible representations of K, to find far more compact representations of the

October 2007 Notices of the AMS 1025 character values.) A character table for G is a list continuous function f on M defines a generalized of all the character values of all the irreducible function by the formula representations. Z If G is a compact Lie group, the notion of char- f (ξ) = f (m)dξ(m). M acter table still makes sense (since the irreducible The trace of a finite-dimensional representation representations are finite-dimensional). What is of a Lie group G is a continuous function on G not so clear is whether it can be written down in a and therefore may be regarded as a generalized finite way. The values of each character must be Θπ function. The following theorem of Harish-Chandra specified at each of the infinitely many conjugacy shows that the character of an irreducible qua- classes in G; and then this task must be repeated sisimple representation of a reductive algebraic Lie for each of the infinitely many π. group G is a generalized function on G. Hermann Weyl solved these problems. I’ll write his solution completely in the simplest case and Theorem 5 (Harish-Chandra). Suppose G is a then say a few words about the general case. reductive algebraic Lie group, π is an irreducible quasisimple representation of G on a Hilbert Theorem 4 (Weyl). Suppose space, and ξ is a test density on G. The operator G = {a + bi + cj + dk | a2 + b2 + c2 + d2 = 1} R π(ξ) = G π(g)dξ(g) is trace class, and defining is the group of unit quaternions, and Θπ (ξ) = tr π(ξ) makes Θπ a generalized function on G. = { + | 2 + 2 = } = { | ∈ } ⊂ T a bi a b 1 exp(iθ) θ R G There is a conjugation-invariant open subset is a maximal torus. a) There is exactly one irre- G0 ⊂ G, whose complement has measure zero, so 0 ducible representation πn of G for each strictly pos- that the restriction of Θπ to G is a conjugation- 0 itive integer n. b) Every conjugacy class in G meets invariant analytic function Θπ , locally integrable T , so a class function on G is determined by its re- on G. The generalized function Θπ is equal to 0 striction to T . c) The value of the character of πn integration against Θπ . = on T is Θπn (exp(iθ)) sin(nθ)/ sin(θ). Writing a character table for the reductive alge- We have in (c) an infinite character table pre- braic Lie group G means writing down each of the 0 sented in finite form. The infinitely many rows are functions Θπ , as π runs over the (infinite) family indexed by n, and the infinitely many columns by of irreducible quasisimple representations of G. θ (more precisely, by θ up to sign and addition of The reason that each such function can be written multiples of 2π). down is that it turns out (just as in the case of In part (a) of the Theorem, one can think of the compact groups) to be a quotient of finite integer integer n−1 as corresponding to a one-dimensional combinations of exponential functions. representation of T , that is, to an element of Πu(T ). The possibility of handling infinitely many π is A version of (a) for general compact Lie groups a consequence of the Jantzen-Zuckerman “transla- is provided by the Cartan-Weyl Theorem 2 in the tion principle”. They partition all irreducible repre- last section. Part (b) makes sense as stated for sentations into finitely many translation families. In a general compact connected Lie group and is the formulas for the characters of representations true. The Weyl character formula for general G in one translation family, only the exponential looks something like (c). There is a denomina- functions change: the coefficients in the formulas tor (generalizing the function sin(θ)) that is a remain the same. In the case of a compact group, trigonometric polynomial on T , independent of there is single translation family, with characters the representation. The numerator (generalizing given by the Weyl character formula; all that varies sin(nθ)) is a trigonometric polynomial built from with the representation are the exponents. For the weight µ that parametrizes the representation. example, for the quaternion group described in For infinite-dimensional representations, the Theorem 4, the parameter for the translation family difficulties with character theory are more funda- is the integer n. mental. The operators π(g) are essentially never Here is a little more detail. The differential of trace class. Harish-Chandra understood that the equations for the character Θπ come from the character makes sense only after “regularization” center Z of the universal enveloping algebra of the in the sense of distribution theory. Each individual Lie algebra of G. They are eigenvalue equations; operator π(g) does not have a trace: one first has the eigenvalues are the complex scalars by which to smooth the operator by averaging over a nice Z acts in the representation π. (That Z does act compact collection of values of g. by scalars is exactly Harish-Chandra’s definition Here is how to do that. Recall that a test density of quasisimplicity.) The eigenvalues are encoded on a smooth manifold M is a compactly supported by an algebra homomorphism λ: Z → C called the complex-valued measure ξ on M, which in local infinitesimal character of π. coordinates is a smooth multiple of Lebesgue mea- After appropriate (very subtle!) changes of sure. A generalized function on M is a continuous variables, the differential equations become (in linear functional on the space of test densities. Any local coordinates) systems of constant-coefficient

1026 Notices of the AMS Volume 54, Number 9 eigenvalue equations on Rn. For each choice λ of Theorem 6 (Langlands and Knapp-Zuckerman). eigenvalues, the solutions are finite linear combina- There is a natural bijection between the set {π} tions of exponential functions. Harish-Chandra was of irreducible representations of G and Harish- able to describe these solutions very explicitly and Chandra’s solutions (D) to the differential equations completely. (Much of the difficulty is understanding for characters. Write πi for the irreducible repre- how solutions on different coordinate patches fit sentation corresponding to the solution Θi . Then together.) For each choice of eigenvalues, he found the (square) matrix P πi ,j in (E) above is a lower an explicit basis triangular integer matrix with 1s on the diagonal. To say that the matrix is lower triangular re- , ,..., (D) Θ1 Θ2 ΘN quires an appropriate ordering of the solutions for the global solutions of the differential equations. Θj . Harish-Chandra’s construction of the solutions (It would be mathematically more precise but nota- analyzes exponential terms of greatest possible λ λ λ growth at infinity on G. If we assume that the are tionally more burdensome to write Θ1 , Θ2 ,..., ΘN(λ), Θj indicating explicitly the fact that the equations ordered so that the later ones have faster growth, being solved depend on the system λ of eigenvalues. then we get the lower triangularity. Another way I will choose the path of unburdened imprecision.) to achieve it is explained after equation (F) below. In this section I will say a bit about the mathemat- As a consequence, each irreducible character Θπ has a unique expression ics underlying the computation of the matrix P πi ,j . The main tool is a geometric reinterpretation of N X the matrix introduced by Beilinson and Bernstein. = P , (E) Θπ π,j Θj It takes place in a smooth complex projective j=1 algebraic variety X (depending on the reductive for some complex numbers P π,j . (The reason for group G) called the complete flag variety X = X(G). calling the coefficients P will emerge in the next One way to define X is as the variety of maximal section: the overline means the image in a quotient solvable Lie subalgebras inside the complexified map, defined from polynomials to coefficients Lie algebra gC of G. by evaluation at 1.) Writing down an irreducible The variety X is degenerate in some very in- character Θπ is therefore equivalent to writing teresting ways. Most algebraic varieties are not 1 down the N complex numbers P π,j . P bundles in any way. The variety X has a finite The last important fact is that the coefficients collection P π,j are all integers. It is not quite clear to whom πs : X → Xs (s ∈ S) (F) this observation should be attributed. At least with 1 forty years of hindsight, it is easy to deduce from of P fibrations. (That is, each πs is a smooth 1 the work of Langlands and Knapp-Zuckerman on submersion with fiber the Riemann sphere CP .) the classification of irreducible representations. The parametrizing set S is the set of simple roots Zuckerman may have been the first to recognize the introduced in (C) above. existence and importance of character formulas In case G is GL(n, R), the variety X may be identified with complete flags in n: increasing (E) with integer coefficients. He wrote an explicit C chains of n linear subspaces F , with dim F = j. formula for the character of a finite-dimensional j j There are n − 1 P1 fibrations; for 1 ≤ j < n, the jth representation (φ, F) in his thesis; in that case the fibration arises by throwing away the j-dimensional coefficients P φ,j are all ±1 or zero. subspace Fj in a complete flag. The ideas of Beilinson and Bernstein concern How to Compute the Characters the equivariant geometry of X. One might expect Equation (E) above says that the character table that what ought to matter is the action of G on X. for a real reductive Lie group G may be ex- For technical reasons, however, what enters their λ pressed as a matrix of integers P π,j ; here I have work is equivariance with respect to K(C), the temporarily reinserted the dependence on the complexification of a maximal compact subgroup infinitesimal character λ. The index j runs over K ⊂ G. Harish-Chandra’s solutions (D) to the differential Theorem 7 (Beilinson and Bernstein) Suppose G is equations (with fixed eigenvalues λ). The index π a real reductive group with complete flag variety X, runs over irreducible representations of G (with K is a maximal compact subgroup of G, and K(C) fixed infinitesimal character λ). is its complexification (an algebraic group acting on The Jantzen-Zuckerman translation principle X). says (in a very explicit and computable way) that, as a) Harish-Chandra’s solutions (D) to the differ- λ varies, there are only finitely many possibilities λ ential equations are naturally in one-to-one corre- for P π,j . Henceforth I will therefore drop the λ and spondence with pairs (Zo, L) consisting of a K(C) speak only of computing one matrix P π,j . Thinking orbit Zo on X and a K(C)-equivariant local system about this matrix is simplified by L on Zo.

October 2007 Notices of the AMS 1027 According to Theorem 6, exactly the same parame- topological invariant of the singular algebraic vari-

ters index the irreducible representations of G. ety Zi . It measures at the same time the nature of

b) Suppose πi is an irreducible representation, the singularity of Zi (in the theorem, the singularity corresponding to the pair (Zi,o, Li ). Write Zi for the at points in Zj,o) and the possibility of extending closure of Zi,o, a (possibly singular) algebraic subva- the local system Li from the open subset Zi,o to all of Z . riety of X. Suppose Θj is one of Harish-Chandra’s i solutions (D), corresponding to the pair (Zj,o, Lj ). As the term “Euler characteristic” suggests, in- tersection homology provides (for each i and j) not Then the character formula coefficient P πi ,j of (E) is equal to the Euler characteristic of the local inter- just a single integer but rather a finite collection of m section homology of Zi with coefficients in the local nonnegative integers pij , the ranks of individual system Li , evaluated at (Zj,o, Lj ). local intersection homology groups. I will modify Because Harish-Chandra solved systems of the indexing of the homology in order to arrange that the index m can run from 0 to the complex differential equations to get the Θj , and Beilinson and Bernstein work with derived categories of codimension of Zj in Zi . (One of the key properties constructible sheaves, you may imagine that of intersection homology is that the top degree there is some work required to pass from what can appear only if Zj = Zi .) A consequence of Beilinson and Bernstein proved to the statement this reindexing is that the Euler characteristic of of Theorem 7. This translation was one of my own Theorem 7(b) is

contributions to the subject. The most difficult dim Zi −dim Zj X m m (−1) (−1) pij . part was convincing some of the experts that the m result was really not quite obvious. If Z is smooth and L is the trivial local system, Despite my promise at the beginning to be his- i i then pm is equal to zero unless m = 0, Z is torically incomplete, I have been asked to interrupt ij j contained in Z , and the local system L is also the mathematics here to say a few words about the i j trivial; in that case p0 is equal to 1. sources of the ideas in Theorem 7. Kazhdan and ij The Kazhdan-Lusztig polynomial for the pair Lusztig in 1979 formulated a precise conjecture (i, j) is by definition describing the characters of irreducible highest weight modules in terms of the combinatorics X m m/2 Pi,j (q) = pij q . of the Weyl group. They observed that the first m appearance in these characters of coefficients The parameters i and j represent local systems on ± other than 1 can be empirically related to the orbits of K(C) on the complete flag variety X. The first failures of local Poincaré duality for singular polynomial can be nonzero only if the orbit Zj,o Schubert varieties. MacPherson suggested that is contained in the closure of the orbit Z ; this their observations might be formalized using inter- i,o explains the “lower triangular” result in Theorem section homology. Kazhdan and Lusztig did this, 6. It turns out that the local groups vanish in odd proving that their combinatorial construction in degrees, so that P is actually a polynomial in q the Weyl group actually calculated the intersection i,j (with nonnegative integer coefficients). (This is a homology of Schubert varieties. This calculation special fact about the varieties Z , not a general fact is short but very deep, using the tools developed i about intersection homology.) The degree of P is by Deligne to prove the Weil conjectures. It seems i,j bounded by half the complex codimension of Z to have been an inspiration for the development j in Z ; the bound is strict if i 6= j. (This is a general by Beilinson, Bernstein, Deligne, and Gabber of i fact about intersection homology.) Because of the the general theory of perverse sheaves, which has vanishing in odd degrees, the Euler characteristic since become a basic tool in representation theory is just the (nonnegative) value at q = 1, times the and algebraic geometry. sign (−1)dim Zi −dim Zj . The Kazhdan-Lusztig conjectural character for- The point of Theorem 7 is that characters can be mula (still for highest weight modules) was now a statement involving intersection homology of computed from Kazhdan-Lusztig polynomials and Schubert varieties. In this form it was proved inde- that these polynomials depend on the geometry of pendently by Brylinski-Kashiwara and by Beilinson- K(C) orbit closures on the complete flag variety Bernstein, using the algebraic theory of differential X. The next theorem describes the geometric tools equations created by Sato, Kashiwara-Kawai, and needed to compute intersection homology for these Beilinson-Bernstein. orbit closures. I will not try to describe “intersection homol- Theorem 8 (Wolf). Suppose G is a real reductive ogy” here. (The book Introduction to Intersection group with complete flag variety X, K is a maximal Homology Theory by Kirwan and Woolf is highly compact subgroup of G, and K(C) is its complexifi- recommended by my colleagues who should know.) cation (an algebraic group acting on X). In order to understand the nature of the statement, a) The action of K(C) on X has finitely many what matters is that intersection homology is a orbits.

1028 Notices of the AMS Volume 54, Number 9 Suppose Zo is an orbit of K(C) on X, and s ∈ S. local systems. Keeping track of these local systems Write Z for the closure of Zo (a projective algebraic under the maps πs is subtle and was another of subvariety of X). Define Zs = πs (Z) (cf. (F) above), a my contributions to this mathematics. (One ends projective algebraic subvariety of Xs , which we call up in some cases with inductive formulas not for s −1 the s-flattening of Z. Define Z = πs (Zs ), which individual Kazhdan-Lusztig polynomials, but for we call the s-thickening of Z. The map πs exhibits sums of two polynomials, corresponding to two s 1 Z as a P bundle over Zs . local systems. Part of the difficulty is to find a way b) The s-thickening Zs is the closure of a unique to solve the resulting collection of equations.) s K(C) orbit Zo. A critical point is that the algorithm needs to c) There are two mutually exclusive possibilities. know the highest degree coefficients and not just 1) The s-thickening Zs is equal to Z, so that Z is the values of the polynomials at q = 1. Even though 1 s a P bundle over Zs . In this case Zo = Zo. 2) The we are interested (for character theory) only in map πs from Z to Zs is generically finite (and in values of the polynomials at 1, the algorithm does particular is finite over the orbit Zo). In this case not allow us to compute only values at 1. s s dim Zo = dim Zo + 1; and Zs = (Z )s . In particular, Once the algorithm has forced us to look at s the thickened orbit Zo falls in case (1). coefficients of the Kazhdan-Lusztig polynomials, it d) Every orbit of K(C) on X arises by a finite is very natural to ask for representation-theoretic succession of thickening operations applied to some interpretations of those coefficients. There is a closed orbit. great deal to say on this subject. I will mention Part (a) of this theorem is due to Wolf. The only that the top degree coefficients mentioned 1 remaining assertions are quite easy, although it is above turn out to be dimensions of Ext groups more difficult (for me at least) to attribute them between irreducible representations. precisely. The idea of constructing and describing the orbits in this way has its roots in the theory of The Atlas of Lie Groups and Schubert varieties and so is very old. Representations Theorem 8 describes the geometry of orbit That brings the mathematical story up to about closures and so leads to Kazhdan and Lusztig’s 1985. I’ll now turn away from abstract mathematics, algorithm for computing intersection homology by toward the story of the atlas project. induction on the dimension. Here is a sketch. An In 2002, Jeff Adams had the idea of getting orbit of minimal dimension is closed and is itself a computers to make interesting calculations about complete flag variety for the algebraic group K(C). infinite-dimensional representations of reductive Such varieties are smooth, so the local intersection Lie groups: ultimately, he hoped, to calculate uni- cohomology is simple. According to part (d), any tary representations. Of course as mathematicians orbit Wo of greater than minimal dimension must we want completely general theorems, and it’s by s arise by thickening: Wo = Zo, with Zo an orbit of no means clear that there is a finite calculation to dimension one less. Now the orbit closure Z is a find the unitary duals of all reductive groups at ramified cover of the flattening Zs (according to once. But the work of Dan Barbasch (for example, (c)(2)); so the intersection homology of Zs is very his classification of the unitary duals of the com- close to that of Z, which is known by induction. plex classical groups) makes it possible to hope Finally the orbit closure W is a P1 bundle over that one can find a finite description of the unitary Ws = Zs ; so the intersection homology of W is duals of all classical Lie groups. The exceptional made in a simple way from that of the flattened groups are finite in number, so treating them is variety Zs . a finite calculation. That became Jeff’s standard Making this sketch precise uses versions of the for measuring the effectiveness of any piece of Weil conjectures for intersection homology, proved representation-theoretic software: could it treat by Beilinson, Bernstein, and Deligne. The most the largest exceptional group E8? subtle point is descent from Z to Zs by the ramified It was clear that the first problem was to write covering map πs . What happens there is that the a program that could work with the Cartan sub- intersection homology down on the flattening Zs groups, maximal compact subgroups, and Weyl arises from that on the covering Z by removing groups of any real reductive group. Jeff recruited something. Exactly what should be removed is Fokko du Cloux to do this, and Fokko began to work determined by certain highest degree intersection in 2003. By 2004 his software could handle this homology of Z; that is, by top degree coefficients structure theory (better than most mathematicians, in Kazhdan-Lusztig polynomials. at least). In the setting of Kazhdan and Lusztig’s original The next step was less obvious, but Fokko work, the orbits Zo are simply connected, so the and Jeff settled on computing Kazhdan-Lusztig local systems involved are all trivial. For general polynomials for real groups. Fokko had written the real groups the orbits have fundamental groups best software in the world to do this for Coxeter of size up to (Z/2Z)rank and therefore a wealth of groups; the algorithms for real groups are similar

October 2007 Notices of the AMS 1029 in structure (although much more complicated Among the exceptional groups, that left the split in detail, because of the complications attached form of E8. to local systems). Theorem 7 above says that knowing these polynomials provides formulas for Warming Up for E8 irreducible characters; it is also a critical step in How big a computation is the character table for several computational approaches to classifying split E8? Fokko’s software told us that there were unitary representations. exactly 453,060 (translation families of) irreducible So late in 2004, Fokko began to add to his soft- representations. According to Theorem 6 above, ware an implementation of the Kazhdan-Lusztig the character table can be described by a square algorithm for real groups. The papers in which matrix of integers, of size 453,060. The number of this algorithm is formulated are extremely dense, entries is therefore about 2 × 1011, or 200 billion. and written with no consideration for computa- Fortunately the matrix is lower triangular, so we tional practice. An expert could easily spend many only need 100 billion entries. months just to understand the mathematical state- Unfortunately we need to calculate not the ments. Fortunately, Jeff Adams had been working entries directly, but rather the Kazhdan-Lusztig on a new formulation of Theorem 6 (parametrizing polynomials whose values at 1 are the entries. The irreducible representations), growing out of earlier degrees of the polynomials are bounded by 31; work that he did with Dan Barbasch and me. Jeff’s we expected an average degree of about 20, and formulation seemed suited to computer implemen- therefore a total number of coefficients around 2 tation; he had been working with Fokko to make it trillion. more so. Fortunately many of the matrix entries are easily Over the course of the next year, Fokko un- seen to be equal. An example is Zuckerman’s derstood the Kazhdan-Lusztig algorithm for real formula for the character of a finite-dimensional groups, recasting it in the language that he and Jeff representation, where I said that all the coefficients had developed. He wrote clear and efficient code are ±1 or 0; this is the last row of the character to implement it. In November of 2005—incredibly matrix. In the case of E8, there are 320,206 nonzero soon!—he finished. Very quickly he and Jeff used terms in this row. Fokko’s software recognizes that the software to compute Kazhdan-Lusztig polyno- all 320,206 of those Kazhdan-Lusztig polynomials mials (and so character tables) for all of the real are going to be equal and stores only the diagonal forms of F , E , and E , and for the non-split form 4 6 7 entry 1. In general one needs to store only one of E . 8 representative polynomial for each family of “obvi- The most complicated of these calculations is for ously equal” entries. Fokko’s software calculated the non-split form of E . There are 73,410 distinct 8 how many such families there were: a bit more than (translation families of) irreducible representations, 6 billion. So we were down to storing about 6 billion so the character table is a 73, 410 × 73, 410 matrix polynomials with about 120 billion coefficients. of integers. The integers are values at q = 1 of Unfortunately we had no clear idea how big the Kazhdan-Lusztig polynomials. These polynomials (nonnegative integer) coefficients of these polyno- have degrees from 0 to 27. Their coefficients are mials could be. In the case of split D , the largest nonnegative integers, of which the largest is 2545. 5 is 5. For split E , the largest is 27, and for split The total number of distinct polynomials appearing 6 E , it’s 3583. This trend was not encouraging; it (among the three billion or so entries below the 7 seemed clear that the coefficients would exceed diagonal in the matrix) is 10,147,581. Here is the 65, 535 = 216 − 1, so that they could not be stored polynomial with largest coefficient: in two bytes (sixteen bits) of computer memory. q13 + 30q12 + 190q11 The next practical size is four bytes. +682q10 + 1547q9 + 2364q8 Fortunately Fokko wrote the software to com- pute with four-byte integers and to test carefully +2545q7 + 2031q6 + 1237q5 for numeric overflow throughout the computation. 4 3 2 +585q + 216q + 60q + 11q + 1 If overflow happened, the plan was to switch to It’s hard to say what constitutes a “typical” eight-byte integers and try again. polynomial, but here is the one at the midpoint of Unfortunately, 120 billion 4-byte integers re- the lexicographically ordered list: quire 480 billion bytes of RAM, or 480G. That’s a q9 + 7q8 + 13q7 + 6q6 + 6q5 lot of RAM. (The nature of the Kazhdan-Lusztig algorithm, which constantly looks at widely dis- 4 3 2 +14q + 18q + 16q + 7q + 1. tributed results from earlier in the computation, Fokko’s software will calculate this character table makes storing results on disk impractically slow. on my laptop in about half an hour, using 1500 We tried!) megabytes of RAM. (I bought a big memory chip Fortunately, some of the six billion polynomials at about the same time as I sold my soul to the are zero, and some of them are equal to others silicon devil.) “by chance” (that is, for reasons that we have yet

1030 Notices of the AMS Volume 54, Number 9 to understand). So Fokko wrote the software to (Not) Buying a Really Big Computer store only one copy of each distinct polynomial. Birne Binegar and Jeff Adams suggested that we He hoped that the number of distinct polynomials start looking seriously at applying for an NSF grant might be a few hundred million: so perhaps 6 billion to buy a machine with perhaps 256G of RAM: coefficients, requiring 25G of RAM. The indexes something that might cost US$150,000 or more. I keeping track of all these polynomials would also asked a number of mathematicians whether they occupy a lot of memory: by the most optimistic might be able to make use of such a computer. estimates perhaps 45G, but quite possibly a lot Noam Elkies had a fascinating reply. First he ex- more. plained some theoretical limits on the computations Unfortunately, we didn’t have a computer with that could use a lot of memory. even 50G of RAM. A computation that actually uses Fortunately computer science is often computer N bytes of storage must take time art, and even Fokko’s work could be improved. at least N. But once N gets as large as 256GB it might not be feasible Fokko worked on that constantly during 2006, to spend much more than N time: and Marc van Leeuwen began to make serious N·log(N) or N·log2(N) is certainly contributions as well. The two of them rearranged OK (e.g., fast integer or polynomial the indexes and the code in some extraordinarily arithmetic, and other applications clever ways. of the Fast Fourier Transform; also Unfortunately, tests running partway through solving f (x) = f (x0) by sorting N the E8 calculation (done mostly by Birne Binegar) values of f (x) and finding a consec- revealed that Fokko’s first hopes about the number utive match); maybe also N3/2 (e.g., of distinct polynomials were too optimistic. Even an linear algebra with dense matrices optimistic reading of Birne’s tests suggested more of size N1/2, or computing the first like 800 million distinct polynomials, meaning N coefficients of modular forms perhaps 60G or more to hold the coefficients. such as ∆ without fast arithmetic); Fortunately Dan Barbasch is now chair of the probably not N2. So there might not math department at Cornell, and in September of be all that much room for making 2006 he managed to gain access to a machine with use of such a huge machine… 128G of RAM and 128G of swap space. He used it He went on to ask to run the E computation to the end. The fact that 8 Is it clear that the E8 computation Fokko’s overflow tests were not set off showed cannot fit into “only” 128 or 64GB? that all the coefficients really fit in four bytes. I explained the demands of polynomial storage: Unfortunately he had no reasonable way to We know that the polynomial co- write the results to disk, so they disappeared. efficients can exceed 216 (by com- (Fokko’s software was written to produce output in putation), and we hope that they human-readable form. In the case of E8, his output don’t exceed 232. Each polynomial for the character table would have consisted of is stored as a vector of 32-bit in- about fifty billion lines (one for each nonzero tegers, of size exactly equal to its entry in the character table) averaging about 80 degree plus one. Assuming an av- characters. As a disk file this would have been erage degree of 19, that’s 80 bytes several terabytes.) Also unfortunately, Dan didn’t per polynomial. have the improvements that Fokko and Marc had On November 30, Noam replied made to the code: Dan’s computation used 224G Well 232 is less than the prod- of memory (half of it swap space). Because of the uct of the ten odd primes less use of swap space, it took twelve days to finish. than 25, so unless the computation Fortunately, by November of 2006, Fokko and requires divisions by numbers oth- Marc had trimmed memory use in the code a great er than 2 you could reduce this deal. Through the persistence of Birne Binegar, and from 80 bytes to something like the generosity of number theorist William Stein, the (5/32)·80 = 12.5 bytes, at the cost atlas group got access to William Stein’s computer of running the computation 9 times sage at the University of Washington (with 64G of (counting once for mod 3 · 5). RAM and 75G of swap). On this machine we could In other words, we needed to stop thinking about finally do some large fraction of the E8 character intersection cohomology for a while and use the table computation. By late November, we believed Chinese Remainder Theorem. Noam’s suggestion that we could finish E8 with about 150G of RAM. was to compute the Kazhdan-Lusztig polynomials Unfortunately, 150G is just a little more than modulo m for several small values of m and sage has, even with swap. to store the results to disk. A second program

October 2007 Notices of the AMS 1031 could (for each polynomial) read in these several Marc fixed things instantly, and on Thursday mod m reductions; apply the Chinese Remainder evening December 21 we started a calculation Theorem to compute the polynomial modulo the mod 256 on sage. This computed 452,174 out of least common multiple of all the moduli; and write 453,060 rows of the character table in 14 hours, the result to disk. This second program would need then sage crashed. We tried again starting late to have only a handful of polynomials in RAM at Friday afternoon, and actually finished with good the same time, so it could run on a much smaller output: the character table mod 256 was written to computer. disk! Because we used multi-threading to speed up I started to compose a reply explaining why the computation, this run took just eleven hours. modular reduction of the Kazhdan-Lusztig algo- On Saturday December 23 we started a calcu- rithm doesn’t work, but I had to throw it away: lation mod 255. This time sage crashed a third the algorithm works perfectly over Z/mZ. Fokko’s of the way through the computation. There was code was beautifully compartmentalized, and Marc no one physically present to reboot it (apparently van Leeuwen is amazing, so by December 4 we were some kind of holiday in Seattle) so we retired for a getting character table entries mod m for any m up bit (still having mod 256 as our only good output to 256. In these calculations, we needed just one files). byte of memory for each polynomial coefficient. A Meanwhile Marc van Leeuwen had written code billion polynomials of degree 20 could live in 20G to combine Kazhdan-Lusztig polynomials from of RAM. several moduli m1, m2,... into Kazhdan-Lusztig polynomials modulo lcm(m1, m2, . . .). We tested Computing Characters Mod m the code on the first hundred million entries of On December 6 Marc’s modifications of Fokko’s the E8 character table modulo 253, 255, and 256 code on sage computed about three-fourths of (which we could calculate on smaller computers the entries in the E8 character table mod 251, than sage), and it worked fine. When sage came finding almost 700 million distinct polynomials back up on December 26, we got a character table and using 108G of memory. Since 90% of that mod 255 written to disk. At 1 a.m. on December 27, was indexes, working on their structure became we started a run mod 253. About halfway through, worthwhile. Marc redesigned the indexes rather sage crashed. completely (replacing 8-byte pointers by 4-byte The experts I consulted assured me that the counters several billion times, for example). In the atlas software couldn’t possibly be crashing sage. end he reduced the size of the indexes to about My own opinions about the causes of the crashes 35G; they would have required more than 100G for wavered between black helicopters from the NSA the original code. He also added code to output and Sasquatch. We resolved to keep our hands off the answers to (small machine-readable) disk files. sage until we were older and wiser: say for a year. Meanwhile Birne Binegar ran various versions On Wednesday January 3 we were all one year of the code on sage. Among other things he older, which made perhaps thirty years of addi- established for certain that there were more than tional wisdom counting all the atlas people. This one billion distinct polynomials. factor of thirty seemed like a suitable margin Early on December 19, Marc’s modified code of safety, so that afternoon we started another began a computation for E8 mod 251, with the computation mod 253. This finished in twelve possibility of actually writing the result usefully hours. at the end. Essentially it worked, finishing the computation in about 17 hours. From diagnostic The Chinese Remainder Calculation output of the software, we learned that there were By 4 a.m. Thursday January 4th we had output exactly 1,181,642,979 distinct Kazhdan-Lusztig for three moduli (253, 255, and 256) with least polynomials mod 251. (That turned out to be the common multiple 16,515,840: bigger (we had some number over Z as well.) The calculation used only hope) than all the coefficients of the Kazhdan- 65G of memory; the improvement over 108G on Lusztig polynomials. Marc van Leeuwen took unfair December 6 was because of Marc’s redesigned advantage of the time difference in Europe to start indexing system. running his Chinese Remainder Theorem utility on But writing the answer to disk took two days. the results. Its first task was to correlate the indices Marc and I went over Marc’s output code to see why. of the three output files, to determine which (of We figured it out, and Marc improved the speed. 1.1 billion) polynomials mod 253 corresponded to But we found at the same time a bug: he wrote which mod 255. That finished in nine hours. size() in one line where he meant capacity(). At that point we encountered another speed The result was that, even though the polynomials problem. The first version of Marc’s software had a were all correctly written to disk, the index files counter displaying the number of the polynomial (explaining which polynomial was stored where) to which the Chinese Remainder Theorem was were missing something like half their contents. being applied, to allow for monitoring progress.

1032 Notices of the AMS Volume 54, Number 9 Since there are more than a billion polynomials, the beginning of this article.) I was convinced that this meant writing several billion characters to the we’d find larger coefficients among the 350 million display. It turns out that takes a (very) long time. So polynomials that were not correctly evaluated the we started over on Friday morning January 5, with a first time and that we’d need a larger modulus counter that updates only every 4096 polynomials. than 16,515,840 to get them all. Everything went nicely until sage crashed. So at 6 a.m. on Sunday January 7th I was able William Stein identified sage’s problem as a to restart Marc’s current (and correct) Chinese flaky hard drive. The situation for atlas was Remainder Theorem utility, this time adding mod- this: sitting on sage’s flaky hard drive were 100 ulus 251. Of course nothing went wrong (because gigabytes of output files, the Kazhdan-Lusztig what could go wrong?), and the last polynomial polynomials modulo 253, 255, and 256 for E8. was written to disk just before 9 a.m. Eastern time Each of these files represented something like on Monday January 8. twelve hours of (multi-threaded) computation; the hundreds of hours of unsuccessful computations What Next? made them feel a great deal more valuable. Sixty gigabytes is too much information to look William Stein replaced the bad hard drive with at, even for nineteen mathematicians working in a good one, on which he had made daily backups 1 seamless harmony. Here are some of the “clean of all the work on sage. He did this more or less and simple results” that I promised in the in- instantly: we still had our data files. I was already troduction. Attached to any representation are deeply indebted to his generosity in allowing the many beautiful geometric invariants. Knowledge atlas group access to sage, but this raised him of the character table allows us to compute some even higher in my esteem. of them. We have computed the Gelfand-Kirillov We restarted the Chinese Remainder calculation dimension of each irreducible representation of E . late Friday afternoon January 5. 8 This is an integer between 0 and 120 that mea- Early Saturday morning, the disk file of polyno- sures how infinite-dimensional the representation mial coefficients mod 16515840 had grown to be is. Finite-dimensional representations are those about 7 billion bytes larger than it was supposed of GK dimension 0, and generic representations to be. Since it was a day with a y in it, I assumed that Marc van Leeuwen would be working. I asked (in a technical sense coming from the theory of him to find out what was wrong. He was visiting automorphic forms) are those of GK dimension his family in the Netherlands for the weekend and 120. The finite-dimensional representations were had extremely limited access to the Internet. identified by Cartan and Weyl (Theorem 2 above) The bug was (to my eyes) unbelievably subtle. around 1930, and the generic representations by Since the number of polynomials is about a billion, Kostant in 1978 (in both cases for all real reductive Marc’s code represented the index of a polyno- groups). mial by a 4-byte integer (perfectly good up to Now we can say for E8 exactly what happens be- 4,294,967,295). At some point this integer needs to tween these extremes. For instance, of the 453,060 be multiplied by 5 (the number of bytes in the index (translation families of) representations we studied, entry for one polynomial); the result is put into an there are exactly 392 of GK dimension 57. We can 8-byte integer, where it fits nicely. But when the say which ones they are. (I chose 57 because it’s polynomial number exceeds 858,993,459, and the the smallest possible dimension of a nontrivial multiplication is done in four bytes, it overflows. homogeneous space Z57 for E8. These 392 families The result was that the code worked perfectly in of representations appear in sections of vector any reasonable test (like the one we ran with a bundles over Z57.) In the same way we can identify hundred million polynomials). James Arthur’s special unipotent representations, To complicate Marc’s task further, the bug was which conjecturally play a fundamental role in the not present in his most recent version of the code; theory of automorphic forms. There are 111 of what I was running on sage was a couple of days these among the 453,060 representations. older. In the longer term, our goal is to determine So he was looking for a subtle bug that wasn’t completely the unitary irreducible representations there, without Internet access to the machine where for the exceptional Lie groups. Our hope is that the problem occurred. It took him almost twenty knowledge of the character table will allow us to hours to find and fix it (here of course I assume that make a computation of these unitary representa- he neither slept nor ate nor spoke to his family). tions. Armed with a list of unitary representations, Marc’s analysis showed that the bug came into we can try to explain (most of) it using the Kirillov- play only around polynomial number 858 million; Kostant orbit method, or Langlands’ ideas about so all the coefficients (modulo 16,515,840) calcu- lated before that were correct. The largest of these 1This is a theoretical assertion. I have no practical experi- coefficients was 11,808,808, at polynomial number ence with a team of nineteen mathematicians working in 818,553,156. (That is the polynomial displayed at seamless harmony.

October 2007 Notices of the AMS 1033 functoriality, or perhaps even something entirely Members of the Atlas of Lie Groups and new. Representations Despite the length of this article, I have left out a great deal. I have said nothing about the meetings Jeffrey Adams of the atlas group, where the insights of all of Dan Barbasch the mathematicians involved contributed to the Birne Binegar shape of the software that Fokko was writing, and Bill Casselman to our evolving understanding of the mathematics Dan Ciubotaru beneath it. Fokko du Cloux The greatest omission is the personal story of Scott Crofts Fokko du Cloux. He was diagnosed with ALS (a Tatiana Howard progressive neurological disease) just after finish- Marc van Leeuwen ing the Kazhdan-Lusztig computation software Alfred Noel in November of 2005. By February 2006 he had Alessandra Pantano little use of his hands, and by May he was entirely Annegret Paul paralyzed below his neck. But he continued to Siddhartha Sahi share his skills and insights into the mathematics Susana Salamanca and the programming—and his great joy at meeting John Stembridge a formidable mathematical challenge—with Jeff Peter Trapa Adams and with Marc van Leeuwen and with me, David Vogan until his death on November 10, 2006. Wai-Ling Yee The atlas has introduced me to great mathe- Jiu-Kang Yu maticians I barely knew, like Marc van Leeuwen and We are very grateful to Brian Conrey and John Stembridge, and it has shown entirely new the American Institute of Mathematics, which depths in people I knew well, like Jeff Adams and provided financial support and a wonder- Dan Barbasch. So it’s a very high bar…but what has ful mathematical meeting place from the been best of all, mathematically and personally, beginning of the atlas project; and to the Na- has been spending time with Fokko. It’s still the tional Science Foundation, which has provided best: every minute I spend on this project is a support through FRG grant 0554278. chance to think about him, and that’s always good —D.V. for a smile. So thank you to Fokko, who did this all by himself. Thank you to everyone who helped him—Marc van Leeuwen did more of that than anybody, but there were a lot of indispensable people. I haven’t had a boss since I worked in a lum- beryard in the summer of 1972, until Jeff Adams. Thank you, boss! I hope to be back here when we have some unitary representations to share.

1034 Notices of the AMS Volume 54, Number 9 A Certain Ambiguity “Mixing fiction with nonfiction, A Certain Ambiguity is a veritable history of mathematics disguised as a novel. Starting with the A Mathematical Novel Pythagorean theorem, it moves through number theory and geometry Gaurav Suri & to Cantor’s alephs, non-Euclidean geometry, Gödel, and even Hartosh Singh Bal relativity.” —Martin Gardner

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The Mathematician’s “Fascinating and quite eclectic. Ruelle has a pragmatic approach to Brain discussing philosophical and psychological questions. He is equally pragmatic with regard to ethical and political issues involved in the David Ruelle professional world of the mathematician. As Ruelle repeatedly says, mathematics is a human activity.” —William Messing, University of Minnesota

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Wave Scattering by “Professor Roach is an acknowledged expert in applied analysis. Wave Time-Dependent Scattering by Time-Dependent Perturbations is a significant contribution to the mathematical literature—there are no similar books. There Perturbations is a need to bring some of this analysis to the attention of those An Introduction people who actually want to know how best to solve time-dependent G. F. Roach scattering problems.” —Paul Martin, executive editor of The Quarterly Journal of Mechanics and Applied Mathematics Princeton Series in Applied Mathematics Ingrid Daubechies, Weinan E, Jan Karel Lenstra & Endre Süli, series editors Cloth $65.00 978-0-691-11340-1

Prime-Detecting This book seeks to describe the rapid development in recent decades Sieves of sieve methods able to detect prime numbers. No other book has Glyn Harman undertaken such a systematic treatment of prime-detecting sieves. It contains much that is accessible to beginning graduate students, yet also provides insights that will benefit established researchers.

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800.777.4726 math.press.princeton.edu Paul Halmos: In His Own Words John Ewing

Paul Halmos died on October 2, 2006, at the age of 90. After his death, many people wrote about his career and praised both his mathematical and his expository skills. Paul would have complained about that: He often said he could smell great mathematicians, and he himself was not one of them. But he was wrong. He was a master of mathematics in multiple ways, and he influenced math- ematicians and mathematical culture throughout his career. Unlike most other master mathemati- cians, Paul’s legacy was not merely mathematics but rather advice and opinion about mathematical life—writing, publishing, speaking, research, or even thinking about mathematics. Paul wrote about each of these topics with an extraordinary mixture of conviction and humility. Mathematicians paid attention to what he wrote, and they often quoted it (and still do—“every talk ought to have one proof”). They disagreed and frequently wrote rebuttals. They passed along his wisdom to their stu- dents, who passed it along to theirs. Paul Halmos’s writing affected the professional lives of nearly every mathematician in the latter half of the twentieth century, and it will continue to influence the profession for years to come. How does one write about great writing? Explanations of great exposition always fall flat, like analyses of great poems or elucidations of famous paintings. Art is best exhibited, not explained. And so here is a collection of excerpts from the writing of Paul Halmos, giving advice, offering opinions, or merely contemplating life as a mathematician—all in his own words. —J. E.

On Writing born with it are not usually born with full knowl- edge of all the tricks of the trade. A few essays Excerpts from: such as this may serve to “remind” (in the sense of “How to write mathematics”, Enseign. Math. (2) Plato) the ones who want to be and are destined to 16 (1970), 123–152. be the expositors of the future of the techniques …I think I can tell someone how to write, but I found useful by the expositors of the past. can’t think who would want to listen. The ability The basic problem in writing mathematics is to communicate effectively, the power to be intel- the same as in writing biology, writing a novel, or ligible, is congenital, I believe, or, in any event, writing directions for assembling a harpsichord: it is so early acquired that by the time someone the problem is to communicate an idea. To do reads my wisdom on the subject he is likely to be so, and to do it clearly, you must have something invariant under it. To understand a syllogism is to say, and you must have someone to say it to, not something you can learn; you are either born you must organize what you want to say, and you with the ability or you are not. In the same way, must arrange it in the order you want it said in, effective exposition is not a teachable art; some can you must write it, rewrite it, and re-rewrite it sev- do it and some cannot. There is no usable recipe eral times, and you must be willing to think hard for good writing. about and work hard on mechanical details such Then why go on? A small reason is the hope that as diction, notation, and punctuation. That’s all what I said isn’t quite right; and, anyway, I’d like a there is to it.… chance to try to do what perhaps cannot be done. A It might seem unnecessary to insist that in order more practical reason is that in the other arts that to say something well you must have something to require innate talent, even the gifted ones who are say, but it’s no joke. Much bad writing, mathemati- This article was prepared and edited by John Ewing, cal and otherwise, is caused by a violation of that executive director of the AMS. His email address is jhe@ first principle. Just as there are two ways for a ams.org. sequence not to have a limit (no cluster points or

1136 Notices of the AMS Volume 54, Number 9 too many), there are two ways for a piece of writing the use of a complicated alphabetic apparatus, not to have a subject (no ideas or too many). avoid it. A good attitude to the preparation of writ- The first disease is the harder one to catch. It is ten mathematical exposition is to pretend that it is hard to write many words about nothing, especially spoken. Pretend that you are explaining the subject in mathematics, but it can be done, and the result to a friend on a long walk in the woods, with no is bound to be hard to read. There is a classic crank paper available; fall back on symbolism only when book by Carl Theodore Heisel [The Circle Squared it is really necessary. Beyond Refutation, Heisel, Cleveland, 1934] that serves as an example. It is full of correctly spelled On Speaking words strung together in grammatical sentences, Excerpts from: but after three decades of looking at it every now “How to talk mathematics”, Notices of AMS 21 and then I still cannot read two consecutive pages (1974), 155–158. and make a one-paragraph abstract of what they What is the purpose of a public lecture? Answer: say; the reason is, I think, that they don’t say to attract and to inform. We like what we do, and anything. we should like for others to like it too; and we The second disease is very common: there are believe that the subject’s intrinsic qualities are many books that violate the principle of having good enough so that anyone who knows what they something to say by trying to say too many things. are cannot help being attracted to them. Hence, … better answer: the purpose of a public lecture is The second principle of good writing is to write to inform, but to do so in a manner that makes it for someone. When you decide to write something, possible for the audience to absorb the informa- ask yourself who it is that you want to reach. Are tion. An attractive presentation with no content is you writing a diary note to be read by yourself only, worthless, to be sure, but a lump of indigestible a letter to a friend, a research announcement for information is worth no more.… specialists, or a textbook for undergraduates? The Less is more, said the great architect Mies van problems are much the same in any case; what var- der Rohe, and if all lecturers remember that adage, ies is the amount of motivation you need to put in, all audiences would be both wiser and happier. the extent of informality you may allow yourself, Have you ever disliked a lecture because it was the fussiness of the detail that is necessary, and too elementary? I am sure that there are people the number of times things have to be repeated. All who would answer yes to that question, but not writing is influenced by the audience, but, given the many. Every time I have asked the question, the audience, the author’s problem is to communicate person who answered said no, and then looked with it as best he can.… a little surprised at hearing the answer. A public Everything I’ve said so far has to do with writing lecture should be simple and elementary; it should in the large, global sense; it is time to turn to the not be complicated and technical. If you believe local aspects of the subject. and can act on this injunction (“be simple”), you The English language can be a beautiful and can stop reading here; the rest of what I have to say powerful instrument for interesting, clear, and is, in comparison, just a matter of minor detail. completely precise information, and I have faith To begin a public lecture to 500 people with that the same is true for French or Japanese or “Consider a sheaf of germs of holomorphic func- Russian. It is just as important for an expositor to tions…” (I have heard it happen) loses people and familiarize himself with that instrument as for a antagonizes them. If you mention the Künneth surgeon to know his tools. Euclid can be explained formula, it does no harm to say that, at least as far in bad grammar and bad diction, and a vermiform as Betti numbers go, it is just what happens when appendix can be removed with a rusty pocket you multiply polynomials. If you mention functors, knife, but the victim, even if he is unconscious of say that a typical example is the formation of the the reason for his discomfort, would surely prefer duals of vector spaces and the adjoints of linear better treatment than that.… transformations. My advice about the use of words can be Be simple by being concrete. Listeners are summed up as follows. (1) Avoid technical terms, prepared to accept unstated (but hinted) gener- and especially the creation of new ones, whenever alizations much more than they are able, on the possible. (2) Think hard about the new ones that spur of the moment, to decode a precisely stated you must create; consult Roget; and make them abstraction and to re-invent the special cases as appropriate as possible. (3) Use the old ones that motivated it in the first place. Caution: being correctly and consistently, but with a minimum concrete should not lead to concentrating on the of obtrusive pedantry.… trees and missing the woods. In many parts of Everything said about words, applies, mutatis mathematics a generalization is simpler and more mutandis, to the even smaller units of mathemati- incisive than its special parent. (Examples: Artin’s cal writing, the mathematical symbols. The best solution of Hilbert’s 17th problem about definite notation is no notation; whenever possible to avoid forms via formally real fields; Gelfand’s proof of

October 2007 Notices of the AMS 1137 Wiener’s theorem about absolutely convergent Make It Simple, and You Won’t Go Wrong.… Fourier series via Banach algebras.) In such cases Excerpt from: there is always a concrete special case that is I Want to Be a Mathematician, p. 401, Springer- simpler than the seminal one and that illustrates Verlag, New York (1985). the generalization with less fuss; the lecturer who …As for working hard, I got my first hint of knows his subject will explain the complicated what that means when Carmichael told me how special case, and the generalization, by discussing long it took him to prepare a fifty-minute invited the simple cousin. address. Fifty hours, he said: an hour of work Some lecturers defend complications and tech- for each minute of the final presentation. When nicalities by saying that that’s what their subject is many years later, six of us wrote our “history” like, and there is nothing they can do about it. I am paper (“American mathematics from 1940…”), I skeptical, and I am willing to go so far as to say that calculated that my share of the work took about such statements indicate incomplete understand- 150 hours; I shudder to think how many man- ing of the subject and of its place in mathematics. hours the whole group put in. A few of my hours Every subject, and even every small part of a sub- went toward preparing the lecture (as opposed to ject, if it is identifiable, if it is big enough to give the paper). I talked it, the whole thing, out loud, an hour talk on, has its simple aspects, and they, and then, I talked it again, the whole thing, into a the simple aspects, the roots of the subject, the dictaphone. Then I listened to it, from beginning to connections with more widely known and older end, six times—three times for spots that needed parts of mathematics, are what a non-specialized polishing (and which I polished before the next audience needs to be told. time), and three more times to get the timing right Many lecturers, especially those near the foot of (and, in particular, to get the feel for the timing the academic ladder, anxious to climb rapidly, feel of each part.) Once all that was behind me, and under pressure to say something brand new—to I had prepared the transparencies, I talked the impress their elders with their brilliance and pro- whole thing through one final rehearsal time (by fundity. Two comments: (1) the best way to do that myself—no audience). That’s work.… is to make the talk simple, and (2) it doesn’t really have to be done. It may be entirely appropriate to On Exposition make the lecturer’s recent research the focal point Excerpt from: of the lecture, but it may also be entirely appropri- ate not to do so. An audience’s evaluation of the Response from Paul Halmos on winning the merits of a talk is not proportional to the amount Steele Prize for Exposition (1983). of original material included; the explanation of Not long ago I ran across a reference to a pub- the speaker’s latest theorem may fail to improve lication titled A Method of Taking Votes on More his chance of creating a good impression. Than Two Issues. Do you know, or could you guess, An oft-quoted compromise between trying who the author is? What about an article titled “On to be intelligible and trying to seem deep is this automorphisms of compact groups”? Who wrote advice: address the first quarter of your talk to that one? The answer to the first question is C. L. your high-school chemistry teacher, the second Dodgson, better known as Lewis Carroll, and the to a graduate student, the third to an educated answer to the second question is Paul Halmos. mathematician whose interests are different from Lewis Carroll and I have in common that we both yours, and the last to the specialists. I have done called ourselves mathematicians, that we both my duty by reporting the formula, but I’d fail in my strove to do research, and that we both took duty if I didn’t warn that there are many who very seriously our attempts to enlarge do not agree with it. A good public the known body of mathematical lecture should be a work truths. To earn his liv- of art. It should be ing, Lewis Carroll was an architectural a teacher, and, just for unit whose parts fun, because he loved reinforce each to tell stories, he wrote other in convey- Alice’s Adventures in Won- ing the maximum derland. To earn my liv- possible amount of ing, I’ve been a teacher for information—not a almost fifty years, and, just campaign speech that for fun, because I love to orga- offers something to ev- nize and clarify, I wrote Finite erybody, and more likely Dimensional Vector Spaces. And than not, ends by pleas- what’s the outcome? I doubt if as ing nobody. many as a dozen readers of these words have ever looked at either A Method of Taking Votes… or “On

1138 Notices of the AMS Volume 54, Number 9 automorphisms…” but Lewis Carroll is immortal Adrian Albert used to say that a theory is worth for the Alice stories, and I got the Steele Prize for studying if it has at least three distinct good hard exposition. I don’t know what the Reverend Mr. C. examples. Do not therefore define and study a new L. Dodgson thought about his fame, but, as for me, class of functions, the ones that possess left upper I was brought up with the Puritan ethic: if some- bimeasurably approximate derivatives, unless you thing is fun, then you shouldn’t get recognized and can, at the very least, fulfill the good graduate rewarded for doing it. As a result, while, to be sure, student’s immediate request: show me some that I am proud and happy, at the same time I can’t help do and show me some that don’t. feeling just a little worried and guilty. A striking criterion for how to decide not to I enjoy studying, learning, coming to understand, publish something was offered by my colleague and then explaining, but it doesn’t follow that com- John Conway. Suppose that you have just finished municating what I know is always easy; it can be typing a paper. Suppose now that I come to you, devilishly hard. To explain something you must horns, cloven hooves, forked tail and all, and ask: if know not only what to put in, but also what to leave I gave you $1,000.00, would you tear the paper up out; you must know when to tell the whole truth and forget it? If you hesitate, your paper is lost—do and when to get the right idea across by telling a not publish it. That’s part of a more general rule: little white fib. The difficulty in exposition is not the when in doubt, let the answer be no.… style, the choice of words—it is the structure, the organization. The words are important, yes, but the On Research arrangement of the material, the indication of the Excerpt from: connections of its parts with each other and with I Want to Be a Mathematician, pp. 321–322, other parts of mathematics, the proper emphasis Springer-Verlag, New York (1985). that shows what’s easy and what deserves to be Can anyone tell anyone else how to do research, treated with caution—these things are much more how to be creative, how to discover something important. … new? Almost certainly not. I have been trying for On Publishing a long time to learn mathematics, to understand it, to find the truth, to prove a theorem, to solve Excerpts from: a problem—and now I am going to try to describe “Four panel talks on publishing”, American just how I went about it. The important part of the Mathematical Monthly 82 (1975), 14–17. process is mental, and that is indescribable—but I …Let me remind you that most laws (with the can at least take a stab at the physical part. exception only of the regulatory statutes that gov- Mathematics is not a deductive science—that’s a ern traffic and taxes) are negative. Consider, as an cliché. When you try to prove a theorem, you don’t example, the Ten Commandments. When Moses just list the hypotheses, and then start to reason. came back from Mount Sinai, he told us what to be What you do is trial and error, experimentation, by telling us, eight out of ten times, what not to do. guesswork. You want to find out what the facts are, It may therefore be considered appropriate to say and what you do is in that respect similar to what what not to publish. I warn you in advance that all a laboratory technician does, but it is different in the principles that I was able to distill from inter- the degree of precision and information. Possibly views and from introspection, and that I’ll now tell philosophers would look on us mathematicians you about, are a little false. Counterexamples can the same way we look on the technicians, if they be found to each one—but as directional guides dared. the principles still serve a useful purpose. I love to do research, I want to do research, I First, then, do not publish fruitless speculations: have to do research, and I hate to sit down and do not publish polemics and diatribes against a begin to do research—I always try to put it off just friend’s error. Do not publish the detailed working as long as I can. out of a known principle. (Gauss discovered exactly It is important to me to have something big which regular polygons are ruler-and-compass and external, not inside myself, that I can devote constructible, and he proved, in particular, that my life to. Gauss and Goya and Shakespeare and the one with 65537 sides—a Fermat prime—is Paganini are excellent, their excellence gives me constructible; please do not publish the details of pleasure, and I admire and envy them. They were the procedure. It’s been tried.) also dedicated human beings. Excellence is for the Do not publish in 1975 the case of dimension few but dedication is something everybody can 2 of an interesting conjecture in algebraic geom- have—and should have—and without it life is not etry, one that you don’t know how to settle in worth living. general, and then follow it by dimension 3 in 1976, Despite my great emotional involvement in work, dimension 4 in 1977, and so on, with dimension I just hate to start doing it; it’s a battle and a wrench k – 3 in 197k. Do not, more generally, publish your every time. Isn’t there something I can (must?) do failures: I tried to prove so-and-so; I couldn’t; here first? Shouldn’t I sharpen my pencils, perhaps? In it is—see?! fact I never use pencils, but pencil sharpening has

October 2007 Notices of the AMS 1139 become the code phrase a bad teaching instrument. When given by such for anything that helps legendary outstanding speakers as Emil Artin to postpone the pain of and John von Neumann, even a lecture can be a concentrated creative useful tool—their charisma and enthusiasm come attention. It stands for through enough to inspire the listener to go forth reference searching in and do something—it looks like such fun. For most the library, systematiz- ordinary mortals, however, who are not so bad at ing old notes, or even lecturing as Wiener was—not so stimulating!—and preparing tomorrow’s not so good as Artin—and not so dramatic!—the class lecture, with the lecture is an instrument of last resort for good excuse that once those teaching. things are out of the My test for what makes a good teacher is very way I’ll really be able to concentrate without simple: it is the pragmatic one of judging the per- interruption. formance by the product. If a teacher of graduate When Carmichael students consistently produces Ph.D.’s who are complained that as mathematicians and who create high-quality new dean he didn’t have mathematics, he is a good teacher. If a teacher of

From the Paul Halmos Collection. Halmos Paul the From more than 20 hours calculus consistently produces seniors who turn Paul Halmos a week for research I into outstanding graduate students of mathemat- marveled, and I marvel ics, or into leading engineers, biologists, or econo- still. During my produc- mists, he is a good teacher. If a teacher of third- tive years I probably averaged 20 hours of concen- grade “new math” (or old) consistently produces trated mathematical thinking a week, but much outstanding calculus students, or grocery store more than that was extremely rare. The rare excep- check-out clerks, or carpenters, or automobile tion came, two or three times in my life, when long mechanics, he is a good teacher. ladders of thought were approaching their climax. For a student of mathematics to hear someone Even though I never was dean of a graduate school, talk about mathematics does hardly any more good I seemed to have psychic energy for only three or than for a student of swimming to hear someone four hours of work, “real work”, each day; the rest talk about swimming. You can’t learn swimming of the time I wrote, taught, reviewed, conferred, techniques by having someone tell you where to refereed, lectured, edited, traveled, and generally put your arms and legs; and you can’t learn to solve sharpened pencils all the ways I could think of. problems by having someone tell you to complete Everybody who does research runs into fallow periods. During mine the other professional activi- the square or to substitute sin u for y. ties, down to and including teaching trigonometry, Can one learn mathematics by reading it? I am served as a sort of excuse for living. Yes, yes. I may inclined to say no. Reading has an edge over listen- not have proved any new theorems today, but at ing because reading is more active—but not much. least I explained the law of sines pretty well, and Reading with pencil and paper on the side is very I have earned my keep. much better—it is a big step in the right direc- Why do mathematicians do research? There are tion. The very best way to read a book, however, several answers. The one I like best is that we are with, to be sure, pencil and paper on the side, is curious—we need to know. That is almost the same to keep the pencil busy on the paper and throw as “because we want to,” and I accept that—that’s the book away. a good answer too. There are, however, more an- Having stated this extreme position, I’ll rescind swers, ones that are more practical. it immediately. I know that it is extreme, and I don’t really mean it—but I wanted to be very emphatic On Teaching about not going along with the view that learning Excerpt from: means going to lectures and reading books. If we had longer lives, and bigger brains, and enough “The problem of learning to teach”, American Mathematical Monthly 82 (1975), 466–476. dedicated expert teachers to have a student/ The best way to learn is to do; the worst way to teacher ratio of 1/1, I’d stick with the extreme teach is to talk. views—but we don’t. Books and lectures don’t do a About the latter: did you ever notice that some good job of transplanting the facts and techniques of the best teachers of the world are the worst of the past into the bloodstream of the scientist lecturers? (I can prove that, but I’d rather not lose of the future—but we must put up with a second quite so many friends.) And, the other way around, best job in order to save time and money. But, and did you ever notice that good lecturers are not this is the text of my sermon today, if we rely on necessarily good teachers? A good lecture is usu- lectures and books only, we are doing our students ally systematic, complete, precise—and dull; it is and their students, a grave disservice. ...

1140 Notices of the AMS Volume 54, Number 9 Excerpt from: Weierstrass M-test is supremely important, and “The heart of mathematics”, American that every mathematics student must know that it Mathematical Monthly 87 (1980), 519–524. exists and must understand how to apply it—even ... How can we, the teachers of today, use the then a course on the pertinent branch of analysis problem literature? Our assigned task is to pass might be better for omitting it. Suppose that there on the torch of mathematical knowledge to the are 40 such important topics that a student must technicians, engineers, scientists, humanists, be exposed to in a term. Does it follow that we teachers, and, not least, research mathematicians must give 40 complete lectures and hope that of tomorrow: do problems help? they will all sink in? Might it not be better to give Yes, they do. The major part of every meaning- 20 of the topics just a ten-minute mention (the ful life is the solution of problems; a considerable name, the statement, and an indication of one of part of the professional life of technicians, engi- the directions in which it can be applied), and to neers, scientists, etc., is the solution of mathemati- treat the other 20 in depth, by student-solved prob- cal problems. It is the duty of all teachers, and of lems, student-constructed counterexamples, and teachers of mathematics in particular, to expose student-discovered applications? I firmly believe their students to problems much more than to that the latter method teaches more and teaches facts. It is, perhaps, more satisfying to stride into better. Some of the material doesn’t get covered a classroom and give a polished lecture on the but a lot of it gets discovered (a telling old pun that Weierstrass M-test than to conduct a fumble-and- deserves to be kept alive), and the method thereby blunder session that ends in the question: “Is the opens doors whose very existence might never boundedness assumption of the test necessary for have been suspected behind a solidly built struc- its conclusion?” I maintain, however, that such a ture of settled facts. As for the Weierstrass M-test, fumble session, intended to motivate the student or whatever was given short shrift in class—well, to search for a counterexample, is infinitely more books and journals do exist, and students have valuable. been known to read them in a pinch. ... I have taught courses whose entire content was On Mathematics problems solved by students (and then presented to the class). The number of theorems that the Excerpt from: students in such a course were exposed to was ap- “Mathematics as a creative art”, American proximately half the number that they could have Scientist 56 (1968), 375–389. been exposed to in a series of lectures. In a problem Do you know any mathematicians—and, if you course, however, exposure means the acquiring do, do you know anything about what they do with of an intelligent questioning attitude and of some their time? Most people don’t. When I get into a technique for plugging the leaks that proofs are conversation with the man next to me in a plane, likely to spring; in a lecture course, exposure and he tells me that he is something respectable sometimes means not much more than learning like a doctor, lawyer, merchant or dean, I am the name of a theorem, being intimidated by its tempted to say that I am in roofing and siding. If I complicated proof, and worrying about whether it tell him that I am a mathematician, his most likely would appear on the examination. reply will be that he himself could never balance ... Many teachers are concerned about the his check book, and it must be fun to be a whiz at amount of material they must cover in a course. math. If my neighbor is an astronomer, a biologist, One cynic suggested a formula; since, he said, stu- a chemist, or any other kind of natural or social dents on the average remember only about 40% of scientist, I am, if anything, worse off—this man what you tell them, the thing to do is to cram into thinks he knows what a mathematician is, and he is each course 250% of what you hope will stick. Glib probably wrong. He thinks that I spend my time (or as that is, it probably would not work. should) converting different orders of magnitude, Problem courses do work. Students who have comparing binomial coefficients and powers of 2, taken my problem courses were often compli- or solving equations involving rates of reactions. mented by their subsequent teachers. The com- C. P. Snow points to and deplores the existence pliments were on their alert attitude, on their of two cultures; he worries about the physicist ability to get to the heart of the matter quickly, whose idea of modern literature is Dickens, and he and on their intelligently searching questions that chides the poet who cannot state the second law of showed that they understood what was happening thermodynamics. Mathematicians, in converse with in class. All this happened on more than one level, well-meaning, intelligent, and educated laymen (do in calculus, in linear algebra, in set theory, and, of you mind if I refer to all nonmathematicians as course, in graduate courses on measure theory and laymen?) are much worse off than physicists in functional analysis. converse with poets. It saddens me that educated Why must we cover everything that we hope people don’t even know that my subject exists. students will ultimately learn? Even if (to stay with There is something that they call mathematics, but an example already mentioned) we think that the they neither know how the professionals use the

October 2007 Notices of the AMS 1141 word, nor can they conceive why anybody should exaggerate; when I’m done, I’ll be glad to rescind do it. It is, to be sure, possible that an intelligent anything that was inaccurate or that gave offense and otherwise educated person doesn’t know that in any way. ... egyptology exists, or haematology, but all you have Mathematics is abstract thought, mathematics to tell him is that it does, and he will immediately is pure logic, mathematics is creative art. All these understand in a rough general way why it should statements are wrong, but they are all a little right, and he will have some empathy with the scholar and they are all nearer the mark than “mathemat- of the subject who finds it interesting. ics is numbers” or “mathematics is geometric Usually when a mathematician lectures, he is shapes”. For the professional pure mathematician, a missionary. Whether he is talking over a cup of mathematics is the logical dovetailing of a care- coffee with a collaborator, lecturing to a graduate fully selected sparse set of assumptions with their class of specialists, teaching a reluctant group of surprising conclusions via a conceptually elegant freshman engineers, or addressing a general audi- proof. Simplicity, intricacy, and above all, logical ence of laymen—he is still preaching and seeking analysis are the hallmark of mathematics. to make converts. He will state theorems and he The mathematician is interested in extreme will discuss proofs and he will hope that when he cases—in this respect he is like the industrial ex- is done his audience will know more mathematics perimenter who breaks lightbulbs, tears shirts, and than they did before. My aim today is different—I bounces cars on ruts. How widely does a reasoning am not here to proselytize but to enlighten—I seek apply, he wants to know, and what happens when not converts but friends. I do not want to teach you it doesn’t? What happens when you weaken one what mathematics is, but only that it is. of the assumptions, or under what conditions can I call my subject mathematics—that’s what all you strengthen one of the conclusions? It is the my colleagues call it, all over the world—and there, perpetual asking of such questions that makes quite possibly, is the beginning of confusion. The for broader understanding, better technique, and word covers two disciplines—many more, in reality, greater elasticity for future problems. but two, at least two, in the same sense in which Mathematics—this may surprise or shock you Snow speaks of two cultures. In order to have some some—is never deductive in its creation. The math- words with which to refer to the ideas I want to ematician at work makes vague guesses, visualizes discuss, I offer two temporary and ad hoc neolo- broad generalizations, and jumps to unwarranted gisms. Mathematics, as the work is customarily conclusions. He arranges and rearranges his ideas, used, consists of at least two distinct subjects, and and he becomes convinced of their truth long I propose to call them mathology and mathophys- before he can write down a logical proof. The ics. Roughly speaking, mathology is what is called conviction is not likely to come early—it usually pure mathematics, and mathophysics is called comes after many attempts, many failures, many applied mathematics, but the qualifiers are not discouragements, many false starts. It often hap- emotionally strong enough to disguise that they pens that months of work result in the proof that qualify the same noun. If the concatenation of the method of attack they were based on cannot syllables I chose here reminds you of other words, possibly work and the process of guessing, visu- no great harm will be done; the rhymes alluded to alizing, and conclusion-jumping begins again. A are not completely accidental. I originally planned reformulation is needed and—and this too may to entitle this lecture something like “Mathematics surprise you—more experimental work is needed. is an art,” or “Mathematics is not a science,” and To be sure, by “experimental work” I do not “Mathematics is useless,” but the more I thought mean test tubes and cyclotrons. I mean thought- about it the more I realized that I mean that “Ma- experiments. When a mathematician wants to thology is an art,” “Mathology is not a science,” and prove a theorem about an infinite-dimensional Hil- “Mathology is useless.” When I am through, I hope bert space, he examines its finite-dimensional ana- you will recognize that most of you have known logue, he looks in detail at the 2-and 3-dimensional about mathophysics before, only you were prob- cases, he often tries out a particular numerical ably calling it mathematics; I hope that all of you case, and he hopes that he will gain thereby an in- will recognize the distinction between mathology sight that pure definition-juggling has not yielded. and mathophysics; and I hope that some of you will The deductive stage, writing the result down, and be ready to embrace, or at least applaud, or at the writing down its rigorous proof are relatively trivial very least, recognize mathology as a respectable once the real insight arrives; it is more like the human endeavor. draftsman’s work, not the architect’s. ... In the course of the lecture I’ll have to use The mathematical fraternity is a little like a self- many analogies (literature, chess, painting), each perpetuating priesthood. The mathematicians of imperfect by itself, but I hope that in their totality today train the mathematicians of tomorrow and, they will serve to delineate what I want delineated. in effect, decide whom to admit to the priesthood. Sometimes in the interest of economy of time, Most people do not find it easy to join—mathemati- and sometimes doubtless unintentionally, I’ll cal talent and genius are apparently exactly as rare

1142 Notices of the AMS Volume 54, Number 9 as talent and genius in paint and music—but any- mathematicians feel about the rift, and what’s one can join, everyone is welcome. The rules are likely to happen to it in the centuries to come. ... nowhere explicitly formulated, but they are intui- The pure and applied distinction is visible in tively felt by everyone in the profession. Mistakes the arts and in the humanities almost as clearly are forgiven and so is obscure exposition—the as in the sciences: witness Mozart versus military indispensable requisite is mathematical insight. marches, Rubens versus medical illustrations, or Sloppy thinking, verbosity without content, and Virgil’s Aeneid versus Cicero’s Philippics. Pure lit- polemic have no role, and—this is to me one of the erature deals with abstractions such as love and most wonderful aspects of mathematics—they are war, and it tells about imaginary examples of them much easier to spot than in the nonmathematical in emotionally stirring language. Pure mathematics fields of human endeavor (much easier than, for deals with abstractions such as the multiplication instance, in literature among the arts, in art criti- of numbers and the congruence of triangles, and cism among the humanities, and in your favorite it reasons about Platonically idealized examples of abomination among the social sciences). them with intellectually convincing logic. Although most of mathematical creation is done There is, to be sure, one sense of the word in by one man at a desk, at a blackboard, or taking a which all literature is “applied”. Shakespeare’s son- walk, or, sometimes, by two men in conversation, nets have to do with the everyday world, and so mathematics is nevertheless a sociable science. does Tolstoy’s War and Peace, and so do Caesar’s The creator needs stimulation while he is creating commentaries on the wars he fought; all start from and he needs an audience after he has created. what human beings see and hear, and all speak of Mathematics is a sociable science in the sense that how human beings move and feel. In that same I don’t think it can be done by one man on a desert somewhat shallow sense all mathematics is ap- island (except for a very short time), but it is not a plied. It all starts from sizes and shapes (whose mob science, it is not a team science. A theorem is study leads ultimately to algebra and geometry), not a pyramid; inspiration has never been known to and it reasons about how sizes and shapes change descend on a committee. A great theorem can no and interact (and such reasoning leads ultimately more be obtained by a “project” approach than a to the part of the subject that the professionals great painting: I don’t think a team of little Gausses call analysis). could have obtained the theorem about regular There can be no doubt that the fountainhead, polygons under the leadership of a rear admiral the inspiration, of all literature is the physical and anymore than a team of little Shakespeares could social universe we live in, and the same is true have written Hamlet under such conditions. ... about mathematics. There is no doubt that the physical and social universe daily affects each mu- On Pure and Applied sician, and painter, and writer, and mathematician, and that therefore a part at least of the raw mate- Excerpt from: rial of the artist is the work of facts and motions, “Applied mathematics is bad mathematics”, sights and sounds. Continual contact between the pp. 9–20, appearing in Mathematics Tomorrow, work and art is bound to change the latter, and edited by Lynn Steen, Springer-Verlag, New York perhaps even to improve it. (1981). The ultimate goal of “applied literature”, and It isn’t really (applied mathematics, that is, isn’t of applied mathematics, is action. A campaign really bad mathematics), but it’s different. speech is made so as to cause you to pull the third Does that sound as if I had set out to capture lever on a voting machine rather than the fourth. your attention, and, having succeeded, decided An aerodynamic equation is solved so as to cause forthwith to back down and become conciliatory? a plane wing to lift its load fast enough to avoid Nothing of the sort! The “conciliatory” sentence is complaints from the home owners near the air- controversial, believe it or not; lots of people argue, port. These examples are crude and obvious; there vehemently, that it (meaning applied mathemat- are subtler ones. If the biography of a candidate, ics) is not different at all, it’s all the same as pure a factually correct and honest biography, does mathematics, and anybody who says otherwise not directly mention the forthcoming election, is probably a reactionary establishmentarian and is it then pure literature? If a discussion of how certainly wrong. mathematically idealized air flows around moving If you’re not a professional mathematician, you figures of various shapes, a logically rigorous and may be astonished to learn that (according to some correct discussion, does not mention airplanes or people) there are different kinds of mathematics, airports, is it then pure mathematics? And what and that there is anything in the subject for anyone about the in-between cases: the biography that, to get excited about. There are; and there is; and without telling lies, is heavily prejudiced; and what follows is a fragment of what might be called the treatise on aerodynamics that, without being the pertinent sociology of mathematics: what’s demonstrably incorrect, uses cost-cutting rough the difference between pure and applied, how do approximations—are they pure or applied? ...

October 2007 Notices of the AMS 1143 To confuse the issue still more, pure mathemat- profession with the essential clerical and admin- ics can be practically useful and applied mathemat- istrative jobs, you must be responsible, conscien- ics can be artistically elegant. Pure mathemati- tious, careful, and organized—it helps if you also cians, trying to understand involved logical and have some qualities of leadership and charisma. geometrical interrelations, discovered the theory You can’t be perfect, but if you don’t try, you of convex sets and the algebraic and topological won’t be good enough. study of various classes of functions. Almost as To be a mathematician you must love mathe- if by luck, convexity has become the main tool matics more than family, religion, money, comfort, in linear programming (an indispensable part of pleasure, glory. I do not mean that you must love modern economic and industrial practice), and it to the exclusion of family, religion, and the rest, functional analysis has become the main tool in and I do not mean that if you do love it, you’ll never quantum theory and particle physics. The physicist have any doubts, you’ll never be discouraged, regards the applicability of von Neumann algebras you’ll never be ready to chuck it all and take up (a part of functional analysis) to elementary par- gardening instead. Doubts and discouragements ticles as the only justification of the former; the are part of life. Great mathematicians have doubts mathematician regards the connections as the only and get discouraged, but usually they can’t stop interesting aspect of the latter. De gustibus non doing mathematics anyway, and, when they do, disputandum est? they miss it very deeply. ... Just as pure mathematics can be useful, applied mathematics can be more beautifully useless than is sometimes recognized. Applied mathematics is not engineering; the applied mathematician does not design airplanes or atomic bombs. Ap- plied mathematics is an intellectual discipline, not a part of industrial technology. The ultimate goal of applied mathematics is action, to be sure, but, before that, applied mathematics is a part of theoretical science concerned with the general principles behind what makes planes fly and bombs explode. ... The deepest assertion about the relation be- tween pure and applied mathematics that needs examination is that it is symbiotic, in the sense that neither can survive without the other. Not only, as is universally admitted, does the applied need the pure, but, in order to keep from becoming inbred, sterile, meaningless, and dead, the pure needs the revitalization and the contact with reality that only the applied can provide. ...

On Being a Mathematician Excerpt from: I Want to Be a Mathematician, p. 400, Springer- Verlag, New York (1985) It takes a long time to learn to live—by the time you learn your time is gone. I spent most of a life- time trying to be a mathematician—and what did I learn? What does it take to be one? I think I know the answer: you have to be born right, you must continually strive to become perfect, you must love mathematics more than anything else. Born right? Yes. To be a scholar of mathematics you must be born with talent, insight, concentra- tion, taste, luck, drive, and the ability to visualize and guess. For teaching you must in addition understand what kinds of obstacles learners are likely to place before themselves, and you must have sympathy for your audience, dedicated self- lessness, verbal ability, clear style, and expository skill. To be able, finally, to pull your weight in the

1144 Notices of the AMS Volume 54, Number 9 The American Mathematical Society presents The AMS Einstein Sir Roger Penrose Public Lecture Spacetime Conformal Geometry, in Mathematics and a New Extended Cosmology Saturday, October 6 8:00 P.M. Scott Hall, Room 123 Rutgers University

Sir Roger Penrose, Emeritus Rouse Ball Professor of Mathematics, University of Oxford

Sir Roger Penrose is known worldwide for his work in mathematics and math- ematical physics. He has written many books, received numerous awards, and was knighted in 1994 for his outstanding contributions to science. In this lecture, Sir Roger will speak about a new view of the universe that unites three of the most puzzling aspects of cosmology: dark energy, dark matter, and the extreme specialness of the Big Bang.

“I certainly believe in the importance of conveying to the general public, as far as this is possible, something of the real nature of mathematics, not only for its increasing utility across so many areas of importance to modern society, but also for its beauty and for the inner satisfaction that it brings.” www.ams.org/meetings/einstein-lect.html

This event is part of the AMS 2007 Fall Eastern Sectional at Rutgers, October 6-7.

Sponsored by the American Mathematical Society. Hosted by the Rutgers University Mathematics Department.

Top: NASA, ESA and A. Nota (STScI/ESA); Second row, left: NASA, ESA, STScI, J. Hester and P. Scowen (Arizona State University); Second row, right: NASA, ESA, M. Robberto (STScI/ESA) and the Hubble Space Telescope Orion Treasury Project Team; Third row, left: NASA, ESA, and The Hubble Heritage Team (STScI/AURA); Third row, right: NASA, H. Ford (JHU), G. Illingworth (UCSC/LO), M.Clampin (STScI), G. Hartig (STScI), the ACS Science Team, and ESA; Bottom: NASA, ESA, C.R. O’Dell (Vanderbilt University), M. Meixner and P. McCullough (STScI) WHAT IS... ? a Woodin Cardinal? John R. Steel

All mathematical statements can be expressed Large cardinal hypotheses attempt to capture in the language of set theory (LST), whose vari- the idea that there are more sets than one can ables are understood as ranging over sets, and possibly imagine, by means of the following in- whose only non-logical symbol ∈ stands for the formal reflection principle: suitable properties of membership relation. The vast majority of math- V reflect to some Vα. For one example, V is in- ematical proofs require no more than the axioms finite, and the ordinary Axiom of Infinity asserts of Zermelo-Fraenkel set theory with Choice, or that some Vα shares this property. For another, ZFC. In this way, set theory provides a foundation V is a model of second-order ZFC (also called for all of mathematics. Nevertheless, a surprising Kelley-Morse set theory), so our informal princi- number of basic questions about sets in general ple leads to the assertion that some Vκ satisfies are not decided by the axioms of ZFC; moreover second-order ZFC. This is equivalent to κ being an many of the more abstract questions of analysis, inaccessible cardinal. algebra, and topology are left similarly undecid- The stronger large cardinal hypotheses assert ed. Perhaps the most famous of the undecided the existence of elementary embeddings j : V → M questions is Cantor’s Continuum Problem: what that are nontrivial, i.e., not the identity. Here M is a is the cardinality of the set of all real numbers? transitive class. Elementarity means that whenever LST Another more concrete such question is whether ϕ(v1,...,vn) is a formula of with the displayed all sets of real numbers that are projective are free variables, and a1,...,an are sets, then

Lebesgue measurable. (A set is projective if and V ⊨ ϕ[a1,...,an] ⇔ M ⊨ ϕ[j(a1),...,j(an)]. only if it can be built up from a countable inter- (For N a transitive set or class, and b ,...,b ∈ N, section of open sets by taking continuous images 1 n we say N ⊨ ϕ[b ,...,b ] if and only if ϕ(v ,...,v ) and complements finitely many times.) 1 n 1 n is true when its quantifiers are understood as The most fruitful way to extend ZFC so as to ranging over N, its variable vi is understood as remove some of this incompleteness is to strength- naming bi , and the ∈ symbol of LST is understood en its axiom asserting that there are infinite sets. as standing for set-membership.) For such a j, the Large cardinal hypotheses do this. critical point of j, or crit(j), is the least ordinal For α an ordinal number, we define Vα by κ such that j(κ) 6= κ. Since j is order-preserving, transfinite induction: V0 =∅, Vα+1 ={x | x ⊆ Vα}, this implies κ < j(κ). The reflection here occurs at and Vλ = Sα<λ Vα for λ a limit ordinal. Thus Vα κ: if ϕ(κ) holds in V , and M resembles V enough consists of those sets that can be built up in < α that M ⊨ ϕ[κ], then M ⊨∃α

1146 Notices of the AMS Volume 54, Number 9 of elements of M belongs to M, then we say κ B is projective if and only if membership in B can is λ-supercompact, and we say κ is supercompact be defined within LSA from some real parameter. if and only if κ is λ-supercompact for all λ. We Most questions about projective sets of reals can have listed these properties in order of increasing be phrased in LSA; for example, the Lebesgue strength; indeed, if κ is strong, then Vκ ⊨ “there is measurability and determinacy of projective sets a measurable cardinal”, and if κ is supercompact, can be expressed using sentences in LSA. Then, by then Vκ ⊨ “there is a strong cardinal”. work of Martin, Woodin, and the author, we have S. Ulam first isolated a property equivalent to that the following are equivalent: measurability in 1930: κ is measurable if and only (a) PD, if there is a κ-additive, 2-valued measure defined (b) for each n, every consequence in LSA of on all subsets of κ that gives singletons measure 0. the theory ZFC plus “there are n Woodin (To get a measure from an elementary embedding, cardinals” is true. ⇔ set µ(A) = 1 κ ∈ j(A), for A ⊆ κ. Conversely, Thus PD is precisely the “instrumentalist’s trace” of one gets elementary embeddings from measures Woodin cardinals in the language of second-order using the ultrapower construction.) Embeddings arithmetic. corresponding to stronger large cardinal proper- Underlying the proof that Woodin cardinals ties can be captured in a similar way by systems imply PD is a structure known as the iteration of measures. tree. Roughly speaking, an iteration tree on M is Let κ < δ be cardinals, and A ⊆ Vδ; then κ is a tree of models with root M that is generated A-strong in δ if and only if for all β < δ there is by a certain process. This process involves using an elementary j : V → M such that crit(j) = κ and a system of measures coding an embedding in j(A) ∩ Vβ = A ∩ Vβ. (The case A = Vδ implies κ is one model to generate an embedding with domain β-strong for all β < δ.) We say δ is A-Woodin if and in some other model, and thus equips the tree only if there is a κ < δ that is A-strong in δ, and with commuting elementary embeddings from the we say δ is Woodin in case it is A-Woodin for all models earlier on a given branch to those later on A ⊆ Vδ. The hypothesis that there are Woodin car- that branch. A simple example is an alternating dinals is strictly between the existence of strong chain on M, an iteration tree having two distinct and supercompact cardinals in strength. branches, the “even” branch consisting of models Woodin cardinals were discovered by W. H. Mn for n even (with M0 = M), and the “odd” branch Woodin in 1984. New techniques due to M. Fore- consisting of M0 together with the Mn for n odd. If man, M. Magidor, and S. Shelah had just shown B is a subset of the Bairespace, then an alternating that the Lebesgue measurability of projective sets chain representation of B is a continuous function of real numbers follows from large cardinal hy- A on NN such that for each x ∈ NN, A(x) is an potheses much weaker than had been previously alternating chain on some Vδ, and x ∈ B if and suspected. Woodin showed that in fact the exis- only if the direct limit along the even branch of tence of infinitely many Woodin cardinals implies A(x) is wellfounded. If B has an alternating chain all projective sets of reals are Lebesgue measur- representation, then B is determined. The proof of able. About a year later, in 1985, D. A. Martin and PD from Woodin cardinals goes by showing that if the author showed that the existence of infinite- δ is Woodin, and there are infinitely many Woodin ly many Woodin cardinals implies all projective cardinals above δ, then every projective set has an subsets of the Baire space NN are determined (PD), alternating chain representation on Vδ. a stronger regularity property that, by work of In general, an iteration tree may have transfinite many people in the 1960s and 1970s, is the basis length. The construction of iteration trees, and the for a thorough and detailed structure theory for analysis of the properties of arbitrary iteration ZFC projective sets. (By itself, decides very little trees, is at the heart of many basic open problems about the projective sets.) in pure large cardinal theory. The extent to which Of course, it follows that any large cardinal δ is Woodin (that is, the complexity of those sets hypothesis that implies there are infinitely many A ⊆ V such that δ is A-Woodin) is mirrored in the PD δ Woodin cardinals also implies . In fact, building complexity of the iteration trees one can generate on work of Martin, Woodin had already shown on Vδ. This correspondence is behind the equiva- (just before the work of Foreman, Magidor, and lence mentioned in the paragraph before last, and PD Shelah) that one such hypothesis implies . The is one reason Woodin cardinals continue to be continuing importance of Woodin cardinals is re- important in set theory. lated to the fact that they provide the minimal PD large cardinal hypothesis needed for . To make References this precise, let us say a sentence ϕ belongs to [1] A. Kanamori, The Higher Infinite, Springer-Verlag LSA the language of second-order arithmetic ( ) if 2003. and only if ϕ refers only to natural numbers and [2] D. A. Martin and J. R. Steel, Projective determinacy, sets of natural numbers, but not objects of higher Proc. Natl. Acad. Sci. USA, 85 (1988), pp. 6582–6586. type (like sets of sets of natural numbers). A set

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General and Interdisciplinary Torus Actions and Their The Collected Works Absolute CM-Periods Applications in Topology and of Julia Robinson Hiroyuki Yoshida Codebreakers Combinatorics Solomon Feferman Mathematical Surveys and Monographs, Arne Beurling and the Swedish Victor M. Buchstaber Collected Works, Volume 6 Volume 106 2003; 282 pp.; hardcover; ISBN: 978-0-8218- Crypto Program during World War II and Taras E. 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Bourbaki, A Secret Society of Mathematicians Now that we are in the twenty-first century it is Maurice Mashaal perhaps the right time to look back and try to as- AMS, June 2006 sess the overall impact of Bourbaki, before all the US$29.00, 260 pages principal players leave the scene. The basic histori- ISBN-13: 978-0821839676 cal facts are well known and are set out in both

the books under review. France had lost a whole The Artist and the Mathematician: The Story generation of intellectuals in the 1914–18 war, and of Nicolas Bourbaki, the Genius Mathematician the young mathematicians of Paris, in the inter- Who Never Existed war period of the 1920s and 1930s, were looking Amir D. Aczel for new guidance and inspiration. Only Hadamard Thunder’s Mouth Press, August 2006 and Élie Cartan of the older generation still com- US$23.95, 272 pages manded respect. Talented youth, unconstrained by ISBN-13: 978-1560259312 higher authority, is a powerful force and, whatever one’s views about Bourbaki, there is no doubt that All mathematicians of my generation, and the talent was quite exceptional. The list of the even those of subsequent decades, were aware of early members of Bourbaki is truly impressive: Nicolas Bourbaki, the Napoleonic general whose André Weil, Henri Cartan, Claude Chevalley, Jean reincarnation as a radical group of young French Dieudonné, Laurent Schwartz… Later recruits were mathematicians was to make such a mark on the of similar calibre: Jean-Pierre Serre, Armand Borel, mathematical world. His memory may now have Alexandre Grothendieck… Harnessing the powers faded, the books are old and yellowed, but his of such a formidable group was not an easy task. influence lives on. Many of us were enthusias- There were fierce debates, some serious quarrels, tic disciples of Bourbaki, believing that he had and much passion. The remarkable fact is that the reinvigorated the mathematics of the twentieth group, by and large, stayed together and kept Bour- century and given it direction. But others believed baki alive and active over several decades. This was that Bourbaki’s influence had been pernicious a tribute to the idealistic vision that they shared, and narrow, confining mathematics behind walls that of remoulding the shape of mathematics in of rigour, and cutting off its external sources of the twentieth century. inspiration. Much of the atmosphere of the early days is brought vividly to life by the many informal pho- Sir Michael Atiyah is Honorary Professor of Mathemat- tographs in the Mashaal book. It is fascinating to ics at the University of Edinburgh. His email address is see pictures of the young André Weil, relaxing [email protected]. in a deck chair, though Henri Cartan was always

1150 Notices of the AMS Volume 54, Number 9 impeccably dressed in jacket and tie, resisting is not responsible for the excesses trendy fashion. perpetrated in the name of Chris- I myself attended a Bourbaki conference in my tianity. youth and can attest to the lively experience of Bourbaki was to some extent debating vigorously (and usually critically) the the victim of its own success. latest version of the next book. Summer sunshine The original aim had been the in the south of France and the friendly and casual modest one of writing a mod- atmosphere did much to prevent arguments devel- ern replacement for Goursat’s oping into armed conflict. To paraphrase Winston Cours d’Analyse but, buoyed up Churchill, “never in the course of human argument by enthusiasm and the success has so much been spoken by so many on so little.” of recruiting many of the leading It appeared a miracle that books, many of them, ac- mathematicians of the time, hori- tually emerged from this process, a result undoubt- zons broadened. All of mathemat- edly due to the diligence and energy of Dieudonné. ics was to be included, analysis, al- If Weil was the prime inspiration behind Bourbaki, gebra, and geometry. For obvious it was Dieudonné who carried it to fruition. reasons algebra lent itself best So what were the basic aims of Bourbaki, and to the Bourbaki treatment. The how much was achieved? Perhaps one can pick out volumes on commutative algebra and particularly two central objectives. One was that mathematics on Lie groups were excellent and became standard needed new and broad foundations, embodied references, due in large part to the personal contri- in a series of books that would replace the old- bution of Serre, whose influence and taste guided fashioned textbooks. The other was that the key this whole area. idea of the new foundations lay in the notion of The formal aspects of analysis, as exemplified “structure”, illustrated by the now common word in functional analysis, also had success, though Bourbaki’s treatment of probability came in for “isomorphism”. severe criticism from the experts who argued that There is no doubt that, with its clear emphasis important parts of the theory were excluded by the on “structure”, Bourbaki produced the right idea restriction to locally compact spaces. A concern for at the right time and changed the way most of us elegance had led to too great a price being paid. thought. Of course it fitted in well with Hilbert’s But this little battle over probability was a mere approach to mathematics and the subsequent sideshow in the Bourbaki approach to analysis, a development of abstract algebra. But structure subject too varied, complex, and untidy to be taken was not confined to algebra, and it was particu- over by Bourbaki. Glimmerings of these problems larly fruitful in topology and associated areas of already appear in differential geometry, a subject geometry, all of which were to see spectacular at the interface between analysis and geometry, developments in the period following World where structure, though present, is a less dominat- War II. Here the impact of Bourbaki was decisive, ing concept. Though Riemann surface theory, after and, in the hands of Serre and Grothendieck, alge- a century of active development, could conceiv- braic geometry rose to incredible heights. ably be given a coherent Bourbaki treatment, the Laying universal foundations is another mat- same could hardly be said for the current work of ter. Each time it is tried it inevitably gets bogged Thurston-Perelman in three dimensions. Another down by the sheer scale and ambition of the opera- severe limitation of Bourbaki, no doubt conscious, tion. The “ne plus ultra” in this direction was the was the restriction to pure mathematics. Applied Éléments de Géométrie Algébrique of Grothendieck mathematics is too messy and disparate to be and Dieudonné, which expanded voluminously included, and theoretical physics hovers on an both forward and backward and was in danger of uncertain borderline. One distinguishing feature sinking under its own weight. of Bourbaki was the emphasis on clear and unam- Laying ambitious foundations is not only a dan- biguous definitions and on rigorous proofs. This gerous delusion, it can also be a didactic disaster. was, as in algebraic geometry, a reaction against Encyclopaedias are not textbooks, and much of some sloppy treatments of the past, and it served the critique directed against Bourbaki is that it a purpose in creating a firm platform for the fu- was used, or perhaps misused, to reform school ture. Unfortunately, when taken to extremes, the education. This may be unfair, since many of the requirement for total rigour excludes large areas great mathematicians in Bourbaki were excellent of mathematics which are in their early creative lecturers and knew well the difference between stages. Had Euler worried too much about rigour, formal exposition and the conveying of ideas. But, mathematics would have suffered. as so often happens, the disciples are more extreme Over the past thirty years, arguably in the declin- and fanatical than their masters, and education in ing years of Bourbaki, some of the most exciting France and elsewhere suffered from a dogmatic developments in mathematics have arisen from the and ill-informed attempt at reform. Jesus Christ interface with physics and particularly quantum

October 2007 Notices of the AMS 1151 field theory. New concepts and the entire scene from mathematics to the social explicit results have emerged sciences. The only place where I can examine the from this interaction, notably evidence for this and make an informed comment, Donaldson’s work on four- is in his treatment of mathematics and the people manifolds, mirror symmetry in in it. Here I have profound misgivings, which relate algebraic geometry, and quan- mainly to Grothendieck, who occupies a central tum cohomology. Much of this place in the author’s pantheon. came directly from very heu- There is no doubt that Grothendieck was an ristic work by physicists such exceptional figure in the mathematical world and as Edward Witten. Most of it, that he deserves a scholarly full-length biography, though by no means all, has preferably written by a mathematician who knew now been given a cloak of re- him personally. I believe such a book is in prepara- spectability involving rigorous tion, and I look forward to reading it. Aczel’s book proofs. does not measure up to the level of the subject, Clarity and rigour have a vital because of his uncritical acceptance of Grothen- place in mathematics but they dieck as the great prophet, spurned eventually by must not be used as a barrier his people (including Bourbaki). to new ideas from other fields. I knew Grothendieck well when he was in his Free trade is a benefit to us all and should not prime. I greatly admired his mathematics, his pro- be inhibited by excessive attachment to national digious energy and drive, and his generosity with sovereignty. ideas, which attracted a horde of disciples. But his Although Bourbaki recruited most of the fa- main characteristic, both in his mathematics and mous French mathematicians of the time (and sev- in social life, was his uncompromising nature. This eral from outside France), there were some notable was, at the same time, the cause both of his suc- exceptions, the most obvious being Jean Leray cess and of his downfall. No one but Grothendieck (who left very early) and René Thom. In retrospect could have taken on algebraic geometry in the full it is clear that neither fitted the Bourbaki role. The generality he adopted and seen it through to suc- fact that they were also two of the most original cess. It required courage, even daring, total self- mathematicians of the time does perhaps suggest confidence and immense powers of concentration that such originality has difficulty flourishing in a and hard work. Grothendieck was a phenomenon. constrained atmosphere. Both were also closer to But he had his weaknesses. He could navigate applied mathematics than their colleagues. like no one else in the stratosphere, but he was Of the two books under review, the first by Mau- not sure of his ground on earth—examples did rice Mashaal might be described as “authorized”. not appeal to him and had to be supplied by his It has the sanction of the AMS and was first pub- colleagues. lished several years ago in French. It seems clear Aczel is right when he identifies Grothendieck that the author knew many of the French math- as someone who took the new Bourbaki philoso- ematicians personally and derived his information phy seriously and made a tremendous success and in particular the photographs from this source. of it. Where I part company with Aczel is in his It is reliable on the history, the personalities, and assertion that Bourbaki made a fatal mistake in the mathematics. It is also highly readable and not taking Grothendieck’s advice and rewriting noncontroversial. its foundations in the new language of category The other book by Amir Aczel is totally dif- theory. Aczel believes that Bourbaki had turned ferent. It has a more ambitious aim, which is to its face away from the future in not following examine the Bourbaki influence on “structure” in Grothendieck. I doubt whether history will come the social sciences. It is also highly controversial in to this verdict. Grothendieck’s own EGA, as well its extensive treatment of the Grothendieck story. as the general fate of over-confident universalists, I was not convinced of the total reliability of its might suggest otherwise. Moreover, given Grothen- sources, nor of its philosophical credentials. dieck’s uncompromising nature and supreme self- Although written in English this book is perme- confidence, it is difficult to see how, with him at ated by French intellectual ideas and will probably the helm, Bourbaki could have continued as a col- seem strange to those not part of that scene. A legial enterprise. slightly tenuous link between André Weil and the Aczel’s total endorsement of Grothendieck sociologist Claude Levi-Strauss is used to claim leads him to make such fatuous statements as: that Bourbaki made a major impact on sociology “Weil was a somewhat jealous person who clearly and related fields such as psychology, anthropol- saw that Grothendieck was a far better mathemati- ogy, and linguistics. This grand aim is clearly cian than he was.” Subtle balanced judgement is set out by the title, and I have no expertise in clearly not Aczel’s forte, and it hardly encourages any of these fields. It may be that the author is a the reader to take seriously his confident and polymath, an intellectual colossus, who straddles sweeping assertions in the social sciences.

1152 Notices of the AMS Volume 54, Number 9 NSF Proposal Preparation: The View of an Ex-Program Officer Joseph Brennan

This article is the third in an occasional series intended for graduate students and young mathematicians. The series is coordinated by Notices Associate Editor Lisa Traynor.

The task of obtaining external funding to support Applications to the NSF for funding are made in re- research has become a critical point in the career of sponse to a Program Solicitation. That solicitation might the young mathematician. Obtaining funding can be the program’s description of the area program; it have a profound effect on the recipient’s career might be an explicit solicitation for proposals for the as the imprimatur of external funding provides in particular program; it might take the form of a “Dear the eyes of many a confirmation of the importance Colleague letter”. A prospective applicant should ex- of the recipient’s research activity. While the real- amine the range of solicitations to find the solicitation ity is that the research proposals that are funded that best fits the proposed work. A typical solicitation tend to be the ones that are excellent, there are contains a detailed description of the program, the very many excellent research proposals that are method by which the proposals are to be evaluated, not funded. This note is intended to provide some criteria by which proposals are to be evaluated, budget- insight into the process of funding at the National ary guidelines, and contact information for program Science Foundation (NSF) based on my two years’ officials. Proposals sent in response to a solicitation need to be responsive to the solicitation. In particular experience as a program officer in the Division of the solicitation should be carefully and fully read and Mathematical Sciences. While the advice I give is the issues that are raised by the solicitation need to be directed to the applicant for NSF funding, the basic fully addressed in explicit detail by the proposal. principles are applicable to funding proposals to The statement in bold of the previous paragraph may any external funding source. seem to follow immediately from the definitions. Ob- It is important to recognize that the agenda servation would seem to indicate however that it is not for the process is established by the National Sci- obvious. Every solicitation is an effort to direct funding ence Foundation. This agenda is not ordinarily to accomplish or encourage activity that the foundation established by mathematicians but is instead the views as important to the furthering of the NSF’s agenda. consequence of intellectual, political, and cultural Funding success depends on meeting the criteria speci- concerns of the government. The immediate con- fied in the solicitation, so proposals should explicitly ad- sequence of this is that the direction and employ- dress those criteria. Having identified a potential source ment of funds as well as the criteria for awarding of funding, the next step is to read the guides for the them is established in order to satisfy the NSF’s format and submission of proposals and to follow the own purposes rather than an agenda established criteria established for the program. Agencies have es- by the mathematical community. It is important to tablished guides for proposals. The NSF Grant Proposal be alert to the agenda of the NSF and to understand Guide covers general procedures for grant submission its needs in the process of supporting mathemat- to NSF ( http://www.nsf.gov/pubs/gpg/nsf04_23/). ics. The mission statement of the NSF calls for it It is revised periodically. Individual solicitations at NSF “to promote the progress of science; to advance the will indicate the procedures to be followed for that so- national health, prosperity, and welfare; to secure licitation and deviations from the general procedures the national defense…”. Although the objectives of the Grant Proposal Guide. of the mission statement are not usually explicitly Some programs permit the submission of a proposal addressed in the proposal submission, it may be at any time. Others restrict the submission to certain useful to contemplate how the proposal addresses windows. This can be expressed in two principal ways. these issues—most particularly for mathemat- One is an explicit time window with (sometimes) an ics—in promoting the progress of science. opening date and a deadline for proposal submis- sion. The other is a target date for submission. These Joseph Brennan is associate professor of mathematics windows for proposals are dictated by the beginning at the University of Central Florida. His email address is of budget years, staff workload requirements, as well [email protected]. as other factors. Proposals for funding should be sent

October 2007 Notices of the AMS 1153 within the proposal window. This is absolutely tion. In all cases, the stated goals should match the necessary in the presence of deadlines. Failure to objectives of the funding agency. The goals should adhere to the deadlines for proposal submission be presented in a manner that would permit the may lead to a proposal being returned without decision makers in the funding process (reviewing being reviewed. On the other hand, target dates panel, study session, program manager) to under- are indicators to the eligible that proposals should stand what the objectives of the proposal are. be sent in proximity to that time. Target dates are Furthermore it is extremely important to tell principally used by area programs at NSF, but not the decision makers why they should fund the all such programs have target dates rather than proposal. Each proposal asks someone to invest deadlines. The use of target dates allows for more limited resources into a particular project. The efficient budgetary planning and staff resource al- motivation for doing so varies amongst funding location. Proposals that arrive after the target date organizations but every funding entity looks to will be considered but proposals that are submit- justify their investment. If the proposer is unable ted long after the target date has passed may find to articulate a reason for investment of funds in that, by the time they are reviewed, the budget for a particular project, there is little likelihood that the program has already been allocated. the decision makers will find a reason to invest in Some programs have a pre-proposal phase. The the project. pre-proposal may be required or optional. The The proposer should take it for granted that all character of such a pre-proposal can vary from a (or virtually all) of the proposals that are submitted letter of intent to submit a proposal to a full scale to the program to which they are applying are in mini-proposal. There are usually managerial re- some very real sense excellent. The competition quirements that necessitate a pre-proposal phase. for funding is amongst these excellent proposals. The pre-proposal phase may be used to limit the In this competition, the ones that stand out are number of proposals to those most likely to be those that provide a strong and compelling case successful, or the pre-proposal phase may be used in response to the funding announcement to the only to determine the number and composition question as to why they should be funded. of the reviewing panels. The fact that the purpose This requires explaining in some considerable of the pre-proposal phase is proposal manage- detail to an informed but not necessarily special- ment does not mean it is not important. The pre- ist mathematician reader what real impact the proposal may undergo as complete a review pro- proposed research will have and what insight is cess as any full proposal. being provided to attack the problem. It is however The NSF has established two review criteria that not sufficient to merely explain the mathematical are used in virtually all proposal evaluations. The content of the proposal. What is required is to first review criterion is place the mathematics that is being proposed in a context that indicates its importance in mathemat- What Is the Intellectual Merit of the Proposed ics or in a broader context. This is the answer to Activity? the question: Why would one wish to know the How important is the proposed activity to advanc- consequences of the proposal’s research? ing knowledge and understanding within its own Some careful consideration should be given field or across different fields? How well qualified to the preparation and delivery of this material is the proposer (individual or team) to conduct the in the proposal. A typical failing of an excellent project? (If appropriate, the reviewer will comment but unfunded proposal is a dismissive attitude on the quality of prior work.) To what extent does towards the context of the proposal. The NSF the proposed activity suggest and explore creative funds all types of research in the mathematical and original concepts? How well conceived and sciences, from foundational issues in logic to the organized is the proposed activity? Is there suf- modeling of ice in the Antarctic. The issue is not ficient access to resources? the type of research that is being proposed; the In short, the first criterion is to evaluate the issue is why the research being proposed is im- proposal based on the intellectual merit. Conse- portant. This requires more than a one-sentence quent to this review criterion: The proposal must comment that says that the topic is connected to address the problem of what goals are to be ac- research in another field and hence is important. complished and what the impact of attainment If the proposer of the research is not able to put of those goals would mean. While it might appear the importance of the work in context, is not that this requirement is self-evident the failure able to explain why the work is an important ele- to meet this requirement is the leading cause ment in the “progress of science” or important in for proposals to fail. There are two parts to this advancing “the national health, prosperity, and requirement. The first is that the proposal must welfare” or in “securing the national defense”, then relate what goals are to be accomplished. If the why is the work important enough to rise to the proposal is in response to a solicitation those goals level where it should be funded over other propos- must match the agenda set forth by the solicita- als that do make that argument?

1154 Notices of the AMS Volume 54, Number 9 One also needs to establish why the proposer It is a mistake to think that the proposal should has the ability to perform the work that is being address all of these issues or that these comments proposed. It is not sufficient to propose the or the listing at the above website is an exhaus- solution of one of the millennium problems; it tive list of what is sought. What is required by the is necessary to provide a reasonably educated criterion is to address the question of how the mathematical reviewer with a clear indication of individual proposal addresses the broad national the new idea that is to be exploited in the project. interest that the NSF represents. This does not require the presentation of a proof One should also consider the process in which but does require a detailed exploration of the the proposal will be reviewed. At NSF, depending ideas and difficulties in obtaining the goals of the on the program, the proposal will be reviewed proposed work. by a combination of panels and/or individual To summarize, there is a key but sometimes non-interacting (ad hoc) reviewers. Each of these forgotten distinction between excellent proposals processes has its own peculiar aspects that may and excellent proposals that get funded: The latter dictate differing approaches by the investigator provide, by exploring the intellectual consequences in the presentation of the proposed work. Each of the proposed work, compelling reasons why the of these review processes will present particular work should be funded. challenges to the aspiring investigator. The second review criterion is: Panel reviewers are drawn from established researchers in the general field of the proposal. What Are the Broader Impacts of the Proposed They are less likely to have direct knowledge of a Activity? particular subfield than individual non-interacting How well does the activity advance discovery and reviewers. The proposal will be sent to three or understanding while promoting teaching, train- more of the panelists to review for the panel. These ing, and learning? How well does the proposed reviewers need not be experts in the particular activity broaden the participation of underrepre- subfield of the proposal. In fact it is highly likely that at least one of the panel reviewers will be sented groups (e.g., gender, ethnicity, disability, deliberately chosen outside the particular subfield geographic, etc.)? To what extent will it enhance of the proposal. This may necessitate writing more the infrastructure for research and education, material to describe the setting of the proposed such as facilities, instrumentation, networks, and research and require considerably more detail partnerships? Will the results be disseminated on the importance of the intellectual merit of the broadly to enhance scientific and technological proposal to give context to the proposal to the understanding? What may be the benefits of the reviewers. The panel members each will review proposed activity to society? considerably more proposals than are reviewed The NSF in the second review criterion also by typical non-interacting individual reviewers and demands that the proposal explicitly address the therefore tend to be in a better position to establish broader impact of the proposed work. the relative placement of proposals. Panel review- In short, the second criterion at NSF asks how ers have a considerable amount of reading to do, this proposal will aid in the furtherance of the mis- so proposal-writers will want to establish early and sion, objectives, or goals of the National Science often in the proposal the value of their proposed Foundation. This criterion was written to make it work. The panel reviewers will meet and discuss clear that proposals in which the NSF is providing each proposal individually. The discussion is led funding address not only scientific research objec- by the panelists that reviewed the proposal prior tives but also the broader national needs whose to the panel’s meeting. accomplishment is charged to the foundation. Individuals who review the proposals “ad hoc” The proposer might wish to look at the sample or reviewers from within the NSF are usually in a broader impacts provided by the NSF at http:// better position to understand the requirements of www.nsf.gov/pubs/gpg/broaderimpacts.pdf. the funding entity but are less likely to have an un- These are not however to be regarded without derstanding of the intrinsic value of a proposal. consideration of what are the actual accomplish- Beyond the requirement of addressing the issues ments to be obtained by the proposed work. What raised by the required format of the proposal there outcomes can be seen as emanating from the is one central requirement that must be addressed proposed award? Are graduate students, under- by every submission. How will this work benefit the graduate students, K–12 students (future scientific mission of NSF? Congress exercises considerable workforce) being supported in the proposal? Is the oversight of federal programs, and it is routine for scientific education infrastructure benefiting from senior executives of federal agencies to be called the award—in what manner is this accomplished? to explain funding decisions—even at the level of Will the award have benefit to the crucial problem funding decisions for individual proposals. This of addressing mathematics and science in second- was part of the motivation for the recent NSF de- ary education? cision to require that proposals submitted to the

October 2007 Notices of the AMS 1155 NSF explicitly address two criteria for funding deci- their objective to obtain a degree, offer an op- sions. The second criterion examines the broader portunity to sharply reduce the time to obtain a impact of the proposal. Simply put this asks for the degree. They enable a more focused direction of consequences that funding the proposal will have the students’ work on their thesis. Graduate stu- on the broader community of science. These will dent support can also offer a means to increase vary from proposal to proposal but might include the success in obtaining the scientific goals of the training of students in the techniques of the area proposal. The presence of support for graduate or applications of the work to questions in another students on a proposal also has the potential to area of science. Mission oriented agencies such as indirectly broaden the objectives of the proposal the Office of Naval Research express this in a more by addressing the issue of training a scientific direct manner: asking that proposals explain “Po- workforce for future requirements of the United tential contributions of the effort to the agency’s States. Different funding entities and programs specific mission.” The requirement is the same, have different requirements for the support of however, across all funding agencies: Explain why students. It is important, however, to be able to giving the money to this project furthers the aims give an indication of the student’s identity at the of the funding entity. time of funding. It is very important to remember one of the first One should not neglect the potential for fund- statements of this article: that it is important to ing teachers and K–12 students. The direct scien- recognize that the agenda for the funding process tific impact of funding the participation of these is established by the entity that is doing the fund- groups may not be significant; however, there are ing. The agenda of the entity will be reflected in significant indirect benefits of encouraging and the funding criteria; proposals need to address the strengthening mathematical activity at these early issues raised by the criteria. levels of education. The budget is simultaneously the simplest The budget returns our attention to the insti- and the most complex part of any proposal. The tution, as with the possible exception of some simple solution to the question of budgeting is: fellowships, individuals do not receive awards. The budget should be sufficient to attain all of Individuals do not in general have the ability to the objectives of the proposal. There is an ad- handle the financial reporting requirements im- ditional caveat. The amount requested should posed by governments and foundations. Awards conform to the pre-established award sizes, or are made to institutions. Budgets reflect this real- be comparable to program awards of similar ity. Federal relations with educational institutions complexity. Some agencies and some programs are governed by Office of Management and Budget provide pre-established award sizes. These provide Circular A-21 Principals for determining costs guidance as to the level of complexity expected of applicable to grants, contracts, and other agree- an award. Many funding entities provide examples ments with educational institutions (http://www. of previously funded awards to provide budgetary whitehouse.gov/omb/circulars/a021/a021. guidance. html). The provisions of the circular require that It is most important to note that the funds a cognizant federal agency (usually the Office of requested should be sufficient to fulfill the objec- Cost Allocation of the Program Support Center of tives of the proposal. Proposals are not funded be- the Department of Health and Human Services) cause they request “just a small amount of funds”. enter into an agreement to provide for “costs Proposals are funded because the objectives of the that are incurred for common or joint objectives proposal meet the requirements of the funding and, therefore, cannot be identified readily and entity. Some agencies restrict application of funds specifically with a particular sponsored project, to redirect the investigators’ activity from one an instructional activity, or any other institu- aspect of their job to work on the project—others tional activity.” These are known as Facilities and encourage such buyout. The proposer/investiga- Administration Costs (F&A). These are usually tor needs to work with the sponsored program computed as a percentage of the Modified Total officer at his or her eligible institution to design a Direct Costs. The percentage of the Modified Total budget that conforms to the requirements of the Direct Costs allocated to F&A depends on the na- funding entity. ture and location of the activities supported. This It is important to find mechanisms to support percentage is negotiated between the government students with external funding. This is an impor- and the institution and may change as institu- tant issue for our profession and in addressing tional costs are reevaluated. The modification of the national need for a well-trained scientific the direct costs eliminates certain costs as direct workforce. When grants support undergraduates, costs for calculation of the F&A as specified in the they encourage these and other undergraduates to agreement between the institution and the govern- see mathematics as a viable career choice. Funds ment. For example, tuition costs for supported that support graduate students, and particularly students and costs of conference and workshop funds that support graduate students directly in participants are not included in the Modified

1156 Notices of the AMS Volume 54, Number 9 Total Direct Costs. Proposers should also be alert that some proposals specifically exclude certain participant support costs from the total direct 2007 costs or provide for an alternative computation of the F&A. Joint Meeting At some point in the award process, proposers might be asked to reduce the requested budget. A significant reduction of a budget submitted of the to a federal agency will trigger a requirement to reduce the scope of the project. This means that AMS-NZMS the agency acknowledges that the funds will not be sufficient to obtain all the objectives that were es- Victoria University of Wellington, tablished in the proposal and calls upon the inves- tigators to reduce the level of activity of the project New Zealand and the corresponding objectives to be obtained. December 12–15, 2007 The reduction in scope of the project should be correlated with the change in the budget. Receipt of an award does not end the respon- sibility of the investigator. There is an obligation to spend the funds in accord with the objectives of the project. One might review the semiannual reports to Congress of the Inspector General of NSF (http://www.nsf.gov/oig/pubs.jsp) to provide an indication of the degree of seriousness the federal government takes in auditing its expen- Plenary Speakers ditures. There is also an obligation to fulfill the Marston Conder, University of Auckland conditions upon which the award has been made, Rodney Downey, Victoria University of from promoting seat belt use to periodic reporting Wellington on the accomplishments of the project. One should Michael Freedman, Microsoft Research remember that the obligation remains upon the funding entity, the program, and the program’s Bruce Kleiner, Yale University employees to justify the expenditure. In particu- Gaven Martin, Massey University lar, programs need success stories. These provide Assaf Naor, Courant Institute of Mathematical programs with the opportunity to increase base Sciences funding levels while programs unable to document Theodore Slaman, University of California, successful accomplishment of their goals may face Berkeley below-average increases or even decrease of base Matt Visser, Victoria University of Wellington

funding levels. Janel Curry courtesyPhotograph of Dr. Having funding from a program or funding entity does not preclude seeking additional fund- ing from the same or different programs or enti- For accommodations, travel, ties to support other projects. (Note that seeking and the scientific program, go to: funding for the same project would be unethical www.ams.org/amsmtgs/ and potentially criminal.) One should not become dependent on a single funding source to support internmtgs.html our students or our objectives. or www.mcs.vuw.ac.nz/ A wise man said to me: “Don’t ask me how to %7Emathmeet/amsnzms2007/ obtain funding; rather present to me a good idea index.shtml and a source will be found to fund it.” Ultimately the test of whether a proposal will be funded is if the idea presented in the proposal is found meri- torious in the marketplace of ideas. It is incumbent upon us as mathematicians to provide evidence that support of our discipline is essential to the development of science. Exploring and finding ve- hicles for support of mathematics and mathemat- ics students is essential in that quest.

OCTOBER 2007 NOTICES OF THE AMS 1157 hicles for support of mathematics and mathemat- ics students is essential2007 in that quest. Joint Meeting of the AMS-NZMS

Victoria University of Wellington, New Zealand December 12–15, 2007

Plenary Speakers Marston Conder, University of Auckland Rodney Downey, Victoria University of Wellington Michael Freedman, Microsoft Research Bruce Kleiner, Yale University Gaven Martin, Massey University Assaf Naor, Courant Institute of Mathematical Sciences Theodore Slaman, University of California, Berkeley Matt Visser, Victoria University of Wellington Photograph courtesy of Dr. Janel Curry courtesyPhotograph of Dr.

For accommodations, travel, and the scientific program, go to: www.ams.org/amsmtgs/ internmtgs.html or www.mcs.vuw.ac.nz/ %7Emathmeet/amsnzms2007/ index.shtml

OCTOBER 2007 NOTICES OF THE AMS 1157 Interview with Congressman Jerry McNerney

Jerry McNerney, a Ph.D. mathematician, was elected to the U.S. House of Representatives in November 2006 and represents California’s eleventh district. McNerney received his Ph.D. in mathematics from the University of New Mexico in 1981 and has been an AMS member since 1977. Before his election to Congress, he worked at Sandia National Laboratories and at US Windpower, and also served as an energy consultant for utility companies. Prior to his election he was chief executive officer of a start- up company that will manufacture wind turbines. In the following article, Congressman McNerney provides written responses to questions posed to him by the Notices. Samuel M. Rankin III, director of the AMS Washington Office, helped prepare the questions and facilitated communication with Congressman McNerney. —Allyn Jackson

Notices: Tell us about your personal experience My father was an engineer and I developed an in mathematics. early interest in applications. In fact, I majored in McNerney: Like many mathematicians, my first chemical engineering as an undergraduate, but math experience was with an inspiring teacher. I transferred to the math department as a senior was a sophomore in high school, and like many undergraduate. There was an engineering profes- young adults at that age, I was a little rebellious. sor at UNM who told me that a mathematician who I was taking college prep courses, but on the first understood applications would have engineers day of class the geometry teacher began talking knocking on his or her door. This made an impres- about “mommy and daddy triangles”. I immedi- sion, and motivated me to take physics and keep ately transferred to a different geometry class. Ron in touch with applications even though I stayed in Black was the teacher. It was in Mr. Black’s class differential geometry, a field that many considered that I started to become fascinated by proofs with to be pure mathematics. congruence theorems. My interest was piqued. I Eventually, I graduated with a Ph.D. and decided just ate the class up, immediately taking to the to go into industry instead of staying in academia. material. From that point on, math was always an I felt that several years of applied experience in important part of my life. High school science and industry would make me a better mathematician. math classes were a breeze after that. However, I came to understand later that deci- I didn’t take calculus until college. But seeing sion pretty much disqualified me from returning derivatives and integrals pop out by passing to the to academia for a number of reasons. The most limit was mind boggling—the proverbial light bulb prominent of those was that while working in in- turning on in my head. We were using infinity to dustry I didn’t publish any research papers in math solve real finite problems. journals. Also, most mathematics departments Of course differential equations and all the un- want to hire academic postdoctoral mathemati- dergraduate math courses I took were great, but cians right out of graduate school or out of other the next really big thing for me was real analysis postdoctoral programs. I’m not sure if this is good in graduate school. Getting into the real basics and or bad. There’s no doubt that the very top math- proving things with absolute rigor was outstand- ematicians should spend their careers in academia. ing to see after years of hearing that the details For the rest of us merely good mathematicians, I of the proofs were to be left for later. It became believe that some outside experience, or perhaps clear in graduate school. I loved the certainty and an academic requirement for graduate students the beauty of a simple proof and of the concepts to take graduate courses in other areas such as involved. I loved the connection to philosophy. I neuroscience or sociology, would be beneficial. loved teaching and helping younger students. I also Notices: How does your world-view as a math- loved the community of math. The members of the ematician play a role in your work as a congress- department at the University of New Mexico and man—assessing legislation, dealing with constitu- the graduate students were a family. ents, etc.

1158 Notices of the AMS Volume 54, Number 9 McNerney: What I love about mathematics is opportunity. Staffers serve its precision and beauty. But mathematics is about as the “eyes and ears” of more than just solving problems and proving the member of Congress, theorems. It gives practitioners an insight into the making recommendations relation between the mind and the world. If content and providing members and meaning is taken away, becoming abstract, with research and informa- it is possible to find the form of a solution. This tion about a wide variety gives hope that even the most intractable problems of issues. can be approached and that true progress can be Notices: What do you made. It means that the struggle in and of itself is consider to be the main na- worthwhile and that if we can approach problems tional issues where math- rationally, we can find solutions and make the ematics and mathemati- world a better place. cians can make decisive Notices: Do you think members of Congress un- contributions? derstand the value of mathematical research and McNerney: This is the the role it plays in innovation? million dollar question: McNerney: Most members of Congress ap- how can someone or even Congressman Jerry McNerney preciate that mathematical research is important, a group have a positive im- though some members appreciate it more than pact on human destiny? others. There is general recognition that increasing Mathematics has raw power, but to have an impact, scientific and mathematical achievement will help this power has to be harnessed and exploited for keep the United States competitive internationally. the greater human good. This is where creativity Within the Science and Technology Committee, and real brain power comes into play. Mathema- on which I sit, there is strong support for Science, ticians have shown they have the brain power, Technology, Engineering, and Mathematics (STEM) and the next step is to harness this power to do education and for the doubling of the National Sci- good. Napoleon was a mathematician who used ence Foundation budget over the next ten years. his power to win wars for France, then became the emperor and ultimately found himself exiled Though frankly, I think that is too little and over for his excesses. One of the best qualities about too long a period of time. mathematicians is that, by and large, we are un- We need to restore the Office of Technology assuming. This is a quality that people love. We Assessment, which was eliminated in the mid- simply have to understand the perils we face and 1990s. The goal of OTA was to provide members the enormous responsibility we have to use our of Congress and Congressional committees with power to meet those challenges head on. objective and authoritative analysis of complex scientific and technical issues. Notices: What contributions can mathemati- Notices: How can we better educate members of cians make to the debates on global environmental Congress as to the value of mathematics research issues? and its contribution to innovation? McNerney: I am, of course, very concerned McNerney: Most members of Congress have about global warming. But there are other issues constituent meetings of one form or another in that are equally threatening, such as nuclear prolif- their districts and in Washington. Mathemati- eration. We can model the climate, and eventually, cians should request individual meetings or form engineer or control it. Mathematics offers the tools advisory groups that meet regularly with their to move forward. We have all studied the achieve- representative. Getting to know your representa- ments of past mathematicians. In the early twenti- tive is key. Nothing works in politics like personal eth century, mathematicians were also engineers, relationships. When you meet, if it’s in an office but today, mathematicians are often pure practitio- appointment, take maybe three mathematicians ners. This change has certain advantages, but the who can effectively convey the message and bring world is in desperate need of technical guidance some concrete examples of how their work benefits at the highest levels. Specialization is not what’s the member’s district. It’s important to educate the needed right now, but people who can bridge the specialties and derive concrete solutions. Math- member how mathematics research will benefit ematicians are well poised to fill this need. his or her district. I would also emphasize the importance of mathematics and education to the Notices: How would you assess the state of math- nation’s security and prosperity. ematics education in the U.S.? If you can’t get an office appointment, then go to McNerney: Education in the U.S. is in need of the member’s announced town hall meetings and major improvement, and mathematics education is ask relevant but not embarrassing questions. If you certainly not the exception. We have not invested can’t schedule a meeting directly with the member enough in infrastructure and education, and the of Congress, ask to meet with a member of his or results will become more apparent as time goes on. her staff. Don’t view meeting with staff as a missed Dollars invested in education are repaid tenfold

October 2007 Notices of the AMS 1159 later on. We must make the need to invest in educa- possible futures, then maybe we could discuss what tion clear to the American people, and we need to it would take to avoid catastrophic outcomes. help young people appreciate and take advantage Notices: What do you think the future of math- of the educational opportunities being offered to ematics will be? them. Too many young people do not recognize McNerney: Mathematics is an ancient and ven- the value of getting a good education. Getting a erable discipline. It has been shaped by necessity, degree in engineering, science, or mathematics by people attracted to its challenge, and by its util- takes hard work that begins well before college, ity and beauty. Human beings have not changed in and students may not recognize the importance of a fundamental way since the Egyptians used math making the sacrifice necessary to meet that kind of to build the pyramids. Our civilization is more so- goal. A good education takes work, but the reward phisticated and the challenges have grown. Hard is plentiful. We have to do a better job of helping boiled analysis will be needed on many fronts to our young people see the benefit of that work. enable mankind to grow and prosper. Some of that responsibility lies at the federal level Will the nature of mathematics change? Cer- in helping to set national priorities. tainly it will. The change is already under way, from Notices: Some mathematicians refuse to ac- the mathematics of physics to the mathematics cept U.S. military funding for research. As both a of biology, from individuals working alone with mathematician and a congressman, how do you pencil and paper to collaborative efforts involving look at the issue? telecommunications and digital computers. Math- McNerney: Mathematics is an amoral exercise. ematics will change with the needs and with the Moral and ethical considerations are external to tools available. New problems will challenge new real math. But the impact of the math we do can- generations of mathematicians. Mathematics will not be divorced from the research process. I don’t provide tools to answer questions and will be an judge individuals who choose not to work on mili- integral part of the evolution of society. I believe tary projects, and I do not judge those who accept that mathematics will ultimately be called upon to such assignments. We have to look into ourselves analyze and understand large-scale social interac- and answer that question individually. I simply ask tions such as war and famine. It will map out the that we all do take the time to ask the questions. human brain and the universe. Mathematics will be with us and will provide the tools necessary to Notices: Do you see the recent discussion of define our destiny as we move toward an unknown immigration affecting the entrance of foreign future. graduate students and professionals into U.S. mathematics? McNerney: Certainly. Just the discussion has an impact, not to mention the laws that may get passed. Mathematics does not have political bias. There isn’t a Republican or Democratic theorem. AMERICAN MATHEMATICAL SOCIETY There aren’t American theorems versus Chinese theorems. Mathematics is a tool for all to use to confront the problems ahead. I would be disap- Now Available! pointed to see this country adopt policies that will unintentionally prevent the advance of math- ematics. Notices: If you could give a mathematical lec- 2008 Journal ture to a joint session of Congress, what would the subject be? Subscription McNerney: There are some pretty good theo- rems out there, such as the free will theorem, Rates that would be fun to present and would “wow” members of Congress. However, since this is a hy- pothetical question, I would work with sociologists To view the list of and other behavioral experts to develop models that accurately predict societal behavior. I would print and electronic develop present models to provide us rational journals available tools to use in making difficult and consequential from the AMS, decisions, such as accurately predicting what the societal consequences of ignoring global warming go to www.ams.org/journals. will be or the likely outcome of applying military options in a variety of different scenarios. You often hear the saying, “Do the math.” If the mathematics shows a strong result about

1160 NOTICES OF THE AMS VOLUME 54, NUMBER 9 AMERICAN MATHEMATICAL SOCIETY

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1160 NOTICES OF THE AMS VOLUME 54, NUMBER 9 Bass Receives National Medal of Science

On July 18, 2007, President George W. Bush an- The accompanying nounced the recipients of the 2006 National sidebar provides a brief Medal of Science. Among the eight medalists is account of Bass’s research Hyman Bass, Roger Lyndon Collegiate Professor in mathematics. He has of Mathematics and of Mathematics Education at also worked extensively in mathematics education, the University of Michigan. Bass was cited for “his primarily in collaboration fundamental contributions to pure mathematics, with Deborah Ball of the especially in the creation of algebraic K-theory, his University of Michigan. profound influence on mathematics education, and This work has centered his service to the mathematics research and educa- on subject-matter knowl- tion communities. With his unique combination of edge entailed in teaching, gifts he has had enormous impact over the course practice-based research of a half century.” on teaching and learn- President Bush presented the awards to the ing, teacher education, 2006 and 2005 National Medal of Science recipi- reasoning and proof in school mathematics, and ents in a White House ceremony on July 27, 2007. analysis of curriculum ma- Hyman Bass (Among the 2005 recipients is Stanford University terials. Bass was a member statistician Bradley Efron; an announcement about of the Mathematical Sciences Education Board of that award appeared in the September 2007 issue the National Research Council from 1991 until of the Notices.)

The Mathematical Work of Hyman Bass Hyman Bass’s wide-ranging research in algebra has featured a conceptual clarity and generality that not only powerfully addressed deep questions but provided the tools and framework for others who followed in his pioneering footsteps. His early work considered commutative rings of finite injective dimension, and his recognition of their “ubiquity” resulted in one of the most often-cited papers in commutative algebra. Bass’s interest in projective modules led to his project to systematically translate topological K-theory into algebra, and in particular to the definition of K1​of a ring and the analysis of the latter, including a complete description in the important case of rings of algebraic integers. The answer, as well as the analysis, is connected to the Congruence Subgroup Problem, another area where Bass made fundamental contributions. One of the techniques used in the Congruence Subgroup Problem led to the consider- ation of groups acting on trees and generalizations and in turn to considerations of locally com- pact automorphism groups of trees and the lattices in them. As with algebraic K-Theory, Bass’s work not only solved basic problems in the theory of tree lattices but formulated the foundations for the subject. Along with his genius for setting the stage and systematizing subjects, Bass has many technically demanding achievements, including subtle and significant examples delineating the boundaries of the representation theory of finitely generated groups. No brief summary can do more than suggest the range of topics on which Hyman Bass’s work has made an impact. For a fuller account covering Bass’s work up to 1997, we refer the reader to [1].

—T. Y. Lam, University of California, Berkeley and —A. R. Magid, University of Oklahoma Reference [1] Algebra, K-Theory, Groups, and Education, Contemp. Math. 243 (1999), Amer. Math. Soc., Providence, RI.

October 2007 Notices of the AMS 1161 2000 (chair, 1993–2000). From 1998 until 2006 NEW from A K PETERS he was president of the International Commission on Mathematics Instruction, which operates under Mysteries and Puzzles the auspices of the International Mathematical Union. Crimes and Mathdemeanors Born on October 5, 1932, in Houston, Texas, Hyman Bass received his Ph.D. from the University Leith Hathout $14.95; Paperback; 150 pp. of Chicago in 1959 under the direction of Irving “Leith Hathout, drawing on Kaplansky. Bass was on the faculty of Columbia a great love of mathematics, University before moving to the University of Mich- has with incredible ingenuity igan in 1999. He has held numerous visiting posi- embedded fourteen lovely tions, including at the Institute for Advanced Study problems within fourteen in Princeton, the Tata Institute for Fundamental mystery yarns.” Research in Mumbai, and at the Institut des Hautes —MARTIN GARDNER Études Scientifiques in Paris. He has served on the “This is a truly delightful AMS Council and on many AMS committees, includ- book that should inspire ing the Notices Editorial Board. He was president many a high school student, of the Society during 2001 and 2002. His honors bored with classroom ‘word include the AMS Cole Prize in Algebra (1975) and problems,’ to take a second look at the subject with fresh eyes. The more so if they realize that the Gung and Hu Award for Distinguished Service the author is, like them, a high school student! to Mathematics of the Mathematical Association of America (2006). Bass was elected as a member —KEITH DEVLIN of the American Academy of Arts and Sciences “I am hoping that in the setting of solving (1980), as a fellow of the American Association a mystery, [kids my age] might come to for the Advancement of Science (1980), and as a see math as interesting and useful and member of the U.S. National Academy of Sciences beautiful.” (1982). He was an invited speaker at the Inter- —LEITH HATHOUT national Congress of Mathematicians in Moscow (1966) and in Vancouver (1974), and he delivered Save 20% on these titles a plenary address at the International Congress on discount code AMS Mathematical Education in Copenhagen (2004). He was a member of Bourbaki from 1970 until 1982. The National Medal of Science is the country’s Mathematical Mind-Benders highest distinction for contributions to scientific Peter Winkler $18.95; Paperback; 160 pp. research. According to a news release from the Office of Science and Technology Policy, “The This wonderful book presents, National Medal of Science honors individuals for from diverse sources and pioneering scientific research in a range of fields, with wit and humor, many including physical, biological, mathematical, so- interesting and challenging cial, behavioral, and engineering sciences, that problems, both mathematical and otherwise. Like its enhances our understanding of the world and predecessor, it is a must for leads to innovations and technologies that give the the shelves of a problem United States its global economic edge.” The Na- connoisseur.” tional Science Foundation administers the award, —ANDY LIU which was established by the Congress in 1959. —Allyn Jackson This book is for lovers of mathematics, lovers of puzzles, lovers of a challenge. Most of all, it is for those who think that the world of mathematics is orderly, logical, and intuitive—and are ready to learn otherwise!

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1162 Notices of the AMS Volume 54, Number 9 NEW from A K PETERS Mysteries and Puzzles

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1162 Notices of the AMS Volume 54, Number 9

Mathematics People

Idalia Reid Prize for his fundamental contributions to SIAM Prizes Awarded nonlinear control, especially in the area of differential- The Society for Industrial and Applied Mathematics (SIAM) geometric control theory. The prize is awarded for re- awarded several prizes at recent meetings. search in or other contributions to the broadly defined The SIAM Conference on Applications of Dynamical areas of differential equations and control theory. Systems was held in Snowbird, Utah, from May 28 through Murat Arcak of the Rensselaer Polytechnic Institute June 1, 2007. Lai-Sang Young of the Courant Institute of received the SIAM Activity Group on Control and Systems Mathematical Sciences, New York University, was awarded Theory Prize for his fundamental contributions to the the AWM-SIAM Sonia Kovalevsky Lectureship for her study of large networked systems and for his accom- fundamental contributions in the field of ergodic theory plishments in developing a novel passivity approach to and dynamical systems. Her pioneering research has had large-scale networks, such as communication, power, and a significant impact in the investigation of dynamical biological systems, and deriving fundamental results for complexity, strange attractors, and probabilistic laws of increasing their robustness and performance. chaotic systems. The lectureship is intended to highlight significant contributions of women to applied or compu- —From a SIAM announcement tational mathematics. Salvatore Torquato of the Princeton Institute for the Science and Technology of Materials, Princeton University, Prizes of the London was awarded the Ralph E. Kleinman Prize for his contribu- tions to the modeling, analysis, and computational study Mathematical Society of heterogeneous materials. The London Mathematical Society (LMS) has awarded sev- Andrew Stuart of the University of Warwick received eral prizes for 2007. the J. D. Crawford Prize of the SIAM Activity Group on Bryan Birch of the University of Oxford has been Dynamical Systems (SIAG/DS) for his contributions to awarded the De Morgan Medal in recognition of his in- the fields of stochastic ordinary and partial differential fluential contributions to modern number theory. Birch equations, including mathematical theory, algorithm de- worked with Peter Swinnerton-Dyer of the University of velopment, and the application of stochastic differential Cambridge to create a new area of arithmetic algebraic equations to physical models and the dynamics of inertial geometry, formulating the Birch–Swinnerton-Dyer conjec- partials in random fields. The prize is awarded for recent tures. These conjectures are among seven classic unsolved outstanding work on a topic in nonlinear science, includ- mathematical problems identified by the Clay Mathematics ing dynamical systems theory and its applications, as well Institute in Cambridge, Massachusetts, for proofs of which as experiments and computations/simulations. the institute is offering US$1 million prizes. In addition, Harry L. Swinney of the University of Texas, Austin, Birch’s work on Heegner points has led to huge advances was awarded the Jürgen Moser Lectureship of the SIAG/DS in the arithmetic of elliptic curves. for his elegant and incisive laboratory experiments that Béla Bollobás of the University of Cambridge has been have elucidated the nonlinear dynamics of systems far awarded the Senior Whitehead Prize for his fundamental from equilibrium. contributions to almost every aspect of combinatorics. He The SIAM Conference on Control and Its Applications has written a large number of research papers and influ- was held in San Francisco in July 2007. Héctor J. Suss- ential textbooks, many of which have defined or redefined mann of Rutgers University was awarded the W. T. and whole areas of research.

1164 Notices of the AMS Volume 54, Number 9 Mathematics People

Michael Green of the University of Cambridge received the Naylor Prize and Lectureship in Applied Mathematics in recognition of his founding work in superstring theory, which has dominated theoretical physics over the past twenty years. His contributions to the subject have pro- foundly influenced both pure and applied mathematics. Four Whitehead Prizes were awarded. Nikolay Niko- lov of the University of Oxford and Imperial College, London, was recognized for several important advances in group theory, especially in profinite groups and as- ymptotic aspects of arithmetic groups and finite simple Deputy Director groups. Oliver Riordan of the University of Cambridge was honored for his contributions to graph polynomials, Associate Director random graphs, extremal combinatorics, models of large- scale real-world graphs, and percolation theory. Ivan Applications are invited for the positions of Deputy Smith of the University of Cambridge was recognized for Director and Associate Director at the Mathematical his work on symplectic topology, in which he often blends Sciences Research Institute (MSRI), an independent ideas from algebraic geometry and topology in novel ways. research organization on the campus of the University Catharina Stroppel of the University of Glasgow was of California in Berkeley. The appointments will be for honored for her contributions to representation theory, a term of at least two years starting August 2008. For in particular in the framework of categorifications and its more information, see applications to low-dimensional topology. http://www.msri.org/about/jobs/ddad —From an LMS announcement Applications will be considered starting Nov. 1, 2007.

Royal Society of Canada MSRI is an equal opportunity employer. Elections The following mathematical scientists have been elected to the Royal Society of Canada: David C. Brydges, University of British Columbia; Walter Craig, McMaster University; and Lisa Jeffrey, University of Toronto at Scarborough. Chosen as a Specially Elected Fellow was Peter Hackett Up to 1.65 of the Alberta Ingenuity Fund. million EUR for Research —From a Royal Society of Canada announcement in Germany News from the IMA Sofja Kovalevskaja Award The Institute for Mathematics and its Applications (IMA) Supporting High-level, Innovative Research in has announced the appointment of Fadil Santosa of the Germany for Outstanding Scholars & Scientists University of Minnesota as its next director. His appoint- ment will begin on July 1, 2008. He will replace Douglas One of the most generous research awards in Germany, this program is open to exceptionally promising junior Arnold, who has been director since 2001 and who will researchers from all countries and disciplines. Applicants remain a professor of mathematics at the University of must have completed a doctoral degree with distinction Minnesota. within the past six years and have published in Santosa has taught at the University of Minnesota since prestigious international journals or academic presses. 1995. He previously held positions at Cornell University The Alexander von Humboldt Foundation particularly and the University of Delaware. He currently serves as welcomes applications from qualified, female junior director of the Minnesota Center for Industrial Mathemat- researchers. ics. He was associate director for industrial programs at Funding enables winners to conduct independent the IMA from 1997 until 2001 and deputy director from research, to finance a research team at a German 2001 to 2004. His research interests are in the areas of university or research institution of their choice, and to cover their living expenses in Germany. Application photonics, inverse problems, optimal design, and financial deadline: January 4, 2008. data analysis. Application materials and details are available at: —From an IMA announcement www.humboldt-foundation.de

October 2007 Notices of the AMS 1165 Deputy Director Associate Director

Applications are invited for the positions of Deputy Director and Associate Director at the Mathematical Sciences Research Institute (MSRI), an independent research organization on the campus of the University of California in Berkeley. The appointments will be for a term of at least two years starting August 2008. For more information, see http://www.msri.org/about/jobs/ddad

Applications will be considered starting Nov. 1, 2007.

MSRI is an equal opportunity employer.

Up to 1.65 million EUR for Research in Germany

Sofja Kovalevskaja Award Supporting High-level, Innovative Research in Germany for Outstanding Scholars & Scientists

One of the most generous research awards in Germany, this program is open to exceptionally promising junior researchers from all countries and disciplines. Applicants must have completed a doctoral degree with distinction within the past six years and have published in prestigious international journals or academic presses. The Alexander von Humboldt Foundation particularly welcomes applications from qualified, female junior researchers. Funding enables winners to conduct independent research, to finance a research team at a German university or research institution of their choice, and to cover their living expenses in Germany. Application deadline: January 4, 2008. Application materials and details are available at: www.humboldt-foundation.de

October 2007 Notices of the AMS 1165 Mathematics Opportunities

Voice of America, Discovery Channel Online, National Geo- NSF Postdoctoral Research graphic Television, Popular Science, The Chicago Tribune, Fellowships and Time magazine. Fellows receive a weekly stipend of US$450, plus travel The National Science Foundation (NSF) awards Mathemati- expenses, to work for ten weeks during the summer as cal Sciences Postdoctoral Research Fellowships (MSPRF) reporters, researchers, and production assistants in media for appropriate research in areas of the mathematical organizations. They observe and participate in the process sciences, including applications to other disciplines. A by which events and ideas become news, improve their revised program announcement is available from the ability to communicate about complex technical subjects website http://www.nsf.gov/pubs/2007/nsf07573/ in a manner understandable to the public, and increase nsf07573.htm. The deadline for proposals is Octo-­ their understanding of editorial decision making and of ber 17, 2007. how information is effectively disseminated. Each fellow attends an orientation and evaluation session in Washing- —From an NSF announcement ton, D.C., and begins the internship in mid-June. Fellows submit interim and final reports to the AAAS. A wrap-up session is held at the end of the summer. AMS Epsilon Fund Mathematical sciences faculty are urged to make their graduate students aware of this program. The deadline The AMS Epsilon Fund awards grants to summer math- to apply for fellowships for the summer of 2008 is Janu-­ ematics programs that support and nurture mathemati- ary 15, 2008. Further information about the fellowship cally talented high school students in the United States. program and application procedures is available on- The deadline for application for funding for summer 2008 line at http://www.aaas.org/programs/education/ programs is December 15, 2007. Application materials are MassMedia/; or applicants may contact Stacey Pasco, available at http://www.ams.org/outreach/epsilon. Director, Mass Media Program, AAAS Mass Media Science html or by mail: Membership and Programs Department, and Engineering Fellows Program, 1200 New York Avenue, American Mathematical Society, 201 Charles Street, Provi- NW, Washington, DC 20005; telephone 202-326-6645; fax dence, RI 02904-2294; telephone 800-321-4267, ext. 4170; 202-371-9849; email: [email protected]. email: [email protected]. Further information is also available at http://www. ams.org/government/massmediaann.html and through —AMS announcement the AMS Washington Office, 1527 Eighteenth Street, NW, Washington, DC 20036; telephone 202-588-1100; fax 202- 588-1853; email: [email protected]. AMS-AAAS Mass Media Summer Fellowships —Elaine Kehoe The American Association for the Advancement of Science (AAAS) sponsors the Mass Media Science and Engineering Enhancing the Mathematical Summer Fellows Program, through which graduate stu- dents work during the summer in major media outlets. The Sciences Workforce in the AMS provides support each year for one or two graduate Twenty-First Century students in the mathematical sciences to participate in the program. In past years the AMS-sponsored fellows The long-range goal of the Enhancing the Mathematical have held positions at Scientific American, Business Week, Sciences Workforce in the Twenty-First Century (EMSW21)

1166 Notices of the AMS Volume 54, Number 9 Mathematics Opportunities program of the National Science Foundation (NSF) is to software tools based on existing models and methods will increase the number of well-prepared U.S. citizens, nation- not be accepted in this competition. als, and permanent residents who pursue careers in the The deadline for full proposals is October 1, 2007. See mathematical sciences and in other NSF-supported disci- the website http://www.nsf.gov/funding/pgm_summ. plines. This program builds on the Vertical Integration of jsp?pims_id=5300 for more information. Research and Education (VIGRE) program and includes a broadened VIGRE activity, an additional component for —From an NSF announcement Research Training Groups (RTG), and another for Men- toring through Critical Transition Points (MCTP) in the Mathematical Sciences. The VIGRE program supports projects that involve News from PIMS entire departments in the training process, from the start The Pacific Institute for the Mathematical Sciences (PIMS) of the undergraduate career through the completion of invites nominations of outstanding young researchers in a postdoctoral fellowship. The RTG program involves the mathematical sciences for Postdoctoral Fellowships a group of researchers based in a subarea of the math- for the year 2008–2009. Candidates must be nominated ematical sciences or linked by a multidisciplinary theme by one or more scientists affiliated with PIMS or by a and supports training at educational levels from under- department (or departments) affiliated with PIMS. The fel- graduate to postdoctoral within that focus. The MCTP lowships are intended to supplement support made avail- program supports projects, either departmentally based able through such a sponsor. PIMS expects to support up or conducted by a large group of faculty members, that to 20 fellowships tenable at any of its Canadian member are aimed at critical transition points in the educational universities: Simon Fraser University, the University of careers of students and junior researchers. Alberta, the University of British Columbia, the University The DMS expects to make between nine and fifteen of Calgary, and the University of Victoria, as well as its awards under this program in 2008. The deadline for affiliated universities, the University of Lethbridge and proposals is June 10, 2008. For more information about the University of Regina. the program and all of its components, see the web- For the 2008–2009 competition, the amount of the site http://www.nsf.gov/publications/pub_summ. award is CA$20,000, and the sponsor(s) is (are) required jsp?ods_key=nsf05595. to provide additional funds to finance a minimum stipend —From an NSF announcement of CA$40,000 (including benefits). Award decisions are made by the PIMS PDF Review Panel based on excellence of the candidate, potential for participation in PIMS programs, and potential for involve- Joint DMS/NIGMS Initiative in ment with PIMS partners. PIMS Postdoctoral Fellows will Mathematical Biology be expected to participate in all PIMS activities related to the fellow’s area of expertise and will be encouraged to The Division of Mathematical Sciences (DMS) of the Na- spend time at other sites. To ensure that PIMS Postdoctoral tional Science Foundation (NSF) and the National Insti- Fellows are able to participate fully in institute activities, tute of General Medical Sciences (NIGMS) of the National they may not teach more than two single-term courses Institutes of Health (NIH) have announced an Initiative to per year. Support Research in the Area of Mathematical Biology. Nominees must have a Ph.D. or equivalent (or expect This competition is designed to support research on math- to receive a Ph.D. by December 31, 2008) and be within ematical problems related to biological problems in areas three years of the Ph.D. at the time of the nomination (i.e., supported by NSF/DMS and NIH/NIGMS. A direct relation- the candidate must have received her or his Ph.D. on or ship between a biological application and the mathematics after January 1, 2005). The fellowship may be taken up at is expected. Proposals from research teams that include any time between April 1, 2008, and January 1, 2009. The scientists from both the life sciences community and the mathematical sciences community are encouraged. Both fellowship is for one year and is renewable for at most new and existing collaborations will be supported. Propos- one additional year. als from individual investigators will need to make the Nominations must include: 1) curriculum vitae, 2) state- case that the individual has expertise in both areas. ment of research interests, 3) three letters of reference Successful proposals will identify innovative mathemat- (including one from a sponsoring professor), and 4) state- ics or statistics needed to solve an important biological ment of anticipated support from the sponsor. problem. Research that would apply standard mathemat- Nominations must be received by December 15, ics or statistics to solving biological problems is not ap- 2007. Complete information on Postdoctoral Fellowship propriate for this competition and should be submitted nominations, including contact information and submis- directly to NIH. Similarly, proposals with research in sion guidelines, is available at http://www.pims.math. mathematics or statistics that is not tied to a specific ca/fellowships. biological problem should be submitted to the appropriate DMS program at NSF. Proposals designed to create new —PIMS announcement

October 2007 Notices of the AMS 1167 Mathematics Opportunities

research on mathematics education; and the Felix Klein Teach For America Accepting Award, for lifelong achievement in mathematics education Applications for the 2008 research. Previous recipients of the Freudenthal Award are Celia Hoyles (2003) and Paul Cobb (2005), and previous Corps recipients of the Klein Award are Guy Brousseau (2003) and Ubiratan D’Ambrosio (2005). The United States needs to provide students with a high- An ICMI Awards Committee, chaired by Mogens Niss of quality mathematics education in order to build a robust Roskilde University in Denmark, has been appointed for and diverse pipeline of future mathematicians, engineers, selecting the awardees. The committee is now entering a and other technical professionals. Nowhere is this need third cycle of selecting awardees for 2007. The result of more pressing than in our low-income communities and this process will be known by the end of 2007. The 2007 among students of color. awards, together with the 2005 awards, will be presented By the time they enter eighth grade, students in low- to the recipients at the 11th International Congress on income communities are on average three grade levels Mathematical Education in Monterrey, Mexico, in July behind their peers in high-income communities in math- 2008. ematics and are three times less likely than their high- As was the case for the first two cycles, the ICMI Awards income peers to perform at or above a proficient level in Committee welcomes suggestions coming from the math- mathematics (as defined by the National Assessment of ematics education community. Nominations of candidates Educational Progress). In twelfth grade, African American for the Felix Klein or the Hans Freudenthal Awards have students are nearly five times less likely and Hispanic to be accompanied by summaries presenting the persons students nearly four times less likely than white students nominated and the reasons for the nomination. Moreover, to be at or above proficient level in mathematics. Teach nominations also have to include the names and coordi- For America is seeking mathematics majors to use their nates of two or three persons whom the committee may content knowledge to help us address this academic contact for further information. achievement gap. All proposals must be sent by email to Mogens Niss, Teach For America is the national corps of outstanding [email protected], no later than November 15, 2007. recent college graduates of all academic majors who com- mit two years to teach in urban and rural public schools, —ICMI Awards Committee working to lead students to the kinds of academic gains that change life trajectories. Alumni then use the insights and experience gained from their corps experience to de- Clay Research Fellow velop ways to work subsequently as educators, mathema- ticians, analysts, consultants, and leaders in other fields Nominations to address the underlying problems affecting education in low-income areas. The Clay Mathematics Institute (CMI) is currently accept- Edward F. Burger, chair of the Department of Math- ing nominations for the position of Clay Research Fellow. ematics and Statistics at Williams College, said: “Every Fellows are employed for a period of two to five years mathematics major I’ve known who has participated in and may conduct their research at whatever location or the Teach For America program came away from the ex- combination of locations best suits their research. In ad- perience with a renewed appreciation for mathematics, dition to a generous salary, the fellow receives support education, and the world around them. It is a challenging for travel and research expenses, as well as provisions but exciting opportunity that can change lives.” for collaboration. Notices readers are encouraged to make their under- The primary selection criteria are the exceptional qual- graduate students aware of Teach For America. To hear ity of the candidate’s research and the candidate’s promise about the experiences of our corps members and alumni, to become a mathematical leader. At the time of their to learn how one can join the network of emerging leaders selection, most recent appointees were graduating Ph.D. to make a difference, and to read about our relationships students. However, mathematicians under age thirty have with graduate programs and employers, visit our website, sometimes been appointed. Selection decisions are made http://www.teachforamerica.org. by CMI’s Scientific Advisory Board. To nominate a candidate, please send the following —Teach For America announcement items by October 30, 2007: (1) letter of nomination, (2) names and contact information of two other refer- ences, (3) curriculum vitae, and (4) publication list for the nominee. Nominations should be sent to: Clay Math- Call for Nominations for ICMI ematics Institute, One Bow Street, Cambridge, MA 02138. Awards Electronic submissions are also accepted at nominations@ claymath.org. Address nominations to the attention of The Executive Committee of the International Commis- Christa Carter. sion on Mathematical Instruction (ICMI) some time ago Information about Clay Research Fellows is also avail- created two awards in mathematics education research: able on the CMI website at http://www.claymath. the Hans Freudenthal Award, for a major program of org/fas/research_fellows/. Additional information

1168 Notices of the AMS Volume 54, Number 9 Mathematics Opportunities may be obtained by calling 617-995-2600 or by email: [email protected].

—From a CMI announcement

Call for Nominations for André Aisenstadt Mathematics Prize The Centre de Recherches Mathématiques (CRM) solicits nominations for the André Aisenstadt Mathematics Prize. The prize recognizes outstanding research achievement by a young Canadian mathematician in pure or applied mathematics. Candidates must be Canadian citizens or permanent residents of Canada and must have received the Ph.D. within the preceding seven years. The recipient is invited to deliver a lecture at CRM and to write a brief article on his or her work for publication in the CRM’s Bulletin. Nominations must be submitted by at least two spon- sors and include the following information: a curriculum vitae, a list of publications, a cover letter explaining the basis of the nomination, up to four reprints, and a maximum of four letters of support. The deadline for nominations is October 1, 2007. Nominations must be submitted to the director of the CRM, Université de Mon- tréal, C.P. 6128, Succursale Centre-ville, Montréal, QC H3C 3J7 Canada; fax: 514-343-2254; email: directeur@crm. umontreal.ca.

—From a CRM announcement

AWM Essay Contest To increase awareness of women’s ongoing contributions to the mathematical sciences, the Association for Women in Mathematics (AWM) is holding an essay contest for biographies of contemporary women mathematicians and statisticians in academic, industrial, and government careers. The essays will be based primarily on interviews with women who are currently working in mathematical sci- ences careers. The contest is open to students in the fol- lowing categories: 6th–8th grades, 9th–12th grades, and college undergraduates. At least one winning submission will be chosen from each category. Winners will receive a prize, and their essays will be published online at the AWM website. A grand prize winner will have his or her submission published in the AWM Newsletter as well. The deadline for entries is November 2, 2007. In addition to student entries, organizers are currently seeking women mathematicians to volunteer as the sub- jects of these essays. For more information, see http:// www.awm-math.org/biographies/contest.html.

—From an AWM announcement

October 2007 Notices of the AMS 1169

Inside the AMS

continued the work of the 1999 conference (see below) AMS Department Chairs by bringing together a diverse group of people who are Workshop actively involving undergraduates in research programs of all types in order that they might share their experiences This annual one-day workshop for chairs and leaders and explore ways of creating more such opportunities, of departments of mathematical sciences will be held a with the goal of bringing the most talented students into day before the start of the San Diego Joint Mathematics research-level mathematics. Meetings, on Saturday, January 5, 2008, from 8:00 a.m. to The proceedings volume for the PURM conference, 6:30 p.m. The workshop format is intended to stimulate Proceedings of the Conference on Promoting Undergradu- discussion among attending chairs and workshop leaders. ate Research in Mathematics, was published in June 2007 Sharing ideas and experiences with peers provides a form and is available as a PDF document at http://www.ams. of department chair therapy, creating an environment that org/outreach/PURMproceedings.pdf. enables attending chairs to address departmental matters In 1999 the AMS brought together mathematicians from from new perspectives. across the country who have been involved in summer Past workshop sessions have focused on a range of is- mathematics programs for undergraduates. The purpose sues facing departments today, including personnel issues of the conference was to exchange ideas, discuss issues (staff and faculty), long-range planning, hiring, promotion of common concern, establish contacts, and gather infor- and tenure, budget management, assessments, outreach, mation that would be of use to those in the mathematical stewardship, junior faculty development, communication, community who are interested in establishing summer and departmental leadership. mathematics programs for undergraduates. The work- There is a registration fee for the workshop, which shop was held September 30–October 2, 1999, at Crystal is in addition to and separate from the Joint Meetings City, Arlington, Virginia, with support from the National registration. An invitation to attend the workshop will be Security Agency. sent to department chairs this fall. Information will also The proceedings volume for the 1999 conference was be posted on the AMS website. For further information, published in June 2000 and is available as a PDF document please contact the AMS Washington Office by telephone, Proceedings of the Conference on Summer Undergraduate 202-588-1100, or by email: [email protected]. Mathematics Research Programs at http://www.ams. org/outreach/REUproceedings.pdf. —AMS Washington Office A list of summer REU programs is also maintained on the AMS website at http://www.ams.org/outreach/ reu.html. Undergraduate Research Conference Proceedings —AMS Professional Programs and Services Department Available Deaths of AMS Members In 2006, with funding from the National Security Agency (NSA), the AMS organized the conference “Promoting Un- William T. Alford, associate professor, from Louis- dergraduate Research in Mathematics” (PURM), which took ville, KY, died on May 29, 2003. Born on July 21, 1937, he place on September 28–30, 2006, in Rosemont, IL. PURM was a member of the Society for 41 years.

1170 Notices of the AMS Volume 54, Number 9 Inside the AMS

Bengt G. Carlson, from Santa Fe, NM, died on June 14, 2007. Born on December 26, 1915, he was a member of the Society for 67 years. John G. Harvey, professor emeritus, University of Wis- consin, Madison, died on May 5, 2007. Born on August 10, 1934, he was a member of the Society for 49 years. Tenth Annual John Arnold Kalman, professor, University of Auck- land, New Zealand, died on June 11, 2007. Born on No- vember 19, 1928, he was a member of the Society for 36 years. Masasuke Kawasaki, from Slidell, LA, died on June 8, 2007. Born on March 21, 1925, he was a member of the Society for 14 years. John C. Mairhuber, from Bangor, ME, died on June 13, 2007. Born on December 14, 1922, he was a member of the Society for 55 years. Kyungho Oh, assistant professor, University of February 8 - 10, 2008 Missouri at St. Louis, died on June 11, 2007. Born on May 24, 1959, he was a member of the Society for 25 A national showcase for research years. projects of undergraduate women Roy F. Reeves, professor emeritus, from Granville, OH, died on May 5, 2007. Born on July 8, 1922, he was a in the mathematical sciences. member of the Society for 57 years. Jean B. Richmond, assistant professor emeritus, Southern Methodist University, died on December 27, Main Program 1998. Born on October 13, 1925, she was a member of the Talks by undergraduate women about their Society for 32 years. own research Felice L. L. Ronga, professor, University of Geneva, Switzerland, died on May 22, 2007. Born on November 23, 1942, he was a member of the Society for 34 years. Plenary Speakers John Todd, professor, California Institute of Technol- Katherine Bartley, National Security Agency ogy, died on June 21, 2007. Born on May 16, 1911, he was a member of the Society for 59 years. Rebecca Caldwell, Axciom Corporation Azelle B. Waltcher, from New York, NY, died on Angela Desai, University of Montevallo June 5, 2007. Born on March 27, 1925, she was a member Cornelia Yuen, SUNY Potsdam of the Society for 61 years. Cun Zheng Wang, research professor and engineer, Chengdu Engine Company, People’s Republic of China, All Plenary Speakers are NCUWM Alumnae died on July 10, 2006. Born on August 8, 1938, he was a For undergraduate participants, most local expenses member of the Society for 18 years. are covered and travel support is available. For more information, to register, apply for funding, or sign up to give a talk, visit us on the web at www.math.unl.edu/∼ncuwm or write to us at [email protected] Department of Mathematics University of Nebraska-Lincoln 203 Avery Hall Lincoln, NE 68588-0130 Deadline for registration January 18, 2008

University of Nebraska-Lincoln An equal opportunity educator and employer with a comprehensive plan for diversity

October 2007 Notices of the AMS 1171 Tenth Annual

February 8 - 10, 2008 A national showcase for research projects of undergraduate women in the mathematical sciences.

Main Program Talks by undergraduate women about their own research

Plenary Speakers Katherine Bartley, National Security Agency Rebecca Caldwell, Axciom Corporation Angela Desai, University of Montevallo Cornelia Yuen, SUNY Potsdam

All Plenary Speakers are NCUWM Alumnae

For undergraduate participants, most local expenses are covered and travel support is available. For more information, to register, apply for funding, or sign up to give a talk, visit us on the web at www.math.unl.edu/∼ncuwm or write to us at [email protected] Department of Mathematics University of Nebraska-Lincoln 203 Avery Hall Lincoln, NE 68588-0130 Deadline for registration January 18, 2008

University of Nebraska-Lincoln An equal opportunity educator and employer with a comprehensive plan for diversity

October 2007 Notices of the AMS 1171 Reference and Book List

The Reference section of the Notices Upcoming Deadlines Groups. See http://www.nsf.gov/ is intended to provide the reader September 13, 2007: Applications funding/pgm_summ.jsp?pims_ with frequently sought information in for NSF Research Experiences for id=5671&org=DMS. an easily accessible manner. New Undergraduates (REU) program September 30, 2007: Applica- information is printed as it becomes sites. See http://www.nsf.gov/ tions for Math in Moscow for spring available and is referenced after the publications/pub_summ.jsp?ods_ 2008. See http://www.mccme.ru/ first printing. As soon as information key=nsf07569. mathinmoscow or write to: Math in is updated or otherwise changed, it September 15, 2007: Nominations Moscow, P.O. Box 524, Wynnewood, will be noted in this section. for Sloan Research Fellowships. See PA 19096; fax: +7095-291-65-01; http://www.sloan.org/programs/ email: [email protected]; or contact Contacting the Notices fellowship_brochure.shtml. Math in Moscow Program, Member- The preferred method for contacting September 21, 2007: Full pro- ship and Programs Department, the Notices is electronic mail. The posals for NSF Focused Research American Mathematical Society, 201 editor is the person to whom to send articles and letters for consideration. Where to Find It Articles include feature articles, me- A brief index to information that appears in this and previous issues of the Notices. morial articles, communications, AMS Bylaws—November 2005, p. 1239 opinion pieces, and book reviews. AMS Email Addresses—February 2007, p. 271 The editor is also the person to whom AMS Ethical Guidelines—June/July 2006, p. 701 to send news of unusual interest AMS Officers 2006 and 2007 (Council, Executive Committee, about other people’s mathematics Publications Committees, Board of Trustees)—May 2007, p. 657 research. AMS Officers and Committee Members—October 2007, p. 1178 The managing editor is the person Conference Board of the Mathematical Sciences—September 2007, to whom to send items for “Math- p. 1019 ematics People”, “Mathematics Op- Information for Notices Authors—June/July 2007, p. 765 portunities”, “For Your Information”, Mathematics Research Institutes Contact Information—August 2007, “Reference and Book List”, and “Math- p. 898 ematics Calendar”. Requests for National Science Board—January 2007, p. 57 permissions, as well as all other New Journals for 2005, 2006—June/July 2007, p. 767 inquiries, go to the managing editor. NRC Board on Mathematical Sciences and Their Applications—March The electronic-mail addresses are 2007, p. 426 [email protected] in the case of NRC Mathematical Sciences Education Board—April 2007, p. 546 the editor and [email protected] in NSF Mathematical and Physical Sciences Advisory Committee—February the case of the managing editor. The 2007, p. 274 fax numbers are 405-325-7484 for Program Officers for Federal Funding Agencies—October 2007, the editor and 401-331-3842 for the p. 1173 (DoD, DoE); December 2006, p. 1369 (NSF) managing editor. Postal addresses Stipends for Study and Travel—September 2007, p. 1022 may be found in the masthead.

1172 Notices of the AMS Volume 54, Number 9 Reference and Book List

Charles Street, Providence RI 02904- doctoral Research Fellowships. See 524, Wynnewood, PA 19096; fax: 2294; email: student-serv@ams. http://www.nsf.gov/pubs/2007/ +7095-291-65-01; email: mim@mccme. org. nsf07573/nsf07573.htm. ru; or contact Math in Moscow Pro September 30, 2007: Applications October 17, 2007: Full propos- gram, Membership and Programs for travel grants to ICME-11. See als for NSF Computational Science Department, American Mathematical http://www.nctm.org/icme.aspx Training for Undergraduates in the Society, 201 Charles Street, Providence or contact Margaret Iding, 116 North Mathematical Sciences (CSUMS). RI 02904-2294; email: student-serv@ Kedzie, Division of Science and Math- See http://www.nsf.gov/pub- ams.org. ematics Education, Michigan State lications/pub_summ.jsp?ods_ May 1, 2008: Applications for University, East Lansing, MI 48824; key=nsf06559. AWM Travel Grants. See http:// telephone: 517-355-1708, ext. 105; October 30, 2007: Nominations www.awm-math.org/travelgrants. fax: 517-432-9868; email: idingm@ for Clay Research Fellowships. See html; telephone: 703-934-0163; email: msu.edu. “Mathematics Opportunities” in this [email protected]; or contact Asso- October 1, 2007: Nominations for issue. ciation for Women in Mathematics, André Aisenstadt Mathematics Prize. November 2, 2007: Entries for 11240 Waples Mill Road, Suite 200, See “Mathematics Opportunities” in AWM Essay Contest. See “Mathemat- Fairfax, VA 22030. this issue. ics Opportunities” in this issue. June 10, 2008: Proposals for En- October 1, 2007: Proposals for November 15, 2007: Applica- hancing the Mathematical Sciences Joint DMS/NIGMS Initiative to Sup- tions for NSA Mathematics Sab- Workforce in the Twenty-First Cen- port Research in the Area of Math- batical program. See http://www. tury. See “Mathematics Opportuni- ematical Biology. See “Mathematics nsa.gov/msp/index.cfm or con- ties” in this issue. Opportunities” in this issue. tact the program staff: MSP Director August 18, 2008: Applications October 1, 2007: Applications for Michelle D. Wagner (mdwagn4@nsa. for NSF Research Experiences for AWM Travel Grants. See http:// gov) or MSP Program Administrator Undergraduates (REU) program www.awm-math.org/travelgrants. Rosalie (Jackie) Smith (rjsmit2@nsa. sites. See http://www.nsf.gov/ html; telephone: 703-934-0163; email: gov). To obtain brochures or for ques- publications/pub_summ.jsp?ods_ [email protected]; or contact Asso- tions, please call 301-688-0400 or key=nsf07569. ciation for Women in Mathematics, write to: Mathematical Sciences Pro- October 1, 2008: Applications for 11240 Waples Mill Road, Suite 200, gram, National Security Agency, Suite AWM Travel Grants. See http:// Fairfax, VA 22030. 6557, Fort Meade, MD 20755-6557. www.awm-math.org/travelgrants. October 5, 2007: Full propos- December 1, 2007: Applications html; telephone: 703-934-0163; email: als for NSF IGERT competition. See for AMS Centennial Fellowships. See [email protected]; or contact Asso- http://www.nsf.gov/pubs/2007/ http://www.ams.org/employment/ ciation for Women in Mathematics, nsf07540/nsf07540.htm. centflyer.html or write to the Mem- 11240 Waples Mill Road, Suite 200, October 10, 2007: Proposals for bership and Programs Department, Fairfax, VA 22030. NSF Distinguished International Post- American Mathematical Society, 201 DoD Mathematics Staff doctoral Research Fellowships. See Charles Street, Providence, RI 02904- http://www.nsf.gov/pubs/2001/ 2294; email: [email protected]; Five agencies of the Department of nsf01154/nsf01154.txt. telephone 401-455-4107. Defense fund research in the math- October 15, 2007: Proposals for December 15, 2007: Applications ematical sciences. The names, ad- NSA Mathematical Sciences Program for AMS Epsilon Fund grants. See dresses, and telephone numbers grants. See http://www.nsa.gov/ “Mathematics Opportunities” in this of the pertinent staff members are msp/index.cfm or contact the pro- issue. listed below. gram staff: MSP Director Michelle D. January 5, 2008: Applications for Defense Advanced Research Wagner ([email protected]) or MSP IMA postdoctoral and New Directions Projects Agency Program Administrator Rosalie (Jackie) program. See http://www/ima.umn. Defense Sciences Office Smith ([email protected]). To obtain edu. 3701 North Fairfax Drive brochures or for questions, please call February 1, 2008: Applications for Arlington, VA 22203-1714 301-688-0400 or write to: Mathemati- AWM Travel Grants and AWM Mentor- http://www.darpa.mil/dso cal Sciences Program, National Security ing Grants. See http://www.awm- Agency, Suite 6557, Fort Meade, MD math.org/travelgrants.html; Applied and Computational 20755-6557. telephone: 703-934-0163; email: Mathematics Program October 15, 2007: Preferred dead- [email protected]; or contact As- Carey Schwartz, Program Manager line for January entrance in junior- sociation for Women in Mathematics, 571-218-4536 year program at the Smith College 11240 Waples Mill Road, Suite 200, carey.schwartz@darpa.mil Center for Women in Mathematics. Fairfax, VA 22030. See http://www.math.smith.edu/ April 15, 2008: Applications for Math Fundamental Mathematics center. in Moscow for fall 2008. See http:// Benjamin Mann, Program Manager October 17, 2007: Proposals for www.mccme.ru/mathinmoscow or 571-218-4246 NSF Mathematical Sciences Post- write to: Math in Moscow, P.O. Box [email protected]

October 2007 Notices of the AMS 1173 Reference and Book List

Air Force Office of Scientific John F. Tangney (IF) Program in Computing and Research 703-696-6563 Information Sciences Directorate of Mathematics, [email protected] Information, and Life Sciences Software and Intelligent Systems AFOSR/NM Electromagnetics David W. Hislop, Program Manager 875 North Randolph Street, Arje Nachman 919-549-4255 Suite 325 703-696-8427 [email protected] Arlington, VA 22203-1768 [email protected] Fax: 703-696-8450 Systems and Control http://www.afosr.af.mil Army Research Office Randy Zachery, Program Manager Mathematical and Information 919-549-4368 Dynamics and Control Sciences Directorate [email protected] Scott Wells ATTN: AMSRD-ARL-RO-M 703-696-7796 P.O. Box 12211 Information and Signal Processing [email protected] Research Triangle Park, NC Liyi Dai 27709-2211 919-549-4350 Distributed Intelligence 919-549-4368 [email protected] Amy L. Magnus Fax: 919-549-4248 703-696-8431 http://www.arl.army.mil/ Mobile, Wireless Communications [email protected] www/default.cfm?Action= and Networks 29&Page=216 Robert Ulman, Program Manager Physical Mathematics and Applied 919-549-4330 Analysis Randy Zachery, Acting Director [email protected] Arje Nachman 919-549-4368 703-696-8427 [email protected] Information and Software Assurance [email protected] Cliff Wang, Program Manager Program in Mathematics 919-549-4207 Computational Mathematics [email protected] Fariba Fahroo Computational Mathematics 703-696-8429 Stephen Davis, Program Manager National Security Agency [email protected] 919-549-4284 Mathematical Sciences Program [email protected] Attn: R51A, Suite 6557 Optimization and Discrete Ft. George G. Meade, MD 20755- Mathematics Cooperative Systems 6557 Fariba Fahroo David (Chris) Arney, Division Chief http://www.nsa.gov/msp/ 703-696-8429 919-549-4254 [email protected] [email protected] Michelle Wagner, Director 301-688-0400 Sensing, Surveillance, and Discrete Mathematics and Computer [email protected] Navigation Science Jon Sjogren Joseph M. Coyle, Program Manager Office of Naval Research 703-696-6564 919-549-4256 Mathematics, Computer, and [email protected] joseph.michael.coyle@ Information Research arl.army.mil Office of Naval Research Sensory Systems 875 North Randolph Street, Willard D. Larkin Stochastic Analysis, Applied Suite 1425 703-696-7793 Probability, and Statistics Arlington, VA 22203-1995 [email protected] Mou-Hsiung Chang, Program http://www.onr.navy.mil Manager Software and Systems 919-549-4229 Division Director Robert Herklotz [email protected] 703-696-3191 703-696-6565 [email protected] [email protected] Modeling of Complex Systems John Lavery, Program Manager Intelligent Systems Information Fusion and Artificial 919-549-4253 703-696-5754 Intelligence [email protected] [email protected] Robert Herklotz (AI) 703-696-6565 Computational Analysis [email protected] 703-696-0195 [email protected]

1174 Notices of the AMS Volume 54, Number 9 Reference and Book List

Software and Computer Systems Applied Mathematics Ants, Bikes, and Clocks: Problem 703-696-4304 Anil Deane, Program Manager Solving for Undergraduates, by Wil- [email protected] 301-903-1465 liam Briggs. Society for Industrial and [email protected] Applied Mathematics, 2005. ISBN 0- Command and Control 89871-574-1. 703-696-4961 Energy Sciences Network (ESnet) The Archimedes Codex, by Reviel [email protected] Dan Hitchcock, Program Manager Netz and William Noel. Weidenfeld 301-903-5800 and Nicolson, May 2007. ISBN-13: 978- Operations Research [email protected] 0-29764-547-4. 703-696-4313 The Art of Mathematics: Coffee [email protected] Computational Science Research Time in Memphis, by Béla Bollobás. and Partnerships Cambridge University Press, Sep- Probability and Statistics Walt Polansky, Program Manager tember 2006. ISBN-13: 978-0-52169- 703-696-4320 301-903-5800 395-0. [email protected] [email protected] Arthur Cayley: Mathematician Laureate of the Victorian Age, by Signal and Image Processing National Collaboratories Tony Crilly. Johns Hopkins University 703-588-2439 Mary Anne Scott, Program Manager Press, December 2005. ISBN 0-801- [email protected] U.S. Department of Energy, SC-31 88011-4. 19901 Germantown Road The Artist and the Mathematician: Target Tracking and Sensor Fusion Germantown, MD 20874-1290 The Story of Nicolas Bourbaki, the 703-696-4217 301-903-6368 Genius Mathematician Who Never [email protected] [email protected] Existed, by Amir D. Aczel. Thunder’s Mouth Press, August 2006. ISBN Autonomous Systems Book List 1-560-25931-0. (Reviewed in this 703-696-5754 issue.) [email protected] The Book List highlights books that A Beautiful Math: John Nash, Game have mathematical themes and are Theory, and the Modern Quest for a DoE Mathematics Program aimed at a broad audience potentially Code of Nature, by Tom Siegfried. Office of Advanced Scientific including mathematicians, students, Joseph Henry Press, October 2006. Computing Research and the general public. When a book ISBN 0-309-10192-1. Office of Science has been reviewed in the Notices, a The Best of All Possible Worlds: U.S. Department of Energy reference is given to the review. Gen- Mathematics and Destiny, by Ivar SC-21.1, Germantown Building erally the list will contain only books Ekeland. University of Chicago Press, 1000 Independence Avenue, SW published within the last two years, October 2006. ISBN-13: 978-0-226- Washington, DC 20585-1290 though exceptions may be made in 19994-8. http://www.sc.doe.gov/ascr/ cases where current events (e.g., the Bourbaki, a Secret Society of Math- index.html death of a prominent mathematician, coverage of a certain piece of math- ematicians, by Maurice Mashaal. AMS, Michael Strayer ematics in the news) warrant drawing June 2006. ISBN-13: 978-0-8218- Associate Director readers’ attention to older books. Sug- 3967-6. (Reviewed in this issue.) 301-903-7486 gestions for books to include on the list The Cat in Numberland, by Ivar [email protected]. may be sent to notices-booklist@ Ekeland. Cricket Books, April 2006. gov ams.org. ISBN-13: 978-0-812-62744-2. *Added to “Book List” since the A Certain Ambiguity: A Mathemati- Computer Science Research list’s last appearance. cal Novel, by Gaurav Suri and Har- Frederick C. Johnson, Program tosh Singh Bal. Princeton University Manager An Abundance of Katherines, by Press, June 2007. ISBN-13: 978-0-691- 301-903-3601 John Green. Dutton Juvenile Books, 12709-5. [email protected] September 2006. ISBN 0-525-47688-1. Chases and Escapes: The Math- Alfred Tarski: Life and Logic, by ematics of Pursuit and Evasion, by Collaboratories and Advanced Anita Burdman Feferman and Solo- Paul J. Nahin. Princeton University Networking Research mon Feferman. Cambridge Univer- Press, May 2007. ISBN-13: 978-0- Thomas D. Ndousse-Fetter, Program sity Press, October 2004. ISBN 0- 69112-514-5. Manager 521-80240-7. (Reviewed September Descartes: A Biography, by Desmond 301-903-5800 2007.) Clarke. Cambridge University Press, [email protected] Analysis and Probability: Wavelets, March 2006. ISBN 0-521-82301-3. Signals, Fractals, by Palle E. T. Jor- Einstein’s Heroes: Imagining the gensen. Springer, September 2006. World through the Language of Math- ISBN 0-387-29519-4. ematics, by Robyn Arianrhod. Oxford

October 2007 Notices of the AMS 1175 Reference and Book List

University Press, July 2006. ISBN-13: I Am a Strange Loop, by Douglas R. More Sex Is Safer Sex: The Uncon- 978-0-195-30890-7. Hofstadter. Basic Books, March 2007. ventional Wisdom of Economics, by Ernst Zermelo: An Approach to ISBN-13: 978-0-46503-078-1. (Reviewed Steven E. Landsburg. Free Press, April His Life and Work, by Heinz-Dieter August 2007.) 2007. ISBN-13: 978-1-416-53221-7. Ebbinghaus. Springer, April 2007. John von Neumann: Selected Let- The Motion Paradox: The 2,500- ISBN-13: 978-3-540-49551-2. ters, edited by Miklós Rédei. AMS, Year Old Puzzle behind All the Mys- The Essential Turing, edited by November 2005. ISBN 0-8218-3776-1. teries of Time and Space, by Joseph B. Jack Copeland. Oxford Univer- (Reviewed June/July 2007.) Mazur. Dutton Adult, April 2007. sity Press, September 2004. ISBN Karl Pearson: The Scientific Life ISBN-13: 978-0-52594-992-3. 0-198-25080-0. (Reviewed November in a Statistical Age, by Theodore M. *Music: A Mathematical Offering, 2006.) Porter. Princeton University Press, by David J. Benson. Cambridge Uni- Evolutionary Dynamics: Exploring new edition, December 2005. ISBN-13: versity Press, December 2006. ISBN- the Equations of Life, by Martin Nowak. 978-0-69112-635-7. 13: 978-0-521-61999-8. Belknap Press, September 2006. ISBN Leonhard Euler, by Emil A. Fell- *Music and Probability, by David 0-674-02338-2. mann. Birkhäuser, 2007. ISBN-13: Temperley. MIT Press, January 2007. The Fabulous Fibonacci Numbers, 978-3-7643-7538-6. ISBN-13: 978-0-262-20166-7. by Alfred S. Posamentier and Ingmar Leonhard Euler, a Man to Be *Musimathics: The Mathematical Lehmann. Prometheus Books, February Reckoned With, by Andreas K. Heyne Foundations of Music, by Gareth Loy. 2007. ISBN 1-591-02475-7. and Alice K. Heyne. Birkhäuser, MIT Press, June 2006 and June 2007. Fearless Symmetry: Exposing the 2007. ISBN-13: 978-3-7643-8332-9. Volume 1: ISBN-13: 978-0-262-12282- Hidden Patterns of Numbers, by Avner Letters to a Young Mathematician, 5. Volume 2: ISBN-13: 978-0-262- Ash and Robert Gross. Princeton by Ian Stewart. Perseus Books, April 12285-6. University Press, May 2006. ISBN 2006. ISBN-13: 978-0-465-08231-5. Negative Math: How Mathematics 0-691-12492-2. (Reviewed January (Reviewed May 2007.) Rules Can Be Positively Bent, by Al- 2007.) A Madman Dreams of Turing Ma- berto A. Martinez. Princeton Univer- Fly Me to the Moon: An Insider's chines, by Janna Levin. Knopf, August sity Press, November 2005. ISBN-13: Guide to the New Science of Space 2006. ISBN 1-400-04030-2. 978-0-691-12309-7. Travel, by Edward Belbruno. Prince­ The Man Who Knew Too Much: *New Theories of Everything, by ton University Press, January 2007. Alan Turing and the Invention of the John D. Barrow. Oxford University ISBN-13: 978-0-691-12822-1. Computer, by David Leavitt. Great Press, July 2007. ISBN-13: 978-0-192- From Cosmos to Chaos: The Sci- Discoveries series, W. W. Norton, 80721-2. ence of Unpredictability, by Peter December 2005. ISBN 0-393-05236-2. Nonplussed! Mathematical Proof Coles. Oxford University Press, Au- (Reviewed November 2006.) of Implausible Ideas, by Julian Havil. gust 2006. ISBN 0-198-56762-6. *The Math behind the Music, by Princeton University Press, May 2007. From Zero to Infinity: What Makes Leon Harkleroad. Cambridge Uni- ISBN-13: 978-0-691-12056-0. Numbers Interesting, by Constance versity Press, August 2006. ISBN-13: Reid. Fiftieth anniversary edition, 978-0-521-00935-5. Once upon Einstein, by Thibault A K Peters, February 2006. ISBN Mathematical Illustrations: A Man- D’Amour. A K Peters, March 2006. 1-568-81273-6. (Reviewed February ual of Geometry and PostScript, by Bill ISBN 1-568-81289-2. 2007.) Casselman. Cambridge University Out of the Labyrinth: Setting Math- Gödel’s Theorem: An Incomplete Press, December 2004. ISBN 0-521- ematics Free, by Robert Kaplan and Guide to Its Use and Abuse, by Torkel 54788-1. (Reviewed January 2007.) Ellen Kaplan. Oxford University Press, Franzen. A K Peters, May 2005. ISBN 1- *The Mathematician’s Brain, by January 2007. ISBN-13: 978-0-19514- 568-81238-8. (Reviewed March 2007.) David Ruelle. Princeton University 744-5. Great Feuds in Mathematics: Ten Press, July 2007. ISBN-13: 978-0-691- Piano Hinged Dissections: Time of the Liveliest Disputes Ever, by Hal 12982-2. to Fold!, by Greg Frederickson. A K Hellman. Wiley, September 2006. ISBN Mathematics and Common Sense: Peters, October 2006. ISBN 1-568- 0-471-64877-9. A Case of Creative Tension, by Philip J. 81299-X. The Great π/e Debate: Which Is the Davis. A K Peters, October 2006. ISBN Piero della Francesca: A Mathe- Better Number?, DVD by Colin Adams 1-568-81270-1. matician’s Art, by J. V. Field. Yale and Thomas Garrity. Mathematical Measuring the World, by Daniel University Press, August 2005. ISBN Association of America, 2007. ISBN Kehlmann. Pantheon, November 2006. 0-300-10342-5. (Reviewed March 0-88385-900-9. ISBN 0-375-42446-6. 2007.) How Mathematics Happened, by *The Mind of the Mathematician, The Poincaré Conjecture: In Search Peter S. Rudman. Prometheus Books, by Michael Fitzgerald and Ioan James. of the Shape of the Universe, by Donal October 2006. ISBN 1-591-02477-3. Johns Hopkins University Press, May O’Shea. Walker, March 2007. ISBN-13: How to Cut a Cake: And Other 2007. ISBN-13: 978-0-801-88587-7. 978-08027-1532-6. Mathematical Conundrums, by Ian More Mathematical Astronomy *Poincaré’s Prize: The Hundred- Stewart. Oxford University Press, No- Morsels, by Jean Meeus. Willmann- Year Quest to Solve One of Math’s vember 2006. ISBN 0-199-20590-6. Bell, 2002. ISBN 0-943396-743. Greatest Puzzles, by George Szpiro.

1176 Notices of the AMS Volume 54, Number 9 Reference and Book List

Dutton Adult, June 2007. ISBN-13: The Trouble with Physics: The Rise 978-0-525-95024-0. of String Theory, The Fall of a Sci- About the Cover Prince of Mathematics: Carl Fried- ence, and What Comes Next, by Lee rich Gauss, by M. B. W. Tent. A K Smolin. Joseph Henry Press, October The Mission Basilica San Diego de Peters, January 2006. ISBN 1-568- 2006. ISBN 0-309-10192-1. (Reviewed Alcala, known as Calfornia’s first 81261-2. September 2007.) church, was founded on July 16, Project Origami: Activities for Ex- Useless Arithmetic: Why Environ- 1769, by Father Junipero Serra. ploring Mathematics, by Thomas Hull. mental Scientists Can’t Predict the The watercolor of the mission A K Peters, March 2006. ISBN 1-568- Future, by Orrin Pilkey and Linda was painted for the Notices cover 81258-2. (Reviewed May 2007.) Pilkey-Jarvis. Columbia University by Stephen J. Pomerenke. Pursuit of Genius: Flexner, Einstein, Press, February 2007. ISBN 0-231- San Diego, California, is the and the Early Faculty at the Institute 13212-3. site of the Joint Mathematics for Advanced Study, by Steve Bat- *The Volterra Chronicles: The Life Meetings, January 6–9, 2008. terson. A K Peters, June 2006. ISBN and Times of an Extraordinary Math- 1-568-81259-0. ematician, by Judith R. Goodstein. Pythagoras: His Life, Teaching and AMS, February 2007. ISBN-13: 978-0- Influence, by Christoph Riedweg. 8218-3969-0. Translated by Steven Rendall. Cornell Why Beauty Is Truth: The Story of University Press, March 2005. ISBN- Symmetry, by Ian Stewart. Perseus 13: 978-0-80144-240-7. Books Group, April 2007. ISBN-13: Pythagoras: The Mathemagician, 978-0-46508-236-0. by Karim El-koussa. Cloonfad Press, Yearning for the Impossible: The September 2005. ISBN-13: 978-0- Surprising Truths of Mathematics, by 97694-042-5. John Stillwell. A K Peters, May 2006. Shadows of Reality: The Fourth ISBN 1-568-81254-X. (Reviewed June/ Dimension in Relativity, Cubism, and July 2007.) Modern Thought, by Tony Robbin. You Failed Your Math Test, Com- Yale University Press, March 2006. rade Einstein: Adventures and Misad- ventures of Young Mathematicians, or ISBN 0-300-11039-1. (Reviewed April Test Your Skills in Almost Recreational 2007.) Mathematics, edited by M. Shifman. The Shoelace Book: A Mathematical World Scientific, June 2005. ISBN-13: Guide to the Best (and Worst) Ways to 978-9-812-56279-1. Lace Your Shoes, by Burkard Polster. AMS, June 2006. ISBN 0-8218-3933-0. (Reviewed December 2006.) Solving Mathematical Problems: A Personal Perspective, by Terence Tao. Oxford University Press, September 2006. ISBN-13: 978-0-199-20560-8. The Square Root of 2: A Dialogue Concerning a Number and a Sequence, by David Flannery. Springer, December 2005. ISBN-13: 978-0-38720-220-4. Superior Beings: If They Exist, How Would We Know? Game-Theo- retic Implications of Omnipotence, Omniscience, Immortality, and In- comprehensibility, by Steven Brams. Springer, second edition, November 2007. ISBN-13: 978-0-387-48065-7. Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics, by Mark Ronan. Ox- ford University Press, May 2006. ISBN 0-192-80722-6. (Reviewed February 2007.) The Triumph of Numbers: How Counting Shaped Modern Life, by I. B. Cohen. W. W. Norton, July 2006. ISBN-13: 978-0-393-32870-7.

October 2007 Notices of the AMS 1177 About the Cover

The Mission Basilica San Diego de Alcala, known as Calfornia’s first church, was founded on July 16, 1769, by Father Junipero Serra. The watercolor of the mission was painted for the Notices cover by Stephen J. Pomerenke. San Diego, California, is the site of the Joint Mathematics Meetings, January 6–9, 2008. Officers and Committee Members

Numbers to the left of headings are used as points of reference 1.1. Liaison Committee in an index to AMS committees which follows this listing. Primary and secondary headings are: All members of this committee serve ex officio. Robert J. Daverman 1. Officers John M. Franks 1.1. Liaison Committee Chair James G. Glimm 2. Council Linda Keen 2.1. Executive Committee of the Council 3. Board of Trustees 4. Committees 4.1. Committees of the Council 4.2. Editorial Committees 2. Council 4.3. Committees of the Board of Trustees 4.4. Committees of the Executive Committee and Board of 2.0.1. Officers of the AMS Trustees President James G. Glimm 2008 4.5. Internal Organization of the AMS Immediate Past President 4.6. Program and Meetings James G. Arthur 2007 Vice Presidents Ha¨ım Brezis 2007 4.7. Status of the Profession Robert L. Bryant 2009 4.8. Prizes and Awards Ruth M. Charney 2008 4.9. Institutes and Symposia Secretary Robert J. Daverman 2008 4.10. Joint Committees Associate Secretaries* Susan J. Friedlander 2007 5. Representatives Michel L. Lapidus 2007 6. Index Matthew Miller 2008 Terms of members expire on January 31 following the year given Lesley M. Sibner 2008 unless otherwise specified. Treasurer John M. Franks 2008 Associate Treasurer Donald E. McClure 2008

2.0.2. Representatives of Committees 1. Officers Bulletin Susan J. Friedlander 2008 Colloquium Paul J. Sally, Jr. 2007 President James G. Glimm 2008 Executive Committee Sylvan E. Cappell 2009 Immediate Past President Journal of the AMS Robert K. Lazarsfeld 2009 James G. Arthur 2007 Mathematical Reviews Jonathan I. Hall 2008 Vice Presidents Ha¨ım Brezis 2007 Mathematical Surveys Robert L. Bryant 2009 and Monographs J. Tobias Stafford 2007 Ruth M. Charney 2008 Mathematics of Secretary Robert J. Daverman 2008 Computation Chi-Wang Shu 2007 Proceedings Ronald Fintushel 2009 Associate Secretaries Susan J. Friedlander 2007 Transactions and Michel L. Lapidus 2007 Memoirs Robert Guralnick 2008 Matthew Miller 2008 Lesley M. Sibner 2008 * Only one Associate Secretary at a time is a voting member of the Treasurer John M. Franks 2008 Council, namely the cognizant Associate Secretary for the scientific Associate Treasurer Donald E. McClure 2008 sessions.

1178 NOTICES OF THE AMS VOLUME 54, NUMBER 9 Officers and Committee Members

2.0.3. Members at Large Special Committees

Sara C. Billey 2007 Frank S. Quinn 2009 4.1.3. First-Year College Mathematics Experience, Robert L. Devaney 2009 Katherine St. John 2009 Task Force on William M. Goldman 2008 Marjorie Senechal 2009 David M. Bressoud 2008 Carolyn S. Gordon 2007 Michael F. Singer 2007 Ruth M. Charney 2008 Craig L. Huneke 2008 Francis Edward Su 2009 David H. Collingwood 2008 Sheldon H. Katz 2007 Judy L. Walker 2008 James G. Glimm 2008 Judy Anita Kennedy 2008 Catherine H. Yan 2007 Raymond L. Johnson 2008 Ken Ono 2008 Dan Kannan 2008 Judy Anita Kennedy 2008 William James Lewis 2008 William G. McCallum 2008 2.1. Executive Committee of the Council Robert E. Megginson 2008 James G. Arthur ex officio Robert F. Olin 2008 Sylvain Cappell 2009 Donald G. Saari 2008 Ruth M. Charney 2010 Alan C. Tucker 2008 Robert J. Daverman ex officio 4.1.4. Working Group on Preparation for Technical James G. Glimm ex officio Careers Advisory Board Robert Guralnick 2008 Paul J. Sally, Jr. 2007 Solomon Friedberg 2008 Peter E. Haskell 2008 Andy R. Magid 2008 Paul J. Sally, Jr 2008 3. Board of Trustees W. Stephen Wilson 2008 John B. Conway 2010 4.2. Editorial Committees John M. Franks ex officio Eric M. Friedlander 2009 James G. Glimm ex officio 4.2.1. Abstracts Editorial Committee Chair Linda Keen 2008 All members of this committee serve ex officio. Secretary Donald E. McClure ex officio Chair Robert J. Daverman Jean E. Taylor 2007 Susan J. Friedlander Carol S. Wood 2011 Michel L. Lapidus Matthew Miller Lesley M. Sibner 4. Committees 4.2.2. Bulletin (New Series) Consultant Gerald L. Alexanderson 2007 Book Reviews Editor Robert L. Devaney 2008 4.1. Committees of the Council Chief Editor Susan J. Friedlander 2008 Standing Committees Consultant Jane Kister 2007 Associate Editors for Bulletin Articles 4.1.1. Editorial Boards Eric Bedford 2009 David J. Benson 2007 Bryna R. Kra 2008 Robert L. Bryant 2008 Persi W. Diaconis 2008 Barry Mazur 2008 Margaret Cheney 2007 Lawrence Craig Evans 2008 Robert A. Oliver 2008 Robert J. Daverman ex officio Edward Frenkel 2008 Paul H. Rabinowitz 2007 John H. Ewing ex officio Mark Goresky 2007 Yuri Tschinkel 2008 Stephen Lichtenbaum 2008 Andrew J. Granville 2008 Michael Wolf 2007 Irena Swanson 2009 Associate Editors for Book Reviews Chair Abigail A. Thompson 2007 4.1.2. Nominating Committee Jonathan L. Alperin 2008 Ken Ono 2008 Steven Krantz 2008 Philip E. Protter 2008 Terms begin on January 1 and expire on December 31 of the Peter Kuchment 2007 Lisa Traynor 2008 year listed.

Chair Michael G. Crandall 2008 4.2.3. Collected Works Phillip Griffith 2007 Chair Phillip A. Griffiths 2007 Thomas C. Hales 2009 Dusa McDuff 2008 Roger Howe 2009 Elias M. Stein 2008 David Jerison 2007 Linda Keen 2007 4.2.4. Colloquium M. Susan Montgomery 2008 Yuri Manin 2009 Hema Srinivasan 2009 Chair Paul J. Sally, Jr. 2007 Lisa M. Traynor 2008 Peter Sarnak 2008

OCTOBER 2007 NOTICES OF THE AMS 1179 Officers and Committee Members

4.2.5. Contemporary Mathematics 4.2.10. Mathematical Surveys and Monographs George Andrews 2007 Jerry L. Bona 2009 Andreas R. Blass 2007 Ralph L. Cohen 2009 Chair Dennis DeTurck 2007 Michael G. Eastwood 2009 Abel Klein 2007 Michael P. Loss 2007 Chair J. Tobias Stafford 2007 4.2.6. Electronic Research Announcements 4.2.11. Mathematics of Computation Dimitri Burago 2007 Co-Managing Editor Keith H. Burns 2009 Susanne C. Brenner 2008 Luis A. Caffarelli 2007 Ronald F. Cools 2007 Harald Niederreiter 2007 Tobias Colding 2007 Chair Chi-Wang Shu 2007 J. Brian Conrey 2009 Marc E. Culler 2008 Associate Editors Sergey Fomin 2009 Mark Freidlin 2008 David W. Boyd 2009 Stanley Osher 2007 Timothy Gowers 2009 Zhiming Chen 2009 Joseph E. Pasciak 2007 Robert Louis Greiss 2008 Bernardo Cockburn 2007 Lothar Reichel 2007 Arjeh M. Cohen 2008 Renate Scheidler 2009 Boris Hasselblatt 2009 Ricardo G. Duran 2009 Jie Shen 2007 Co-Managing Editor Svetlana R. Katok 2007 Ivan P. Gavrilyuk 2007 Igor Shparlinski 2007 Carlos Kenig 2007 Viviette Girault 2008 Chris J. Smyth 2009 J´anos Koll´ar 2007 Ernst Hairer 2007 Michael Stillman 2008 Alex Lubotsky 2008 Daniel W. Lozier 2007 Daniel B. Szyld 2009 Barry Mazur 2007 John McKay 2009 Denis Talay 2009 Walter David Neumann 2007 Jean-Francois Mestre 2007 Tao Tang 2008 Leonid Polterovich 2007 Marian Neamtu 2007 Paul Tseng 2008 Klaus Schmidt 2007 Ricardo Horacio Nochetto Jinchao Xu 2009 Paul Seidel 2008 2007 Mikhail Vishik 2008 Guido L. Weiss 2007 4.2.12. Notices Editorial Board Sylvia Wiegand 2007 Terms begin on January 1 and expire on December 31 of the W. Hugh Woodin 2008 year listed. Efim I. Zelmanov 2007 Editor Andy R. Magid 2009 4.2.7. Graduate Studies in Mathematics Associate Editors Chair David A. Cox 2008 Daniel Kalman Biss 2009 Robion C. Kirby 2009 Walter Craig 2007 Susanne C. Brenner 2009 Steven G. Krantz 2009 Nikolai Ivanov 2007 William Casselman 2009 Peter C. Sarnak 2009 Steven G. Krantz 2009 Robert J. Daverman Mark E. Saul 2009 4.2.8. Journal of the AMS ex officio John R. Swallow 2009 Lisette de Pillis 2009 Lisa M. Traynor 2009 Weinan E 2009 Susan J. Friedlander 2009 Chair Robert K. Lazarsfeld 2009 John W. Morgan 2009 4.2.13. Proceedings Andrei Okounkov 2009 Mario Bonk 2011 Karl Rubin 2011 Richard Bradley 2010 Terence Tao 2007 Carmen C. Chicone 2007 Ted C. Chinburg 2009 Associate Editors Coordinating Peter A. Clarkson 2010 Noga Alon 2011 Andrew M. Odlyzko 2009 Walter Craig 2008 Francis Bonahon 2008 Bjorn Poonen 2009 Alexander N. Dranishnikov 2007 Robert L. Bryant 2007 Sorin T. Popa 2011 Chair Ronald A. Fintushel 2009 Pavel I. Etingof 2007 Victor S. Reiner 2009 Paul Goerss 2008 Mark Goresky 2007 Oded Schramm 2008 Matthew J. Gursky 2010 Alexander Kechris 2008 Richard L. Taylor 2008 James Haglund 2009 Robert Edward Kottwitz S. R. S. Varadhan 2007 Jonathan I. Hall 2010 2008 Avi Wigderson 2008 Jane Hawkins 2009 Peter Kronheimer 2008 Lia-Sang Young 2007 Birge Huisgen-Zimmerman 2009 Haynes R. Miller 2008 Shou-Wu Zhang 2007 Marius Junge 2010 Julia Knight 2008 4.2.9. Mathematical Reviews Michael T. Lacey 2008 AMS staff contact: Kevin F. Clancey Gail R. Letzter 2010 Wen-Ching Winnie Li 2009 Lisa Fauci 2008 Coordinating Martin Lorenz 2009 Chair Jonathan I. Hall 2008 Ken Ono 2008 Peter Maass 2008 Daniel Ruberman 2009 Tadao Oda 2009 Coordinating Andreas Seeger 2008 Ronald J. Stern 2007 Mei-Chi Shaw 2008 Trevor D. Wooley 2008 Mikhail Shubin 2008

1180 NOTICES OF THE AMS VOLUME 54, NUMBER 9 Officers and Committee Members

Hart F. Smith 2010 4.2.20. Representation Theory Coordinating Chuu-Lian Terng 2009 Jens Carsten Jantzen 2008 Nicole Tomczak-Jaegermann 2007 George Lusztig 2007 Tatiana Toro 2010 Chair Dragan Milicic 2007 Bernd Ulrich 2009 Hiraku Nakajima 2007 Edward C. Waymire 2007 Henrik Schlichtkrull 2009 Michael Weinstein 2008 Freydoon Shahidi 2008 Richard Wentworth 2009 David A. Vogan 2009 Coordinating Jon Wolfson 2009 4.2.21. Student Mathematics Library 4.2.14. Proceedings of Symposia in Applied Gerald B. Folland 2008 Chair Robin Forman 2007 Mathematics Brad G. Osgood 2007 Mary C. Pugh 2009 Michael Starbird 2008 Leonid Ryzhik 2007 Chair Eitan Tadmor 2007 4.2.22. University Lecture Series Jerry L. Bona 2009 4.2.15. Transactions and Memoirs Chair Eric M. Friedlander 2008 Dan Abramovich 2010 Adriano M. Garsia 2007 Alejandro Adem 2008 Nigel Higson 2009 J. Tobias Stafford 2007 Mladen Bestvina 2007 Krzysztof Burdzy 2007 Chair Robert Guralnick 2008 4.3. Committees of the Board of Trustees Lisa Claire Jeffrey 2008 Alexander Kleshchev 2008 4.3.1. Agenda and Budget Steffan Lempp 2007 All members of this committee serve ex officio. William P. Minicozzi II 2010 AMS staff contact: Ellen H. Heiser V. Kumar Murty 2010 Robert J. Daverman Alexander Nagel 2010 John M. Franks Peter Polacik 2010 Chair James G. Glimm Gustavo Alberto Ponce 2009 Linda Keen Dimitri Shlyakhtenko 2010 Donald E. McClure Robert J. Stanton 2009 4.3.2. Audit John R. Stembridge 2009 All members of this committee serve ex officio. Daniel I. Tartaru 2010 AMS staff contact: Connie Pass. Mina Teicher 2008 Chair John M. Franks Amie Wilkinson 2009 Eric M. Friedlander 4.2.16. Translation from Chinese Linda Keen Donald E. McClure Sun-Yung Alice Chang S.-Y. Cheng 4.3.3. Bulletin Editor Search Chair Tsit-Yuen Lam Robert J. Daverman 2008 Tai-Ping Liu Chair John H. Ewing 2008 James G. Glimm 2008 Chung-Chun Yang Sheldon H. Katz 2008 4.2.17. Translation from Japanese Judy Anita Kennedy 2008 Chair Shoshichi Kobayashi 1999 4.3.4. Eastern Section Associate Secretary, Search Masamichi Takesaki 1999 Committee for Robert J. Daverman 2008 Eric M. Friedlander 2008 Standing Committees Robert M. Guralnick 2008 4.2.18. Conformal Geometry and Dynamics Carol S. Wood 2008 Mario Bonk 2009 4.3.5. Investment Sun-Yung Alice Chang 2010 AMS staff contact: Connie Pass. Chair Gaven J. Martin 2007 Chair John M. Franks ex officio Yair N. Minsky 2008 Linda Keen ex officio Mary Rees 2007 Henry B. Laufer 2009 Caroline Series 2008 Donald E. McClure ex officio 4.3.6. Salary 4.2.19. History of Mathematics All members of this committee serve ex officio. Joseph W. Dauben 2007 AMS staff contact: Gary G. Brownell.

Peter L. Duren 2007 Chair John M. Franks Chair Karen H. Parshall 2007 Linda Keen Michael I. Rosen 2008 Donald E. McClure

OCTOBER 2007 NOTICES OF THE AMS 1181 Officers and Committee Members

4.4. Committees of the Executive 4.5.5. Publications Committee and Board of Trustees AMS staff contact: Carolyn Beattie. Robert L. Bryant 2007 4.4.1. Long Range Planning David A. Cox 2009 Robert J. Daverman ex officio All members of this committee serve ex officio. Robert L. Devaney 2009 AMS staff contact: Ellen H. Heiser. Chair Beverly E. J. Diamond 2007 John H. Ewing ex officio Sylvan Cappell Eric Friedlander 2007 Robert J. Daverman James G. Glimm ex officio John H. Ewing Jacques Hurtubise 2008 John M. Franks John Luecke 2008 Chair James G. Glimm Ken Ono 2008 Elias M. Stein 2008 Robert Guralnick Linda Keen 4.6. Program and Meetings 4.4.2. Nominating Standing Committees All members of this committee serve ex officio. 4.6.1. Meetings and Conferences Michael G. Crandall AMS staff contact: Diane Saxe Chair Eric M. Friedlander Robert Guralnick Robert J. Daverman ex officio John H. Ewing ex officio James G. Glimm ex officio Chair Joel Hass 2007 4.5. Internal Organization of the Judy Anita Kennedy 2008 American Mathematical Society Jonathan P. McCammond 2007 John C. Meakin 2008 David B. Meredith 2009 Standing Committees Gail D. L. Ratcliff 2007 Catherine A. Roberts 2008 4.5.1. Archives Katherine St. John 2009 Judith Grabiner 2007 Carol S. Wood 2007 Catherine H. Yan 2007 Chair Karen H. Parshall 2009 Anthony V. Phillips 2008 4.6.2. Program Committee for National Meetings Robert Calderbank 2009 4.5.2. Books and Journal Donations Steering Gui-Qiang Chen 2009 Committee Gregory Cherlin 2008 Robert J. Daverman ex officio Augustin Banyaga 2009 Chair Lisa C. Jeffrey 2008 Chair Ricardo Cortez 2007 Robion C. Kirby 2009 Dialla Konate 2008 Michel L. Lapidus ex officio Alice Silverberg 2007 4.5.3. Committee on Committees 4.6.3. Short Course Subcommittee Andrea Bertozzi 2008 Joe P. Buhler 2008 Robert J. Daverman ex officio Peter E. Castro 2009 Robert W. Ghrist 2008 Natalia Komarova 2007 James G. Glimm ex officio Yuval Peres 2009 Carolyn S. Gordon 2008 Chair Francis Edward Su 2007 Lisa G. Townsley 2009 Ruth Haas 2008 Joseph C. Watkins 2008 Palle E. T. Jorgesen 2008 Louis H. Kauffman 2008 4.6.4. Central Section Program Committee Tai-Ping Liu 2008 Min Chen 2007 Jonathan Christopher Mattingly 2008 F. Michael Christ 2008 James Wesley Cogdell 2008 Chair Mark Rieffel 2008 Susan J. Friedlander ex officio Stephen Smale 2008 Chair Gopal Prasad 2007 Tara Smith 2008 Yuri Tschinkel 2008 4.6.5. Eastern Section Program Committee Colin C. Adams 2007 4.5.4. Library Committee Robert H. Gilman 2008 Andrew Granville 2008 Co-chair Jonathan M. Borwein 2008 Lesley M. Sibner ex officio Michael Bowman 2009 Chair Yum-Tong Siu 2007 Michael J. Falk 2009 4.6.6. Southeastern Section Program Committee Kristine K. Fowler 2008 Nicholas J. Kuhn 2008 Co-chair Ann Jensen 2007 Loredana Lanzani 2007 Robion C. Kirby 2007 Matthew Miller ex officio Silvio Levy 2009 Chair Kailash C. Misra 2007 George B. Seligman 2007 John G. Ratcliffe 2008

1182 NOTICES OF THE AMS VOLUME 54, NUMBER 9 Officers and Committee Members

4.6.7. Western Section Program Committee 4.7.5. Profession Bruce K. Driver 2008 AMS staff contact: Ellen J. Maycock. Michel L. Lapidus ex officio James H. Curry 2008 Jonathan Rogawski 2007 Robert J. Daverman ex officio Brad Shelton 2008 James A. Donaldson 2009 Chair Hal L. Smith 2007 John H. Ewing ex officio 4.6.8. Agenda for Business Meetings James G. Glimm ex officio Carolyn Gordon 2007 Chair Robert J. Daverman ex officio Chair Jim E. Hoste 2007 4.6.9. Arnold Ross Lecture Series Committee Craig L. Huneke 2008 Chawne M. Kimber 2008 Brian Conrad 2008 Ronald L. Lipsman 2008 Chair Frank Morgan 2009 Lior Pachter 2007 Dan Rockmore 2009 Kimberly R. Pearson 2007 Ravi D. Vakil 2007 Javier Rojo 2007 4.6.10. Colloquium Lecture Francis Edward Su 2009 Jean E. Taylor 2007 Persi W. Diaconis 2008 Chair Bernd Strumfels 2007 4.7.6. Professional Ethics Lai-Sang Young 2009 Sheldon Axler 2009 4.6.11. Gibbs Lecturer for 2007 and 2008, Patricia E. Bauman 2007 Michael Beals 2009 Committee to Select Lance L. Littlejohn 2009 Lawrence Craig Evans 2007 Chair Catherine A. Roberts 2008 Peter Goddard 2007 Bernard Shiffman 2007 Chair Ronald L. Graham 2007 4.7.7. Science Policy 4.7. Status of the Profession AMS staff contact: Samuel M. Rankin III. James G. Arthur ex officio Standing Committees John B. Conway 2007 Isabel Darcy 2007 4.7.1. Academic Freedom, Tenure, and Robert J. Daverman ex officio Employment Security John H. Ewing ex officio Zeljko Cuckovic 2007 James G. Glimm ex officio Chair William Hawkins 2007 Leon M. Hall 2007 Stephen B. Robinson 2009 Chair Sheldon H. Katz 2007 Ratnasingham Shivaji 2008 Robert P. Lipton 2008 Lorenzo Traldi 2009 William McCallum 2007 Sylvia M. Wiegand 2007 Fred S. Roberts 2007 Robert L. Wilson 2008 Marjorie Senechal 2009 Freydoon Shahidi 2009 4.7.2. Education Michael Singer 2007 AMS staff contact: Samuel M. Rankin III. Ronald J. Stern 2009 Judy L. Walker 2008 Robert J. Daverman ex officio Nolan Wallach 2008 John H. Ewing ex officio James G. Glimm ex officio 4.7.8. Young Scholars Awards William Mark Goldman 2008 Terms expire on June 30. Lawrence Firman Gray 2009 David L. Ferguson 2009 Sheldon H. Katz 2007 Chair Jon T. Jacobsen 2008 Linda Keen 2007 Sergei Tabachnikov 2010 William James Lewis 2009 Jeremy T. Teitelbaum 2010 Chair William McCallum 2007 James E. McClure 2009 Frank S. Quinn 2008 4.8. Prizes and Awards Wilfried Schmid 2008 Standing Committees Brad Shelton 2007 2009 4.8.1. AMS Public Policy Award Selection 2009 Committee 4.7.3. Fan Fund James G. Arthur 2007 James G. Glimm 2008 Weinan E 2009 Sheldon H. Katz 2007 Lizhen Ji 2008 Chair Shou-Wu Zhang 2007 4.8.2. Award for Distinguished Public Service, Committee to Select the Winner of the 4.7.4. Human Rights of Mathematicians William James Lewis 2007 M. Salah Baouendi 2007 Carolyn R. Mahoney 2009 Alexander Beilinson 2008 Chair Paul J. Sally, Jr. 2009 Alfonso Castro 2008 Richard A. Tapia 2011 Eduardo Cattani 2009 Margaret Wright 2007 Chair William G. Faris 2007 Mary W. Gray 2007 4.8.3. The Stefan Bergman Trust Fund Joel L. Lebowitz 2009 Ronald Coifman 2009 Wen-Ching Winnie Li 2009 Charles Fefferman 2007 Norbert H. Schlomiuk 2008 Richard B. Melrose 2008

OCTOBER 2007 NOTICES OF THE AMS 1183 Officers and Committee Members

4.8.4. Bocherˆ Prize, Committee to Select 4.8.15. Steele Prizes the Winner of Rodrigo Banuelos 2007 Peter S. Constantin 2007 Enrico Bombieri 2009 Chair Tai-Ping Liu 2007 Russell Caflisch 2009 Elias Stein 2007 L. Craig Evans 2008 Lisa Claire Jeffrey 2009 4.8.5. Centennial Fellowships Nicholas Katz 2008 Terms expire on June 30. Julius L. Shaneson 2008 Richard P. Stanley 2009 Richard T. Durrett 2009 Chair David A. Vogan, Jr. 2007 Wee Teck Gan 2008 John E. Meier 2008 Special Committees Chair Theodore A. Slaman 2008 Michael Thaddeus 2008 4.8.16. Cole Prize, Committee to Select the Winner Susan Tolman 2009 of the Kevin Zumbrun 2009 Nicholas M. Katz 2007 4.8.6. Conant Prize, Committee to Select the Chair Kenneth A. Ribet 2007 Alice Silverberg 2007 Winner of the Noam Elkies 2007 4.8.17. Exemplary Program or Achievement by a Stephen J. Greenfield 2009 Mathematics Department, Committee to Chair Carl R. Riehm 2008 Select the Winner of the Prize for 4.8.7. Joseph L. Doob Prize Steven A. Bleiler 2009 Joel V. Brawley, Jr. 2007 Andrew J. Granville 2012 Chair Karl W. Knight 2008 Robin C. Hartshorne 2012 Donal B. O’Shea 2007 Steven G. Krantz 2007 Roger Wiegand 2009 Chair Dale P. O. Rolfsen 2007 Bhama Srinivasan 2007 4.8.18. Veblen Prize 4.8.8. Leonard Eisenbud Prize for Mathematics Cameron Gordon 2007 and Physics Michael J. Hopkins 2007 Ronald J. Stern 2007 Joel L. Lebowitz 2007 Chair David R. Morrison 2007 Edward Witten 2007 4.9. Institutes and Symposia 4.8.9. Math in Moscow Progam—Travel Support Standing Committees Terms expire on June 30. 4.9.1. Liaison Committee with AAAS Askold Khovanskii 2009 Edward F. Aboufadel ex officio 2010 Douglas Arnold 2008 2010 Jere Confrey ex officio 4.8.10. Menger Prize, Committee to Select the Jack D. Cowan ex officio Thomas C. Hales 2007 Winner of the William H. Jaco ex officio Terms expire on May 31. Chair Carl Pomerance ex officio Donald G. Saari ex officio Edward A. Connors 2007 Ruth J. Williams 2007 Doron Levy 2010 Chair David B. Scott 2009 4.9.2. Von Neumann Symposium Selection 4.8.11. E. H. Moore Research Article Prize, Committee Committee to Select the Winner of the Andrea L. Bertozzi 2007 Robert L. Bryant 2007 Carolyn S. Gordon 2009 Chair Robert Calderbank 2007 Efim I. Zelmanov 2009 2009 2009 4.10. Joint Committees 2009 4.8.12. National Awards and Public Representation 4.10.1. AMS-ASA-AWM-IMS-MAA-NCTM-SIAM Committee on Women in the James G. Arthur ex officio Robert J. Daverman ex officio Mathematical Sciences Avner Friedman 2007 Kathryn E. Brenan (SIAM) 2009 Chair James G. Glimm ex officio Alicia Carriquiry (IMS) 2007 Dusa McDuff 2008 Sandra Clarkson (ASA) 2007 Christine Escher (AMS) 2009 4.8.13. David P. Robbins Prize Judy Green (AWM) 2009 Jonathan Borwein 2008 Priscilla Greenwood (Cindy) (IMS) 2009 Jeffrey C. Lagarias 2008 Jennifer Hontz (MAA) 2008 David I. Lieberman 2008 Chair Janine E. Janosky (ASA) 2009 Richard P. Stanley 2008 Nicole Lazar (ASA) 2008 Robin Thomas 2008 Lisa Mantini (MAA) 2007 Maura Mast (AWM) 2007 4.8.14. Satter Prize, Committee to Select Judith Olson (NCTM) 2007 the Winner of the C. Lanette Poteete-Young (MAA) 2008 Benedict H. Gross 2009 Mary C. Pugh (AMS) 2007 Karen E. Smith 2007 Mary Silber (SIAM) 2008 Chuu-Lian Terng 2007 Margaret F. Symington (AMS) 2007

1184 NOTICES OF THE AMS VOLUME 54, NUMBER 9 Officers and Committee Members

4.10.2. AMS-ASA-IMS-MAA-SIAM Data Committee 4.10.6. AMS-MAA Committee on Mathematicians AMS staff contact: James W. Maxwell. with Disabilities Yousef Alavi (MAA) 2009 Richard J. Cleary (MAA) 2008 Curtis Bennett (MAA) 2008 Amy Cohen-Corwin (MAA) 2007 Theresa C. Michnowicz (MAA) 2009 James Crowley (SIAM) 2007 Judith R. Miller (AMS) 2008 Richard M. Dudley (AMS) 2009 Eileen L. Poiani (AMS) 2007 John W. Hagood (AMS) 2009 Chair Jack R. Porter (AMS) 2007 Abbe H. Herzig (AMS) 2008 Donald R. King (AMS) 2007 4.10.7. AMS-MAA Committee on Teaching Assistants David J. Lutzer (MAA) 2008 and Part-time Instructors (TA/PTI) James W. Maxwell (AMS) ex officio Chair Polly Phipps (ASA) 2009 Kevin Charlwood (MAA) 2006 David E. Rohrlich (AMS) 2007 Chair Larry Chrystal (AMS) 2007 Henry Schenck (AMS) 2007 John D. Eggers (AMS) 2009 Jianguo Sun (IMS) 2009 Diane L. Herrmann (AMS) 2009 Lisa A. Mantini (MAA) 2006 4.10.3. AMS-ASA-MAA-SIAM Joint Policy Board for Janet M. McShane (AMS) 2008 Mathematics Dennis Pence (MAA) 2007 ASA and SIAM members’ terms expire December 31 of the (MAA) 2007 year listed. 4.10.8. AMS-MAA Joint Archives Committee Mary E. Bock (ASA) 2007 William W. Dunham (MAA) 2008 James Crowley (SIAM) 2007 Judith Grabiner (AMS) 2007 Robert J. Daverman (AMS) 2008 Mary W. Gray (MAA) 2009 John H. Ewing (AMS) 2009 Chair Karen H. Parshall (AMS) 2009 Joseph A. Gallian (MAA) 2008 Anthony V. Phillips (AMS) 2008 James G. Glimm (AMS) 2008 James J. Tattersall (MAA) 2009 Martin Golubitsky (SIAM) 2007 Sallie Keller-McNulty (ASA) 2007 4.10.9. AMS-MAA Joint Meetings Committee Clive Moler (SIAM) 2008 All members of this committee serve ex officio. Martha Siegel (MAA) 2008 William B. Smith (ASA) 2007 Robert J. Daverman Tina H. Straley (MAA) 2008 John H. Ewing Consultant Diane Saxe 4.10.4. AMS-ASL-IMS-SIAM Committee on Tina H. Straley Translations from Russian and Other Slavic Chair James J. Tattersall Languages 4.10.10. AMS-MAA Exhibits Advisory Subcommittee Chair James D. Stasheff (AMS) Cheryl Adams AMS Subcommittee Members Roger Astley James Chin Consultant V. I. Arnol
d Robert J. Daverman Luchezar Avramov John Grafton Igor Dolgachev Elizabeth Huber Consultant S. G. Gindikin Patricia Kearney Consultant Askol
dGeorgieviˇc Khovanski˘ı Bob Mathews Robert D. MacPherson Elaine Pedreira-Sullivan Grigorii A. Margulis Penny Pina Consultant N. K. Nikol
ski˘ı Bob Pirtle Chair James D. Stasheff Diane M. Saxe ASL Subcommittee Members Sandi Lynn Scherer Amy Sell Marat Arslanov Jackie Smith Sergei N. Artemov Chair James J. Tattersall Oleg Belegradek AMS-MAA Joint Program Committee for the San Elisabeth Bouscaren 4.10.11. Wilfried Buchholz Diego Meeting January 6–9, 2008 Chair Steffen Lempp Gui-Qiang Chen (AMS) Mariko Yasugi Chair Annalisa Crannell (MAA) Ellen E. Krikman (MAA) IMS Subcommittee Members Alice Silverberg (AMS) Chair M. I. Freidlin 4.10.12. AMS-MAA-SIAM Joint Committee on B. Pittel Employment Opportunities A. Rukhin W. J. Studden AMS staff contact: Ellen Maycock. 4.10.5. AMS-MAA Committee on Cooperation Edward F. Aboufadel (AMS) 2009 Annalisa Crannell (MAA) 2007 All members of this committee serve ex officio. David A. Field (SIAM) 2007 James G. Arthur (AMS) Ellen Maycock (AMS) ex officio Carl C. Cowen (MAA) Michael Pearson (MAA) ex officio Robert J. Daverman (AMS) Margaret Robinson (MAA) 2009 John H. Ewing (AMS) Lee Seitelman (SIAM) 2007 Joseph A. Gallian (MAA) Randall J. Swift (MAA) 2007 James G. Glimm (AMS) Linda Thiel (SIAM) ex officio Martha J. Siegel (MAA) Chair Emil J. Volcheck (AMS) 2007 Tina H. Straley (MAA) Sarah J. Witherspoon (AMS) 2008

OCTOBER 2007 NOTICES OF THE AMS 1185 Officers and Committee Members

4.10.13. AMS-MAA-SIAM Frank and Brennie Morgan 5.0.7. MAA Committee on Undergraduate Program Prize for Outstanding Research in in Mathematics (CUPM) Mathematics by an Undergraduate Student Alfonso Castro 2008 Kelly J. Black (SIAM) 2007 Mario Umberto Martelli 2008 James H. Curry (SIAM) 2007 5.0.8. U.S. National Committee on Theoretical and Karen Smith (MAA) 2008 Applied Mechanics Kannan Soundararajan (AMS) 2009 Judy L. Walker (AMS) 2007 Term expires on October 31. Chair Paul Zorn (MAA) 2009 David Kinderlehrer 2008 Special Committees 4.10.14. AMS-Brazilian Mathematical Society (BMS) 6. Index Joint Program Committee, June 4–7, 2008 ABCCommittee...... 4.3.1 Harold Rosenberg AMSPublicPolicyAwardSelectionCommittee...... 4.8.1 Michael Shub AMS-ASA-AWM-IMS-MAA-NCTM-SIAM Committee on Women in Lesley M. Sibner ex officio theMathematicalSciences...... 4.10.1 Hector J. Sussman AMS-ASA-IMS-MAA-SIAM Data Committee ...... 4.10.2 AMS-ASA-MAA-SIAM Joint Policy Board for Mathematics . . . 4.10.3 4.10.15. AMS-New Zealand Mathematical Society AMS-ASL-IMS-SIAM Committee on Translations from Russian (NZMS) Joint Program Committee, andOtherSlavicLanguages...... 4.10.4 December 12–15, 2008 AMS-Brazilian Mathematical Society (BMS) Joint Program Jeff Cheeger Committee, June 4–7, 2008 ...... 4.10.14 Peter W. Jones AMS-MAACommitteeonCooperation...... 4.10.5 Vaughan F. R. Jones AMS-MAA Committee on Mathematicians with Disabilities . . 4.10.6 Matthew Miller ex officio AMS-MAA Committee on Teaching Assistants and Part-time Instructors(TA/PTI)...... 4.10.7 4.10.16. AMS-Polish Mathematical Society (PMS) AMS-MAAExhibitsAdvisorySubcommittee...... 4.10.10 Joint Program Committee, Summer 2007 AMS-MAAJointArchivesCommittee...... 4.10.8 AMS-MAAJointMeetingsCommittee...... 4.10.9 Mladen Bestiva AMS-MAA Joint Program Committee for the San Diego Meeting Krzysztof Burdzy January 6–9, 2008 ...... 4.10.11 Susan J. Friedlander ex officio AMS-MAA-SIAM Frank and Brennie Morgan Prize for Peter Sarnak Outstanding Research in Mathematics by an 4.10.17. AMS-Shanghai Mathematical Society (SMS) UndergraduateStudent...... 4.10.13 AMS-MAA-SIAM Joint Committee on Employment Opportunities 4.10.12 Joint Program Committee, December 17–21, AMS-New Zealand Mathematical Society (NZMS) Joint Program 2008 Committee, December 12–15, 2008 ...... 4.10.15 Robert L. Bryant AMS-Polish Mathematical Society (PMS) Joint Program Gui-Qiang Chen Committee, Summer 2007 ...... 4.10.16 Susan J. Friedlander ex officio AMS-Shanghai Mathematical Society (SMS) Joint Program Shou-Wu Zhang Committee, December 17–21, 2008 ...... 4.10.17 AbstractsEditorialCommittee...... 4.2.1 Academic Freedom, Tenure, and Employment Security . . . . 4.7.1 AgendaandBudget...... 4.3.1 AgendaforBusinessMeetings...... 4.6.8 5. Representatives American Association for the Advancement of Science . . . . 5.0.1 American Mathematics Competition, Committee on ...... 5.0.4 5.0.1. American Association for the Advancement Archives...... 4.5.1 ArnoldRossLectureSeriesCommittee...... 4.6.9 of Science Audit...... 4.3.2 Terms expire on February 21. Award for Distinguished Public Service, Committee to Select theWinnerofthe...... 4.8.2 Section A Donald G. Saari 2009 BoardofTrustees...... 3 Section Q Jere Confrey 2009 Books and Journal Donations Steering Committee ...... 4.5.2 5.0.2. Canadian Mathematical Society Bulletin(NewSeries)...... 4.2.2 BulletinEditorSearch...... 4.3.3 Catherine Huafei Yan 2007 Bocherˆ Prize, Committee to Select the Winner of ...... 4.8.4 5.0.3. Commission on Professionals in Science and CAFTES...... 4.7.1 Technology CBMS...... 5.0.5 COE...... 4.7.2 Polly Phipps 2007 CPUB...... 4.5.5 CSP...... 4.7.7 5.0.4. Committee on the American Mathematics CanadianMathematicalSociety...... 5.0.2 Competition (MAA) CentennialFellowships...... 4.8.5 Term expires on June 30. CentralSectionProgramCommittee...... 4.6.4 Chinese,Translationfrom...... 4.2.16 Kiran S. Kedlaya 2009 Cole Prize, Committee to Select the Winner of the ...... 4.8.16 5.0.5. Conference Board of the Mathematical CollectedWorks...... 4.2.3 Colloquium...... 4.2.4 Sciences ColloquiumLecture...... 4.6.10 James G. Glimm 2008 Commission on Professionals in Science and Technology . . . 5.0.3 CommitteeonCommittees...... 4.5.3 5.0.6. Delbert Ray Fulkerson Prize Selection Committee on the American Mathematics Competition (MAA) 5.0.4 Committee Committees...... 4 Daniel J. Kleitman 2009 CommitteesoftheBoardofTrustees...... 4.3

1186 NOTICES OF THE AMS VOLUME 54, NUMBER 9 Officers and Committee Members

CommitteesoftheCouncil...... 4.1 Professionals in Science and Technology, Commission on . . 5.0.3 Committees of the Executive Committee and Board of Trustees 4.4 Program Committees Conant Prize, Committee to Select the Winner of the . . . . . 4.8.6 Central...... 4.6.4 Conference Board of the MathematicalSciences...... 5.0.5 Eastern...... 4.6.5 ConformalGeometryandDynamics...... 4.2.18 NationalMeetings...... 4.6.2 ContemporaryMathematics...... 4.2.5 Southeastern...... 4.6.6 Council...... 2 Western...... 4.6.7 DataCommittee...... 4.10.2 ProgramandMeetings...... 4.6 DavidP.RobbinsPrize...... 4.8.13 Publications...... 4.5.5 Delbert Ray Fulkerson Prize Selection Committee ...... 5.0.6 RepresentationTheory...... 4.2.20 E. H. Moore Research Article Prize, Committee to Select the Representatives...... 5 Winnerofthe...... 4.8.11 RepresentativesofCommittees...... 2.0.2 EC...... 2.1 Russian and Other Slavic Languages, Translations from . . . 4.10.4 Eastern Section Associate Secretary, Search Committee for . . 4.3.4 Salary...... 4.3.6 EasternSectionProgramCommittee...... 4.6.5 Satter Prize, Committee to Select the Winner of the ...... 4.8.14 EditorialBoards...... 4.1.1 SciencePolicy...... 4.7.7 EditorialCommittees...... 4.2 ShortCourseSubcommittee...... 4.6.3 Education...... 4.7.2 SoutheasternSectionProgramCommittee...... 4.6.6 ElectronicResearchAnnouncements...... 4.2.6 StaffSalaries...... 4.3.6 EmploymentOpportunities...... 4.10.12 StatusoftheProfession...... 4.7 Ethics...... 4.7.6 SteelePrizes...... 4.8.15 ExecutiveCommitteeoftheCouncil...... 2.1 StudentMathematicsLibrary...... 4.2.21 Exemplary Program or Achievement by a Mathematics TA/PTI...... 4.10.7 Department, Committee to Select the Winner of the TheStefanBergmanTrustFund...... 4.8.3 Prizefor...... 4.8.17 TheoreticalandAppliedMechanics...... 5.0.8 FanFund...... 4.7.3 TransactionsandMemoirs...... 4.2.15 First-Year College Mathematics Experience, Task Force on . . 4.1.3 Translations: Chinese...... 4.2.16 Gibbs Lecturer for 2007 and 2008, Committee to Select . . . 4.6.11 Japanese...... 4.2.17 GraduateStudiesinMathematics...... 4.2.7 Russian and Other Slavic Languages ...... 4.10.4 HistoryofMathematics...... 4.2.19 Trustees...... 3 HumanRightsofMathematicians...... 4.7.4 U.S. National Committee on Theoretical and Applied Mechanics 5.0.8 InstitutesandSymposia...... 4.9 Undergraduate Program in Mathematics, MAA Committee on 5.0.7 Internal Organization of the American Mathematical Society . 4.5 UniversityLectureSeries...... 4.2.22 Investment...... 4.3.5 VeblenPrize...... 4.8.18 JCEO...... 4.10.12 Von Neumann Symposium Selection Committee ...... 4.9.2 JPBM...... 4.10.3 WesternSectionProgramCommittee...... 4.6.7 Japanese,Translationfrom...... 4.2.17 WomenintheMathematicalSciences...... 4.10.1 JointArchivesCommittee...... 4.10.8 Working Group on Preparation for Technical Careers Advisory JointCommittees...... 4.10 Board...... 4.1.4 JointMeetingsCommittee...... 4.10.9 YoungScholarsAwards...... 4.7.8 JointPolicyBoard...... 4.10.3 JosephL.DoobPrize...... 4.8.7 JournaloftheAMS...... 4.2.8 LRP...... 4.4.1 Leonard Eisenbud Prize for Mathematics and Physics . . . . . 4.8.8 LiaisonCommittee...... 1.1 Liaison Committee with AAAS ...... 4.9.1 LibraryCommittee...... 4.5.4 LongRangePlanning...... 4.4.1 MAA Committee on Undergraduate Program in Mathematics (CUPM)...... 5.0.7 MathinMoscowProgam—TravelSupport...... 4.8.9 MathematicalReviews...... 4.2.9 MathematicalSurveysandMonographs...... 4.2.10 MathematicsofComputation...... 4.2.11 MeetingsandConferences...... 4.6.1 MembersatLarge...... 2.0.3 Memoirs...... 4.2.15 Menger Prize, Committee to Select the Winner of the . . . . . 4.8.10 Monographs...... 4.2.10 Morgan Prize Committee for Outstanding Research in Mathematics iby an Undergraduate Student, AMS-MAA-SIAMCommitteeon...... 4.10.13 National Awards and Public Representation...... 4.8.12 NationalMeetings...... 4.6.2 Nominating...... 4.4.2 NominatingCommittee...... 4.1.2 Nominating Committee of the ECBT ...... 4.4.2 NoticesEditorialBoard...... 4.2.12 Officers...... 1 OfficersoftheAMS...... 2.0.1 PSAM...... 4.2.14 PrizesandAwards...... 4.8 Proceedings...... 4.2.13 Proceedings of Symposia in Applied Mathematics ...... 4.2.14 Profession...... 4.7.5 ProfessionalEthics...... 4.7.6

OCTOBER 2007 NOTICES OF THE AMS 1187 From the AMS Secretary

Statistics on Women Invited Hour Address Speakers Mathematicians Compiled by at AMS Meetings (1997–2006) Male: 386 84% the AMS Female: 72 16% Unknown: 0 0% At its August 1985 meeting the Council of the AMS Total: 458 approved a motion to regularly assemble and report in the Notices information on the relative numbers of men versus women in at least the following categories: membership in Speakers at Special Sessions the AMS, invited hour addresses at AMS meetings, speakers at AMS Meetings (2002–2006) at Special Sessions at AMS meetings, percentage of women speakers in AMS Special Sessions by gender of organizers, Male: 9,862 79% and members of editorial boards of AMS journals. Female: 2,080 17% It was subsequently decided that this information would Unknown: 486 4% Total: 12,428 be gathered by determining the sex of the individuals in the above categories based on name identification if no other means was available and that additional information on the number of Ph.D.’s granted to women would also Percentage of Women Speakers be collected using the AMS-ASA-IMS-MAA-SIAM Annual in AMS Special Sessions Survey. Since name identification was used, the informa- by Gender of Organizers (2006) tion for some categories necessitated the use of three Special Sessions classifications: with at Least One Woman Organizer Male: names that were obviously male Female: names that were obviously female Male: 580 76% Unknown: names that could not be identified as clearly Female: 180 23% male or female (e.g., only initials given, non-gender-specific Unknown: 6 1% names, etc.) Total: 766 The following is the twenty-second reporting of this information. Updated reports will appear annually in the Special Sessions Notices. with No Women Organizers

Male: 1,376 83% Female: 260 16% Unknown: 31 2% Total: 1,667

2006 Members of the AMS Trustees and Council Members Residing in the U.S. 2003 2004 2005 2006 Male: 14,387 68% Female: 3,741 18% Male: 36 75% 29 71% 30 71% 27 66% Unknown: 3,136 15% Female: 12 25% 12 29% 12 29% 14 34% Total: 21,264 Total: 48 41 42 41

Members of AMS Editorial Committees 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Male: 189 89% 182 85% 198 86% 186 85% 190 85% 195 85% 189 84% 180 84% 184 83% 193 84% Female: 24 11% 31 15% 32 14% 33 15% 34 15% 35 15% 35 16% 34 16% 38 17% 36 16% Total: 213 213 230 219 224 230 224 214 222 229

Ph.D.’s Granted to U.S. Citizens 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Male: 368 71% 423 72% 367 66% 379 71% 343 69% 291 70% 341 68% 347 68% 355 72% 399 72% Female: 148 29% 163 28% 187 34% 158 29% 151 31% 127 30% 158 32% 166 32% 141 28% 153 28% Total: 516 586 554 537 494 418 499 513 496 552

1188 Notices of the AMS Volume 54, Number 9 Mathematics Calendar

The most comprehensive and up-to-date Mathematics Calendar information is available on the AMS website at http://www.ams.org/mathcal/.

October 2007 Foata (Strasbourg), Franck Jedrzejewski (CEA Paris), Pierre Jehel (ENS Cachan), Eberhard Knobloch (Berlin), Franc¸ois Nicolas (ENS * 22–26Thepracticeandtheoryofstochasticsimulation,American Paris), Norbert Schappacher (IRMA) and G´erard Wanner (Gen`eve). Institute of Mathematics, Palo Alto, California. Information:http://www-irma.u-strasbg.fr/article515.html; Description: This workshop, sponsored by AIM and the NSF, email: [email protected]. concerns approaches for the numerical integration of stochastic systems which span many temporal-scales. Molecular dynamics * 15–21 Advanced School on Numerical Solutions of Partial and stochastic simulations in chemical kinetics, in particular, Differential Equations: New Trends and Applications,Centrede are two important examples among several other which require Recerca Matem`atica, Bellaterra, Italy. efficient and accurate integrators. The simulations of these systems Coordinators:Jos´e A. Carrillo, ICREA-UAB; Rosa Donat, Universitat generate many important questions which, so far, remain mostly de Val`encia; Carlos Par´es, Universidad de M´alaga; Yolanda Vidal, open. Can stochastic differential equations (SDEs) represent a viable Universitat Polit`ecnica de Catalunya. alternative to thermostats such as Nose-Hoover or Andersen for the Speakers: Blanca Ayuso, Universidad Autonoma´ de Madrid; Sonia simulation of systems in ensembles other than the microcanonical Fern´andez-M´endez, Universitat Polit`ecnica de Catalunya; Enrique one? How to guarantee the ergodicity of integrators for such SDEs Fern´andez-Nieto, Universidad de Sevilla; Francis Filbet, Universit´e and assess their rate of convergence, accuracy and efficiency? de Claude Bernard –Lyon I; Gabriella Puppo, Politecnico di Torino. How to efficiently compute expectation and free energies using Further information: http://www.crm.cat/ASPDEs. such integrators, especially in systems displaying metastability? Activities at the workshop will focus on new developments and January 2008 related issues in these areas. Information:email:[email protected] event_day1; http:// * 1–March 31DocCourse in Combinatorics and Geometry: Additive aimath.org/ARCC/workshops/stochasticsim.html. Combinatorics, Centre de Recerca Matem`atica, Bellaterra, Italy. Coordinators: Javier Cilleruelo, Universidad Autonoma´ de Madrid; November 2007 Marc Noy, Universitat Polit`ecnica de Catalunya; Oriol Serra, Univer- sitat Polit`ecnica de Catalunya. * 15–16 Leonhard Euler (Mathematics and Music), Institut de Speakers: Alfred Geroldinger, University of Graz, Institute for Recherche Math´ematique Avanc´ee, Universit´eLouisPasteur,7rue Mathematics and Scientific Computing, Algebraic Methods in Ad- Descartes, 67084, Strasbourg, France. ditive Combinatorics; Imre Z. Ruzsa, Alfr´ed R´enyi Institute of Description: To celebrate the three hundredth anniversary of the Mathematics, Budapest, Sumsets and structure. birth of Leonhard Euler, the conference will present some aspects Information: http://www.crm.cat/AdditiveCombinatorics. of his work on mathematics, acoustics and theoretical music. Speakers will include: Patrice Bailhache (Nantes), Dominique * 2–4 Tenth International Symposium on Artificial Intelligence

respect to participation in the meeting, this fact should be noted. This section contains announcements of meetings and conferences All communications on meetings and conferences in the mathematical of interest to some segment of the mathematical public, including ad sciences should be sent to the Editor of the Notices in care of the American hoc, local, or regional meetings, and meetings and symposia devoted Mathematical Society in Providence or electronically to [email protected] to specialized topics, as well as announcements of regularly scheduled or [email protected]. meetings of national or international mathematical organizations. A In order to allow participants to arrange their travel plans, organizers of complete list of meetings of the Society can be found on the last page of meetings are urged to submit information for these listings early enough each issue. to allow them to appear in more than one issue of the Notices prior to An announcement will be published in the Notices if it contains a call the meeting in question. To achieve this, listings should be received in for papers and specifies the place, date, subject (when applicable), and Providence eight months prior to the scheduled date of the meeting. the speakers; a second announcement will be published only if there The complete listing of the Mathematics Calendar will be published are changes or necessary additional information. Once an announcement only in the September issue of the Notices. The March, June/July, and has appeared, the event will be briefly noted in every third issue until December issues will include, along with new announcements, references it has been held and a reference will be given in parentheses to the to any previously announced meetings and conferences occurring within month, year, and page of the issue in which the complete information the twelve-month period following the month of those issues. New appeared. Asterisks (*) mark those announcements containing new or information about meetings and conferences that will occur later than revised information. the twelve-month period will be announced once in full and will not be In general, announcements of meetings and conferences held in North repeated until the date of the conference or meeting falls within the America carry only the date, title of meeting, place of meeting, names of twelve-month period. speakers (or sometimes a general statement on the program), deadlines The Mathematics Calendar, as well as Meetings and Conferences of for abstracts or contributed papers, and source of further information. the AMS, is now available electronically through the AMS website on the Meetings held outside the North American area may carry more detailed World Wide Web. To access the AMS website, use the URL: http://www. information. In any case, if there is any application deadline with ams.org/.

OCTOBER 2007 NOTICES OF THE AMS 1189 Mathematics Calendar

and Mathematics (ISAIM 2008), Fort Lauderdale, Florida. Department at [email protected]. Description: We seek submissions of recent results with a particular emphasis on the foundations of AI and mathematical methods May 2008 used in AI. Papers describing applications are also encouraged, * 10–13 SIAM Conference on Optimization, Boston Park Plaza Hotel but the focus should be on principled lessons learned from the and Towers, Boston, Massachusetts. development of the application. Invited Plenary Speakers: Etienne de Klerk, Tilburg University, Deadline: Paper Submission: October 1, 2007. Netherlands; Matthias Heinkenschloss, Rice University; Jan Moder- Invited Speakers: David McAllester, Toyota Technological Institute sitzki, University of Lubeck, Germany; Annick Sartenaer, Universite at Chicago, USA; Francesca Rossi, Padova University, Italy; Naftali NotreDamedelaPaix,Belgium;Stefan Scholtes, Cambridge Uni- Tishby, The Hebrew University, Israel. versity, United Kingdom; Pascal Van Hentenryck, Brown University; Information: http://isaim2008.unl.edu. Andreas W¨achter, IBM Research; Robert Weismantel, University of Special Topic Invited Sessions: Logic in Artificial Intelligence Magdeburg, Germany. Special Session in Honor of the 65th Birthday of Victor Marek. Deadlines: Minisymposium proposals: October 9, 2007 EDT. Ab- Organized by Michael Kaminski and Mirek Truszczynski; Compu- stracts for all contributed and minisymposium presentations: tation and Social Choice. Organized by Toby Walsh, NICTA and November 8, 2007 EST. University of New South Wales. Other special sessions may be Information: The Call for Presentations for this conference is avail- announced soon. able at: http://www.siam.org/meetings/op08/. For additional information, contact SIAM Conference Department at meetings@ February 2008 siam.org. * 4–14 Advanced Course on Simplicial Methods in Higher Cate- gories, Centre de Recerca Matem`atica, Bellaterra, Italy. June 2008 Coordinators:CarlesCasacuberta,UniversitatdeBarcelona;Joachim * 23–27 Homotopical Group Theory and Topological Algebraic Kock, Universitat Autonoma` de Barcelona. Geometry, Max Planck Institute for Mathematics, Bonn, Germany. Speakers:Andr´eJoyal,Universit´eduQu´ebec `a Montr´eal, The theory Conference Topics: The conference focuses on the new interactions of quasi-categories and its applications; Ieke Moerdijk, Universiteit of Algebraic Topology with Group Theory, Algebraic Geometry and Utrecht, Dendroidal sets; Bertrand To¨en, Universit´e Paul Sabatier, Mathematical Physics which come from looking at these fields Simplicial presheaves and derived geometries. through the eye of a homotopy theorist. It celebrates one of the Further information: http://www.crm.cat/ACQuasiCategories. contributors to the subject by honoring the 60th birthday of Haynes Miller (MIT). * 12–16 Foundations of Lattice-Valued Mathematics with Appli- Registration: All participants are required to register. cations to Algebra and Topology,Linz,Austria. Organizers: M. Ando (UIUC), J. Grodal (Copenhagen), G. Laures Description: The last decade has witnessed a significant develop- (Bochum), B. Shipley (UIC). ment of the categorical, logical, and order-theoretic foundations of Financial support: The conference is partially supported by the lattice-valued mathematics and their impact on algebra and topol- DFG Graduiertenkolleg 1150 “Homotopy and Cohomology” and ogy. These developments have created or significantly strengthened the Max Planck Institute Bonn. Support from the National Science bridges between lattice-valued mathematics, logic, sheaves, alge- Foundation for beginning researchers is under application. braic theories, quantales and order-theoretic structures, various Information: http://www.ruhr-uni-bochum.de/topologie/ subdisciplines of topology, and theoretical computer science. The conf08/. purpose of the 29th Linz Seminar is to discuss the synergy be- tween these fields as well as identify important open questions. November 2009 Accordingly, the topics of the Seminar will include but not be 1–30 limited to: Categorical and logical approaches to lattice valued * 5thAsianMathematicalConference(AMC2009),Penang/Ku- algebraic structures, powerset theories, topological structures, lalumpur, Malaysia. Lattice valued categories, equivalences, locales, orders, topologies Description: Activities of the conference will include the following: Presheaf and sheaf theoretic approaches to lattice valued structures Keynote addresses by internationally renowned mathematicians; Programming semantics, semantic domains, topological systems. Invited talks by prominent regional mathematicians; Contributed Information:email:[email protected];http://www.flll. papers; Workshops Focus Areas of this conference are; Algebra; Al- jku.at/research/linz2008/index.html. gebraicGeometry;Analysis;OperatorAlgebra&FunctionalAnalysis; Lie Groups and Lie Algebras; Number Theory; Combinatorics; Logic March 2008 & Foundations of Mathematics; Ordinary Differential Equations and Dynamical Systems; Partial Differential Equations; Topology; * 12–19 Advanced Course on Geometric Flows and Hyperbolic Mathematical Aspects of Computer Science; Numerical Analysis Geometry, Centre de Recerca Matem`atica, Bellaterra, Italy. and Scientific Computing; Control Theory, Optimization and Op- Coordinators: Joan Porti, Universitat Autonoma` de Barcelona; erations Research; Probability and Stochastic Process; Statistics; Vicente Miquel, Universitat de Val`encia. Application of Mathematics in Sciences. Speakers: Ben Chow, University of California at San Diego, Some Information:email:[email protected]; http://math.usm.my/ geometric and analytic aspects of geometric flows; Manuel Ritor´e, amc2009. Universidad de Granada, Geometric flows, isoperimetric inequal- ities, and hyperbolic geometry; Carlo Sinestrari, Universit`adegli StudidiRomaTorVergata,Formation of singularities in mean curvature flow. Further information: http://www.crm.cat/ACGeometryFlows.

April 2008 * 24–26 SIAM International Conference on Data Mining,Hyatt Regency Hotel, Atlanta, Georgia. Information: Abstract due: October 5, 2007. Manuscripts due: Octo- ber 12, 2007. For additional information, contact SIAM Conference

1190 NOTICES OF THE AMS VOLUME 54, NUMBER 9 AMS SHORT COURSE Mark Your Calendar Applications of Knot Theory January 4-5, 2008 San Diego, California

Organizers: Dorothy Buck Department of Mathematics and Centre for Bioinformatics Imperial College London Erica Flapan Department of Mathematics Pomona College Over the past twenty years, knot theory has rekindled its historic ties with biology, chemistry, and physics. While the original motivation for under- standing and classifying knots came from chemistry, knot theory remained a primarily pure field of math- ematics until the 1980s, when chemists, biologists, and physicists began searching for more sophisticated descriptions of entanglements of natural phenomena— from strings to small organic compounds to DNA. is AMS Short Course will introduce knot theory, and some of its recent applications in molecular biology, chemistry, and physics. No prior knowledge of knot theory, biology, chemistry, or physics is assumed— there will be introductory talks on the first day. Speakers will survey their own work in these areas, as well as describing new avenues for interested researchers (and their students) to explore. The Short Course will conclude with a panel discussion of the putative trajectories of these applica- tions of knot theory, and summarize the major open problems and challenges. References will be available in advance and lecture notes published afterwards.

List of speakers: Colin Adams (Williams College) Dorothy Buck (Imperial College London) Erica Flapan (Pomona College) Lou Kau man (University of Illinois at Chicago) Ned Seeman (New York University) Jon Simon (University of Iowa) Advance registration fees: member/nonmember $90/120 Student/unemployed/emeritus $40 See You There! On-site registration fees: member/nonmember $120/151 student/unemployed/emeritus $60 New Publications Offered by the AMS To subscribe to email notification of new AMS publications, please go to http://www.ams.org/bookstore-email.

Applications Differential Equations

Recent Trends in Recent Developments Coding Theory and Its in Nonlinear Partial Applications Differential Equations Wen-Ching Winnie Li, Donatella Danielli, Purdue Pennsylvania State University, University, West Lafayette, IN, University Park, PA, Editor Editor

Coding theory draws on a remarkable This volume contains research and selection of mathematical topics, expository articles based on talks both pure and applied. The various presented at the 2nd Symposium on contributions in this volume introduce coding theory and its Analysis and PDEs, held at Purdue University. The symposium most recent developments and applications, emphasizing both focused on topics related to the theory and applications of mathematical and engineering perspectives on the subject. This nonlinear partial differential equations that are at the forefront of volume covers four important areas in coding theory: algebraic current international research. Papers in this volume provide a geometry codes, graph-based codes, space-time codes, and comprehensive account of many of the recent developments in the quantum codes. Both students and seasoned researchers will field. benefit from the extensive and self-contained discussions of the The topics featured in this volume include: kinetic formulations development and recent progress in these areas. of nonlinear PDEs; recent unique continuation results and their This item will also be of interest to those working in algebra and applications; concentrations and constrained Hamilton–Jacobi algebraic geometry. equations; nonlinear Schrödinger equations; quasiminimal sets for Hausdorff measures; Schrödinger flows into Kähler manifolds; and Titles in this series are co-published with International Press, parabolic obstacle problems with applications to finance. Cambridge, MA. The clear and concise presentation in many articles makes this Contents: Algebraic geometry codes: M.-C. Kang, Introduction to volume suitable for both researchers and graduate students. algebraic geometry codes; W.-C. W. Li, Upper and lower bounds for A(q); W.-C. W. Li, Elkies’ modularity conjecture; H. Maharaj, Contents: L. C. Evans, Lectures on kinetic formulations of Explicit towers and codes; W.-C. W. Li, Improved algebraic geometry nonlinear PDE; C. E. Kenig, Some recent applications of unique bounds; A. Garcia and H. Stichtenoth, On the Galois closure of continuation; G. Barles and B. Perthame, Concentrations and towers; Graph-based codes: N. Boston, Graph-based codes; New constrained Hamilton-Jacobi equations arising in adaptive aspects of Reed Muller codes: A. R. Calderbank, Reed Muller codes dynamics; J. Colliander, M. Keel, G. Staffilani, H. Takaoka, and and symplectic geometry; Quantum codes: A. Ashikhmin and S. T. Tao, The energy-critical nonlinear Schrödinger equation in Litsyn, Foundations of quantum error correction; K. Feng, A new R3; G. David, Quasiminimal sets for Hausdorff measures; C. E. description of quantum error-correcting codes. Kenig, G. Ponce, and L. Vega, The initial value problem for the general quasi-linear Schrödinger equation; A. Petrosyan and H. AMS/IP Studies in Advanced Mathematics, Volume 41 Shahgholian, Parabolic obstacle problems applied to finance. A August 2007, 200 pages, Softcover, ISBN: 978-0-8218-4298-0, LC free-boundary-regularity approach. 2007060819, 2000 Mathematics Subject Classification: 94Bxx, AMS Contemporary Mathematics, Volume 439 members US$47, List US$59, Order code AMSIP/41 October 2007, 133 pages, Softcover, ISBN: 978-0-8218-3740-5, LC 2007060822, 2000 Mathematics Subject Classification: 49K99, 35Q55, 49L25, 35B25, 92D15, 35R35, 35K60, 58J35, AMS members US$39, List US$49, Order code CONM/439

1192 Notices of the AMS Volume 54, Number 9 New Publications Offered by the AMS Lectures on Analytic General and Interdisciplinary Differential Equations Yulij Ilyashenko, Cornell University, Ithaca, NY, and Assistantships and Independent University of Graduate Fellowships Moscow, Russia, and Sergei Yakovenko, Weizmann Institute in the Mathematical of Science, Rehovot, Israel Sciences 2007

The book combines the features of a From a review of a previous edition: graduate-level textbook with those of a research monograph and This directory is a tool for undergraduate survey of the recent results on analysis and geometry of differential mathematics majors seeking information equations in the real and complex domain. As a graduate textbook, about graduate programs in mathematics. it includes self-contained, sometimes considerably simplified Although most of the information can be demonstrations of several fundamental results, which previously gleaned from the Internet, the usefulness of this directory for the appeared only in journal publications (desingularization of prospective graduate student is the consistent format for comparing planar analytic vector fields, existence of analytic separatrices, different mathematics graduate programs without the hype. positive and negative results on the Riemann–Hilbert problem, Published annually, the information is up-to-date, which is more Ecalle–Voronin and Martinet–Ramis moduli, solution of the than can be said of some Websites. Support for graduate students Poincaré problem on the degree of an algebraic separatrix, etc.). As a in mathematics is a high priority of the American Mathematical research monograph, it explores in a systematic way the algebraic Society, which also provides information for fellowships and grants decidability of local classification problems, rigidity of holomorphic they offer as well as support from other societies and foundations. foliations, etc. Each section ends with a collection of problems, The book is highly recommended for academic and public libraries. partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the — American Reference Books Annual more recent results surveyed in the text. This valuable reference source brings together a wealth of The exposition of the book is mostly geometric, though the information about resources available for graduate study in algebraic side of the constructions is also prominently featured. mathematical sciences departments in the U.S. and Canada. On several occasions the reader is introduced to adjacent areas, November 2007, approximately 112 pages, Softcover, ISBN: 978-0- such as intersection theory for divisors on the projective plane or 8218-4322-2, Individual member US$18, List US$23, Order code geometric theory of holomorphic vector bundles with meromorphic ASST/2007 connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area. Contents: Normal forms and desingularization; Singular points Mathematical of planar analytic vector fields; Local and global theory of linear Omnibus systems; Functional moduli of analytic classification of resonant germs and their applications; Global properties of complex Thirty Lectures on Classic polynomial foliations; Appendix. First aid; Bibliography; Index. Mathematics Graduate Studies in Mathematics, Volume 86 Dmitry Fuchs, University of November 2007, approximately 636 pages, Hardcover, ISBN: 978- California, Davis, CA, and Serge 0-8218-3667-5, 2000 Mathematics Subject Classification: 34A26, Tabachnikov, Pennsylvania State 34C10; 14Q20, 32S65, 13E05, AMS members US$63, List US$79, University, University Park, PA Order code GSM/86 The book consists of thirty lectures on diverse topics, covering much of the mathematical landscape rather than focusing on one area. The reader will learn numerous results that often belong to neither the standard undergraduate nor graduate curriculum and will discover connections between classical and contemporary ideas in algebra, combinatorics, geometry, and topology. The reader’s effort will be rewarded in seeing the harmony of each subject. The common thread in the selected subjects is their illustration of the unity and beauty of mathematics. Most lectures contain exercises, and solutions or answers are given to selected exercises. A special feature of the book is an abundance of drawings (more than four hundred), artwork by an award-winning artist, and about a hundred portraits of mathematicians. Almost every lecture contains surprises for even the seasoned researcher. Contents: Algebra and arithmetics: Arithmetic and combinatorics: Can a number be approximately rational?; Arithmetical properties of binomial coefficients; On collecting like terms, on Euler, Gauss,

October 2007 Notices of the AMS 1193 New Publications Offered by the AMS and MacDonald, and on missed opportunities; Equations: Equations the AMS member price. The LMS is registered with the Charity of degree three and four; Equations of degree five; How many roots Commissioners. does a polynomial have?; Chebyshev polynomials; Geometry of Contents: Early youth and abitur; 1928-1938—Weimar Republic equations; Geometry and topology: Envelopes and singularities: and National Socialism in peace. From the beginning of studies Cusps; Around four vertices; Segments of equal areas; On plane to the extension of the unscheduled assistantship for another curves; Developable surfaces: Paper sheet geometry; Paper Möbius year with effect from 1 October 1938; 1939-1942—From the band; More on paper folding; Straight lines: Straight lines on beginning of the war to dismissal from the Wehrmacht and the curved surfaces; Twenty-seven lines; Web geometry; The Crofton wartime habilitation under Helmut Hasse; The fight over “German formula; Polyhedra: Curvature and polyhedra; Non-inscribable logic” from 1940 to 1945: A battle between amateurs; Recovery polyhedra; Can one make a tetrahedron out of a cube?; Impossible and docent position 1942 to 1944; Arrest, imprisonment, death tilings; Rigidity of polyhedra; Flexible polyhedra; Two surprising and Nachlass; Conclusion; Tables of the life of Gerhard Gentzen; topological constructions: Alexander’s horned sphere; Cone Appendix A: Gentzen and geometry, by C. Smory´nski;Appendix B: eversion; On ellipses and ellipsoids: Billiards in ellipses and Hilbert’s programme, by C. Smory´nski;Appendix C: Three lectures, geodesics on ellipsoids; The Poncelet porism and other closure by Gerhard Gentzen; Appendix D: From Hilbert’s programme to theorems; Gravitational attraction of ellipsoids; Solutions to Gentzen’s programme, by Jan von Plato; Bibliography; Index. selected exercises; Bibliography; Index. History of Mathematics, Volume 33 October 2007, 463 pages, Hardcover, ISBN: 978-0-8218-4316-1, November 2007, 442 pages, Hardcover, ISBN: 978-0-8218-3550-0, 2000 Mathematics Subject Classification: 00A05, AMS members 2000 Mathematics Subject Classification: 01A60, AMS members US$47, List US$59, Order code MBK/46 US$71, List US$89, Order code HMATH/33

Logic’s Lost Genius Geometry and Topology The Life of Gerhard Gentzen Recurrence and Eckart Menzler-Trott, Munich, Topology Germany John M. Alongi, Northwestern Gerhard Gentzen (1909–1945) is the University, Evanston, IL, and founder of modern structural proof Gail S. Nelson, Carleton College, theory. His lasting methods, rules, and Northfield, MN structures resulted not only in the technical mathematical discipline called “proof theory” but also in Since at least the time of Poisson, verification programs that are essential in computer science. The mathematicians have pondered the notion appearance, clarity, and elegance of Gentzen’s work on natural of recurrence for differential equations. deduction, the sequent calculus, and ordinal proof theory continue Solutions that exhibit recurrent behavior to be impressive even today. provide insight into the behavior of general solutions. In Recurrence The present book gives the first comprehensive, detailed, accurate and Topology, Alongi and Nelson provide a modern understanding scientific biography expounding the life and work of Gerhard of the subject, using the language and tools of dynamical systems Gentzen, one of our greatest logicians, until his arrest and death in and topology. Prague in 1945. Recurrence and Topology develops increasingly more general Particular emphasis in the book is put on the conditions of topological modes of recurrence for dynamical systems beginning scientific research, in this case mathematical logic, in National with fixed points and concluding with chain recurrent points. For Socialist Germany, the ideological fight for “German logic”, and each type of recurrence the text provides detailed examples arising their mutual protagonists. Numerous hitherto unpublished sources, from explicit systems of differential equations; it establishes the family documents, archival material, interviews, and letters, as general topological properties of the set of recurrent points; and it well as Gentzen’s lectures for the mathematical public, make this investigates the possibility of partitioning the set of recurrent book an indispensable source of information on this important points into subsets which are dynamically irreducible. The text mathematician, his work, and his time. The volume is completed by includes a discussion of real-valued functions that reflect the two deep substantial essays by Jan von Plato and Craig Smory´nski structure of the sets of recurrent points and concludes with a on Gentzen’s proof theory; its relation to the ideas of Hilbert, thorough treatment of the Fundamental Theorem of Dynamical Brouwer, Weyl, and Gödel; and its development up to the present Systems. day. Smory´nskiexplains the Hilbert program in more than the usual Recurrence and Topology is appropriate for mathematics graduate slogan form and shows why consistency is important. Von Plato students, though a well-prepared undergraduate might read most shows in detail the benefits of Gentzen’s program. of the text with great benefit. This important book is a self-contained starting point for any work Contents: Flows; Recurrent points; Irreducible sets; Test functions; on Gentzen and his logic. The book is accessible to a wide audience Afterword; Appendix A. Discrete dynamical systems; Appendix B. with different backgrounds and is suitable for general readers, Circle rotations; Appendix C. The Hausdorff metric; Bibliography; researchers, students, and teachers. Index. Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at

1194 Notices of the AMS Volume 54, Number 9 New Publications Offered by the AMS

Graduate Studies in Mathematics, Volume 85 ideas, topological language, topological philosophy, and specially developed tools of algebraic topology to solve problems of August 2007, 221 pages, Hardcover, ISBN: 978-0-8218-4234-8, engineering and computer science. Examples of research in both LC 2007060754, 2000 Mathematics Subject Classification: 37-01, these directions are given by articles in this volume, which is 37B20, 37B25, 37B35, 54H20; 37C10, 37C15, 37C25, 37C27, 37C50, designed to be a mixture of various interesting topics of pure 37C70, 34D45, AMS members US$36, List US$45, Order code mathematics and practical engineering. GSM/85 This item will also be of interest to those working in applications. Contents: R. Ghrist, Winding numbers for networks with weak Decompositions of angular data; E. Rodriguez, The snake charmer’s algorithm; B. Tovar, L. Freda, and S. M. LaValle, Using a robot to learn Manifolds geometric information from permutations of landmarks; Robert J. Daverman, University J.-Cl. Hausmann, Geometric descriptions of polygon and chain spaces; Y. Gur and N. Sochen, Diffusion over tensor fields via of Tennessee, Knoxville, TN Lie group pde flows: Lagrangian action approach; M. Farber, M. Grant, and S. Yuzvinsky, Topological complexity of collision Decomposition theory studies decompo- free motion planning algorithms in the presence of multiple moving sitions, or partitions, of manifolds into obstacles; M. Farber and M. Grant, Symmetric motion planning; simple pieces, usually cell-like sets. Since L. Lechuga and A. Murillo, Topological complexity of formal its inception in 1929, the subject has spaces; S. Yuzvinsky, Topological complexity of generic become an important tool in geometric hyperplane complements; A. D. Ames, Homotopy meaningful topology. The main goal of the book is to hybrid model structures; D. Farley, Presentations for the help students interested in geometric topology to bridge the gap cohomology rings of tree braid groups; Y. Gabriely and E. Rimon, between entry-level graduate courses and research at the frontier as Competitive disconnection detection in on-line mobile robot well as to demonstrate interrelations of decomposition theory with navigation. other parts of geometric topology. With numerous exercises and problems, many of them quite challenging, the book continues to be Contemporary Mathematics, Volume 438 strongly recommended to everyone who is interested in this subject. October 2007, 192 pages, Softcover, ISBN: 978-0-8218-4246-1, LC The book also contains an extensive bibliography and a useful index 2007060806, 2000 Mathematics Subject Classification: 55-06, 58-06, of key words, so it can also serve as a reference to a specialist. 68T40, AMS members US$47, List US$59, Order code CONM/438 Contents: Introduction; Preliminaries; The shrinkability criterion; Cell-like decompositions of absolute neighborhood retracts; The cell-like approximation theorem; Shrinkable decompositions; Nonshrinkable decompositions; Applications to manifolds; References; Index. Mathematical Physics AMS Chelsea Publishing September 2007, 317 pages, Hardcover, ISBN: 978-0-8218-4372-7, LC 2007020224, 2000 Mathematics Subject Classification: 57-01; Prospects in 54B15, AMS members US$44, List US$49, Order code CHEL/362.H Mathematical Physics José C. Mourão and João P. Topology and Nunes, Instituto Superior Tecnico, Lisbon, Portugal, Roger Picken, Robotics Institute Superior Tecnico, Lisbon, M. Farber, University of Portugal, and Jean-Claude Durham, United Kingdom, Zambrini, University of Lisbon, R. Ghrist, University of Illinois Portugal, Editors at Urbana-Champaign, IL, M. Burger, ETH, Zurich, This book includes papers presented at the Young Researchers Symposium of the 14th International Congress on Mathematical Switzerland, and D. Koditschek, Physics, held in July 2003, in Lisbon, Portugal. The goal of the book University of Pennsylvania, is to illustrate various promising areas of mathematical physics in a Philadelphia, PA, Editors way accessible to researchers at the beginning of their careers. Two of the three laureates of the Henri Poincaré Prizes, Huzihiro Ever since the literary works of Capekˇ and Asimov, mankind has Araki and Elliott Lieb, also contributed to this volume. The book been fascinated by the idea of robots. Modern research in robotics provides a good survey of some active areas of research in modern reveals that along with many other branches of mathematics, mathematical physics. topology has a fundamental role to play in making these grand Contents: M. Aizenman, R. Sims, and S. L. Starr, Mean-field spin ideas a reality. This volume summarizes recent progress in the glass models from the cavity–ROSt perspective; C. D’Antoni, field of topological robotics—a new discipline at the crossroads of G. Morsella, and R. Verch, Scaling algebras for charge carrying topology, engineering and computer science. quantum fields and superselection structure at short distances; Currently, topological robotics is developing in two main directions. H. Araki, Equilibrium statistical mechanics of quantum lattice On one hand, it studies pure topological problems inspired by systems; E. A. Carlen, The rate of local equilibration in kinetic robotics and engineering. On the other hand, it uses topological theory; A. Hernández-Garduño, Bifurcations of relative equilibria

October 2007 Notices of the AMS 1195 New Publications Offered by the AMS in simple mechanical systems; V. F. R. Jones, In and around the tion: 00B25; 37-06, AMS members US$87, List US$109, Order code origin of quantum groups; E. H. Lieb and J. Yngvason, A second TRANS2/221 look at the second law of thermodynamics; F. Lledó and O. Post, Generating spectral gaps by geometry; M. Loss, Stability of matter; M. Mariño, String theory and knot invariants; N. M. Romão, Slow dynamics of CP1 lumps on a cylinder; Y. Sinai, A new approach Number Theory to the study of the 3D-Navier-Stokes system; J. Teschner, From Liouville theory to the quantum geometry of Riemann surfaces. Contemporary Mathematics, Volume 437 Analytic Number September 2007, 246 pages, Softcover, ISBN: 978-0-8218-4270-6, LC Theory 2007060805, 2000 Mathematics Subject Classification: 35-02, 37- 02, 47-02, 60-02, 76-02, 81-02, 82-02, 83-02, AMS members US$55, A Tribute to Gauss and List US$69, Order code CONM/437 Dirichlet William Duke, University of Moscow Seminar on California, Los Angeles, CA, and Mathematical Physics, Yuri Tschinkel, Courant Institute, New York University, NY, Editors II Articles in this volume are based on talks given at the Yu. Neretin, M. Olshanetsky, Gauss–Dirichlet Conference held in Göttingen on June 20–24, 2005. and A. Rosly, Institute for The conference commemorated the 150th anniversary of the Theoretical and Experimental death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Physics, Moscow, Russia, Editors Dirichlet. The volume begins with a definitive summary of the life and work of The Institute for Theoretical and Dirichlet and continues with thirteen papers by leading experts on Experimental Physics (ITEP) is research topics of current interest in number theory that were internationally recognized for achievements in various branches of directly influenced by Gauss and Dirichlet. Among the topics are the theoretical physics. For many years, the seminars at ITEP have distribution of primes (long arithmetic progressions of primes been among the main centers of scientific life in Moscow. This and small gaps between primes), class groups of binary quadratic volume is a collection of articles by participants of the seminar on forms, various aspects of the theory of L-functions, the theory of mathematical physics that has been held at ITEP since 1983. This is modular forms, and the study of rational and integral solutions to the second such collection; the first was published in the same polynomial equations in several variables. series, AMS Translations, Series 2, vol. 191. Titles in this series are co-published with the Clay Mathematics The papers in the volume are devoted to several mathematical Institute (Cambridge, MA). topics that strongly influenced modern theoretical physics. Among these topics are cohomology and representations of infinite Lie Contents: J. Elstrodt, The life and work of Gustav Lejeune Dirichlet algebras and superalgebras, Hitchin and Knizhnik-Zamolodchikov- (1805–1859); T. D. Browning, An overview of Manin’s conjecture Bernard systems, and the theory of D-modules. for del Pezzo surfaces; J. Brüdern and T. D. Wooley, The density of integral solutions for pairs of diagonal cubic equations; A. Diaconu The book is intended for graduate students and research and D. Goldfeld, Second moments of GL2 automorphic L-functions; mathematicians working in algebraic geometry, representation J. Funke, CM points and weight 3/2 modular forms; D. A. Goldston, theory, and mathematical physics. J. Pintz, and C. Y. Yıldırım, The path to recent progress on Contents: B. Enriquez and V. Rubtsov, Hecke-Tyurin small gaps between primes; A. Granville and K. Soundararajan, parametrization of the Hitchin and KZB systems; B. Feigin, A. N. Negative values of truncations to L(1, χ); B. Green, Long arithmetic Kirillov, and S. Loktev, Combinatorics and geometry of higher progressions of primes; P. Michel and A. Venkatesh, Heegner level Weyl modules; V. V. Fock, Cosh-Gordon equation and points and non-vanishing of Rankin/Selberg L-functions; K. Ono, quasi-Fuchsian groups; A. Gerasimov, S. Kharchev, D. Lebedev, Singular moduli generating functions for modular curves and and S. Oblezin, On a class of representations of quantum surfaces; P. Salberger, Rational points of bounded height on groups and its applications; A. L. Gorodentsev, A. S. Khoroshkin, threefolds; P. Sarnak, Reciprocal geodesics; K. Soundararajan, The and A. N. Rudakov, On syzygies of highest weight orbits; fourth moment of Dirichlet L-functions; H. M. Stark, The Gauss A. L. Gorodentsev and S. A. Kuleshov, On finest and modular class-number problems. t-stabilities; D. Kaledin, Hochschild homology and Gabber’s Clay Mathematics Proceedings, Volume 7 theorem; S. Khoroshkin and S. Pakuliak, Method of projections of Drinfeld currents; A. Levin and A. Zotov, On rational and elliptic September 2007, 256 pages, Softcover, ISBN: 978-0-8218-4307-9, forms and Painlevé VI equation; Y. A. Neretin, Determinantal point LC 2007060818, 2000 Mathematics Subject Classification: 01Axx, processes and fermionic Fock space; Y. A. Neretin, On adelic model 11Dxx, 11Exx, 11Mxx, 11Nxx, 14Gxx, AMS members US$39, List of boson Fock space; M. Verbitsky, Hypercomplex manifolds with US$49, Order code CMIP/7 trivial canonical bundle and their holonomy. American Mathematical Society Translations—Series 2 (Advances in the Mathematical Sciences), Volume 221 October 2007, approximately 213 pages, Hardcover, ISBN: 978-0- 8218-4371-0, LC 91-640741, 2000 Mathematics Subject Classifica-

1196 Notices of the AMS Volume 54, Number 9 New AMS-Distributed Publications Probability New AMS-Distributed Filtering and Publications Prediction: A Primer B. Fristedt, N. Jain, and N. Krylov, University of Minnesota, Minneapolis, MN Algebra and Algebraic

Filtering and prediction is about observing Geometry moving objects when the observations are corrupted by random errors. The main focus is then on filtering out the errors and extracting from the observations the most Algebraic Groups and Homogeneous precise information about the object, which itself may or may not be Spaces moving in a somewhat random fashion. Next comes the prediction step where, using information about the past behavior of the object, Vikram B. Mehta, Tata Institute of Fundamental one tries to predict its future path. Research, Mumbai, India, Editor The first three chapters of the book deal with discrete probability The area of algebraic groups and homogeneous spaces is one in spaces, random variables, conditioning, Markov chains, and which major advances have been made in recent decades. This was filtering of discrete Markov chains. The next three chapters deal the theme of the (twelfth) International Colloquium organized by with the more sophisticated notions of conditioning in nondiscrete the Tata Institute of Fundamental Research in January 2004, and situations, filtering of continuous-space Markov chains, and of this volume constitutes the proceedings of that meeting. Wiener process. Filtering and prediction of stationary sequences is This volume contains articles by several leading experts in central discussed in the last two chapters. topics in the area, including representation theory, flag varieties, The authors believe that they have succeeded in presenting Schubert varieties, vector bundles, loop groups and Kac–Moody Lie necessary ideas in an elementary manner without sacrificing the algebras, Galois cohomology of algebraic groups, and Tannakian rigor too much. Such rigorous treatment is lacking at this level categories. in the literature. In the past few years the material in the book In addition to the original papers in these areas, the volume was offered as a one-semester undergraduate/beginning graduate includes a survey on representation theory in characteristic p by course at the University of Minnesota. Some of the many problems H. Andersen and an article by T. A. Springer on Armand Borel’s work suggested in the text were used in homework assignments. in algebraic groups and Lie groups. This item will also be of interest to those working in applications. A publication of the Tata Institute of Fundamental Research. Contents: Preliminaries; Markov chains; Filtering of discrete Markov Distributed worldwide except in India, Bangladesh, Bhutan, chains; Conditional expectations; Filtering of continuous-space Maldavis, Nepal, Pakistan, and Sri Lanka. Markov chains; Wiener process and continuous time filtering; Contents: T. A. Springer, Armand Borel’s work in the theory Stationary sequences; Prediction of stationary sequences; of linear algebraic Groups; H. H. Andersen, Cohomology of Bibliography; Index. line bundles; P. Belkale, Extremal unitary local systems on 1 Student Mathematical Library, Volume 38 P − {p1, . . . , ps }; I. Biswas and T. L. Gómez, Higgs fields and flat connections on a principal bundle over a compact Kähler October 2007, 252 pages, Softcover, ISBN: 978-0-8218-4333-8, manifold; M. Brion, Construction of equivariant vector bundles; LC 2007060783, 2000 Mathematics Subject Classification: 60-01; J.-L. Colliot-Thélène and J.-J. Sansuc, The rationality problem for 60G99, AMS members US$31, List US$39, Order code STML/38 fields of invariants under linear algebraic groups (with special regards to the Brauer group); C. De Concini and C. Procesi, On the geometry of graph arrangements; P. Deligne, La catégorie des représentations du groupe symétrique St , lorsque t n’est pas un entier naturel; H. Garland, Eisenstein series on loop groups: Maass-Selberg relations 1; W. van der Kallen, A reductive group with finitely generated cohomology algebras; S. S. Kannan, Cohomology of line bundles on Schubert varieties in the Kac-Moody setting; F. Knop, Composition Kostka functions; V. Kreiman, V. Lakshmibai, P. Magyar, and J. Weyman, On ideal generators for affine Schubert varieties; H. Nakajima, Crystal, canonical and PBW bases of quantum affine algebras; R. Orellana and A. Ram, Affine braids, Markov traces and the category O; R. Parthasarathy, Quantum analogues of a coherent family of modules at roots of One: g2; V. L. Popov, Generically multiple transitive algebraic group actions; T. A. Springer, Some subvarieties of a group compactification. Tata Institute of Fundamental Research

October 2007 Notices of the AMS 1197 New AMS-Distributed Publications

June 2007, 535 pages, Hardcover, ISBN: 978-81-7319-802-1, 2000 Work that matters. Mathematics Subject Classification: 20-XX, 14-XX; 20Gxx, 14Lxx, AMS members US$40, List US$50, Order code TIFR/11 The CNA Corporation is a non-profit institution that oper- ates on the principle of conducting impartial, accurate, The Collected Papers of M. S. actionable research and analysis to inform the important work of public sector leaders. Narasimhan M. S. Narasimhan, Tata Institute of Fundamental It’s work that matters, and that reflects a commitment to Research, Mumbai, India serve the public’s interests and the common good. M. S. Narasimhan (b. 1932) has made outstanding contributions We offer career opportunities for people with degrees in to diverse areas of mathematics, including algebraic geometry, engineering, mathematics, economics, physics, chemistry, differential geometry, representation theory of Lie groups, partial international relations, national security, history, and many differential equations, and mathematical aspects of physics. His other scientific and professional fields of study. famous joint work with Seshadri started a new period in the study of holomorphic vector bundles on projective varieties, and he, along with his collaborators, made pioneering progress in the study of Diverse views, objectivity, imaginative techniques, their moduli. His work with Ramanan on universal connections and process driven, results oriented – committed to the com- his work with Okamoto on geometric realization of discrete series mon good. Join us. are of fundamental importance. In a research career spanning five decades, he has authored about 50 research papers. He is the recipient of several honours and awards, including a Royal Society of London fellowship and the 2006 King Faisal Prize. This single volume, with about 800 pages, will be of enduring value www.cna.org to mathematicians with diverse interests and backgrounds. A publication of the Tata Institute of Fundamental Research. Distributed worldwide except in India, Bangladesh, Bhutan, Maldavis, Nepal, Pakistan, and Sri Lanka. “Our work is more than a job, Contents: Papers of M. S. Narasimhan; Notes; Bibliography. it's a career of mission- Tata Institute of Fundamental Research June 2007, 850 pages, Hardcover, ISBN: 978-81-85931-77-7, 2000 focused investigation.” Mathematics Subject Classification: 14-XX, 22E45, 35-XX, 32-XX, 53- XX, AMS members US$80, List US$100, Order code TIFR/10

Anita Hattiangadi Research Analyst M.A. Economics

1198 Notices of the AMS Volume 54, Number 9 Work that matters.

The CNA Corporation is a non-profit institution that oper- ates on the principle of conducting impartial, accurate, actionable research and analysis to inform the important work of public sector leaders.

It’s work that matters, and that reflects a commitment to serve the public’s interests and the common good.

We offer career opportunities for people with degrees in engineering, mathematics, economics, physics, chemistry, international relations, national security, history, and many other scientific and professional fields of study.

Diverse views, objectivity, imaginative techniques, process driven, results oriented – committed to the com- mon good. Join us.

www.cna.org

“Our work is more than a job, it's a career of mission- focused investigation.”

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California CALIFORNIA INSTITUTE OF three years with an additional three-year TECHNOLOGY terminal extension expected. CALIFORNIA INSTITUTE OF Harry Bateman Research Eligibility: Offered to a candidate within TECHNOLOGY Instructorships in Mathematics six years of having received the Ph.D. who Tenure-Track Position shows strong research promise in one of Description: Appointments are for two the areas in which Caltech’s mathematics The Division of Physics, Mathematics, years. The academic year runs from ap- faculty is currently active. proximately October 1 to June 1. Instruc- and Astronomy at the California Institute Deadline: January 1, 2007. of Technology invites applications for tors are expected to teach one course per Application information: Please apply a tenure-track position at the assistant quarter for the full academic year and to professor level in mathematics. We are devote the rest of their time to research. online at mathjobs.org. To avoid duplica- especially interested in the following During the summer months there are no tion of paperwork, your application may research areas: topology/geometry and duties except research. also be considered for an Olga Taussky analysis, but other fields may be consid- Eligibility: Open to persons who have and John Todd Instructorship and a Harry ered. The term of the initial appointment recently received their doctorates in math- Bateman Research Instructorship. is normally four years and appointment is ematics. Caltech is an Affirmative Action/Equal contingent upon completion of the Ph.D. Application information: Please apply Opportunity Employer. Women, minori- Exceptionally well-qualified applicants online at mathjobs.org. To avoid duplica- ties, veterans, and disabled persons are may also be considered at the associate tion of paperwork, your application may encouraged to apply. or full professor level. We are seeking also be considered for an Olga Taussky 000080 highly qualified applicants who are com- and John Todd Instructorship. mitted to a career in research and teach- Caltech is an Affirmative Action/Equal ing. Applicants should write promptly Opportunity Employer. Women, minori- to: Tenure-Track Search, Mathematics ties, veterans, and disabled persons are CALIFORNIA INSTITUTE OF 253-37, California Institute of Technol- encouraged to apply. TECHNOLOGY ogy, Pasadena, CA 91125. Please include 000079 Olga Taussky and John Todd a curriculum vitae, list of publications, Instructorships in Mathematics description of research, and ensure that at least three letters of recommendation be CALIFORNIA INSTITUTE OF Description: Appointments are for three sent to the above address. You may also TECHNOLOGY years. There are three terms in the Caltech apply online at mathjobs.org. Scott Russell Johnson Senior academic year, and instructors are ex- 000078 Postdoctoral Scholar in Mathematics pected to teach one course in all but two terms of the total appointment. These two Description: There are three terms in terms will be devoted to research. During the Caltech academic year. The fellow the summer months there are no duties is expected to teach one course in two except research. terms each year, and is expected to be Eligibility: Offered to persons within in residence even during terms when not three years of having received the Ph.D. teaching. The initial appointment is for who show strong research promise in one

Suggested uses for classified advertising are positions available, books or issue–October 26, 2007; February 2008 issue–November 28, 2007; March lecture notes for sale, books being sought, exchange or rental of houses, 2008–December 28, 2007; April 2008 issue–January 28, 2008. and typing services. U.S. laws prohibit discrimination in employment on the basis of color, age, The 2007 rate is $110 per inch or fraction thereof on a single column (one- sex, race, religion, or national origin. “Positions Available” advertisements inch minimum), calculated from top of headline. Any fractional text of 1/2 from institutions outside the U.S. cannot be published unless they are inch or more will be charged at the next inch rate. No discounts for multiple accompanied by a statement that the institution does not discriminate on ads or the same ad in consecutive issues. For an additional $10 charge, these grounds whether or not it is subject to U.S. laws. Details and specific announcements can be placed anonymously. Correspondence will be wording may be found on page 1373 (vol. 44). forwarded. Situations wanted advertisements from involuntarily unemployed math- Advertisements in the “Positions Available” classified section will be set ematicians are accepted under certain conditions for free publication. Call with a minimum one-line headline, consisting of the institution name above toll-free 800-321-4AMS (321-4267) in the U.S. and Canada or 401-455-4084 body copy, unless additional headline copy is specified by the advertiser. worldwide for further information. Headlines will be centered in boldface at no extra charge. Ads will appear Submission: Promotions Department, AMS, P.O. Box 6248, Providence, in the language in which they are submitted. Rhode Island 02940; or via fax: 401-331-3842; or send email to There are no member discounts for classified ads. Dictation over the [email protected]. AMS location for express delivery packages is telephone will not be accepted for classified ads. 201 Charles Street, Providence, Rhode Island 20904. Advertisers will be Upcoming deadlines for classified advertising are as follows: November 2007 billed upon publication. issue–August 28, 2007; December 2007 issue–October 1, 2007; January 2008

1200 Notices of the AMS Volume 54, Number 9 Classified Advertisements of the areas in which Caltech’s mathemat- plicants should have a recent Ph.D., or the ics faculty is currently active. equivalent, in an area of pure or applied Deadline: January 1, 2008. UNIVERSITY OF CALIFORNIA AT mathematics. Applicants should send a Application information: Please apply BERKELEY resume, reprints, preprints and/or dis- online at mathjobs.org. To avoid duplica- Department of Mathematics sertation abstract, and ask three people to send letters of evaluation to The Vice tion of paperwork, your application may Tenured or Tenure-Track Positions also be considered for a Harry Bateman Chair for Faculty Affairs at the above ad- Research Instructorship. Pending budget approval, we invite ap- dress. All letters of evaluation are subject Caltech is an Affirmative Action/Equal plications for three positions effective to Berkeley campus policies on confiden- Opportunity Employer. Women, minori- July 1, 2008, at either the tenure-track tiality of letters of evaluation, a summary ties, veterans, and disabled persons are (assistant professor) or tenured (associate of which can be found at http://math. encouraged to apply. or full professor) level, in pure or applied berkeley.edu/employment_academic. 000081 mathematics. html. We request that applicants use Tenure-track applicants are expected to the AMS standardized application form have demonstrated outstanding research and indicate their subject area using the AMS subject classification numbers. The UNIVERSITY OF CALIFORNIA, BERKELEY potential, normally including major con- tributions beyond the doctoral disser- form is the Academic Employment in Department of Civil and Environmental Mathematics, Application Cover Sheet. Engineering tation. Such applicants should send a resume, and reprint or preprints, and/or It is available courtesy of the American Mathematical Society. The Department of Civil and Environ- dissertation abstract, and ask three people Applications must be postmarked by mental Engineering at the University of to send letters of evaluation to The Vice December 1, 2007. Applications post- California, Berkeley, invites applications Chair for Faculty Affairs at the above marked after the deadline will not be for a tenure-track assistant professor address. It is the responsibility of the considered. The University of California position in surface water hydrology. The tenure-track applicants to make sure that is an Equal Opportunity, Affirmative Ac- appointment will be effective July 1, 2008. letters of evaluation are sent. All letters of tion Employer. The successful candidate must hold a evaluation are subject to Berkeley campus 000075 doctoral degree in an appropriate field policies on confidentiality of letters of and must demonstrate potential for high- evaluation, a summary of which can be quality research and teaching. Research found at http://math.berkeley.edu/ interests should incorporate a funda- employment_academic.html. UNIVERSITY OF CALIFORNIA AT mental approach to the hydrologic cycle Tenure applicants are expected to BERKELEY that could encompass theoretical aspects demonstrate leadership in research and Department of Mathematics of water transport, measurement tech- should send a curriculum vitae, list of Temporary Postdoctoral Positions nologies, integrative data analysis, and publications, a few selected reprints or predictive modeling. Examples of research preprints, and the names and addresses Several temporary positions beginning approaches include, but are not limited of three references to The Vice Chair for in Fall 2008 are anticipated for new and to, mechanistic studies in large-scale Faculty Affairs at the above address. Ap- recent Ph.D.’s of any age, in any area of water circulation, ecosystem response to plicants should indicate whether they are pure or applied mathematics. The terms dynamic water stressors, human-altered applying for an associate professor or a of these appointments may range from systems, responses to climate change, full professor position. The department one to three years. Applicants for NSF terrestrial and atmospheric coupling, and will assume responsibility to solicit letters or other postdoctoral fellowships are the water-energy nexus. Expanding the of evaluation and will provide evaluators encouraged to apply for these positions. disciplinary basis of hydrologic science with a copy of the summary of policies on Mathematicians whose research interests is highly desirable. The faculty member confidentiality of letters of evaluation. are close to those of regular department will teach undergraduate and graduate All applicants are requested to use members will be given some preference. courses as part of the Civil & Environ- the AMS standardized application form Applicants should send a resume and mental Engineering curricula. The faculty and to indicate their subject area using reprints, preprints, and/or dissertation member will be expected to interact with the AMS subject classification numbers. abstract, and ask three people to send faculty in the Department of Civil and The form is the Academic Employment letters of evaluation to The Vice Chair for Environmental Engineering, the College of in Mathematics, Application Cover Sheet. Faculty Affairs at the above address. All Engineering, research centers on campus, It is available courtesy of the American letters of evaluation are subject to Berke- and relevant professional organizations. Mathematical Society. ley campus policies on confidentiality of Applicants must send by November 9, Applications for both tenure-track and letters of evaluation, a summary of which 2007, a detailed resume, a statement of tenure applications must be postmarked can be found at http://math.berkeley. teaching and research interests, copies of by December 1, 2007. Applications post- edu/employment_academic.html. We no more than two publications or manu- marked after the deadline will not be request that applicants use the AMS stan- scripts, and the names and contact infor- considered. The University of California dardized application form and indicate mation for five references. Submission of is an Equal Opportunity, Affirmative Ac- their subject area using the AMS subject electronic applications is preferred. Please tion Employer. classification numbers. The form is the go to our department website at: http:// 000074 Academic Employment in Mathematics, www.ce.berkeley.edu. Alternately, hard Application Cover Sheet. It is available copy applications can be sent to Lisa Al- courtesy of the American Mathematical Society. varez-Cohen, Chair, Department of Civil UNIVERSITY OF CALIFORNIA AT Applications must be postmarked by and Environmental Engineering, MC 1710, BERKELEY ATTN: Hydrology Faculty Search Com- December 1, 2007. Applications post- Department of Mathematics mittee, University of California, Berkeley, marked after the deadline will not be Berkeley, CA 94720-1710. Applications Charles B. Morrey Jr. Assistant considered. The University of California postmarked after the deadline will not be Professorships is an Equal Opportunity, Affirmative Ac- considered. The University of California is tion Employer. We invite applications for these special an Equal Opportunity, Affirmative Action 000076 (non-tenure-track) positions effective July Employer. 1, 2008. The terms of these appointments 000064 may range from two to three years. Ap-

October 2007 Notices of the AMS 1201 Classified Advertisements

UNIVERSITY OF CALIFORNIA, UNIVERSITY OF CALIFORNIA, and/or leadership are particularly encour- LOS ANGELES SAN DIEGO aged to apply. Rank & Salary: assistant Department of Mathematics Department of Mathematics professor (9 month basis, step and salary 2008-2009 Faculty Positions commensurate with qualifications and The Department of Mathematics at the experience). Minimum Qualifications: The Mathematics Department is in a pe- University of California, San Diego, is seek- Ph.D. or equivalent in mathematics; dem- riod of increased hiring of tenured and ing outstanding candidates to fill approxi- onstrated achievements or potential for tenure-track faculty. Subject to adminis- mately 6 tenure-track/tenured positions excellence in research, teaching, profes- trative approval, we expect to make sev- to start July 2008. The level for the large sional service and leadership. Position eral regular appointments in a wide range majority of these positions is at the Assis- Available: July 1, 2008. Closing Date: of possible fields. We will also be making tant Professor level, however, one or two Positions are open until filled. Screening temporary and visiting appointments positions are available for distinguished will begin with applications postmarked mathematicians with exceptional research beginning in the academic year 2008-09 by November 15, 2007. To ensure full records of the highest caliber. in the following categories: consideration, applications and letters of (1) Tenure-Track/Tenured Faculty Posi- Applicants for all positions must pos- recommendation must arrive by the initial sess a Ph.D. and should have outstand- tion. screening date. Applicants must submit ing accomplishments in both research (2) E. R. Hedrick Assistant Professor- hard copies of the AMS Cover Sheet, a and teaching. We encourage applications ships. Salary is $55,400. And appoint- curriculum vitae, a research statement, from any area of pure mathematics, ap- ments are for three years. The teaching a teaching statement, and four letters of load is four quarter courses per year. plied mathematics, or statistics. Level of appointment will be based on quali- recommendation (at least one letter must (3) Research Assistant Professorships in address teaching experience and ability). Computational and Applied Mathematics fications with appropriate salary per UC pay scales. To receive full consideration, (Letters of recommendation will be treated (CAM). The salary is $55,400, and appoint- as confidential documents). Please direct ments are for three years. The teaching applications should be submitted online your letter writers to the UCSC Confi- load is normally reduced to two or three through http://www.mathjobs.org/ by dentiality Statement at: http://ahr. quarter courses per year by research fund- November 1, 2007. For further instruc- ucsc.edu/academic_policies_and_ ing as available. tions and information, see http://www. procedures/cappm/confstm.htm. (4) Assistant Adjunct Professorships in math.ucsd.edu/about/employment/ the Program in Computing (PIC). Appli- faculty. All applications should be sent to: Fac- cants for these positions must show very In compliance with the Immigration ulty Recruitment Committee, Mathematics strong promise in teaching and research Reform and Control Act of 1986, individu- Department, University of California, 1156 in an area related to computing. The teach- als offered employment by the University High Street, Santa Cruz, CA 95064. Please ing load is four one-quarter programming of California will be required to show refer to position #839-08 in your reply. courses each year and one seminar every documentation to prove identity and au- Inquiries [not applications] can be sent to two years. Initial appointments are for thorization to work in the United States [email protected]. UCSC is an EEO/AA one year and possibly longer, up to a before hiring can occur. UCSD is an Equal employer. See http://www.math.ucsc. maximum service of four years. The sal- Opportunity/Affirmative Action Employer edu/about/jobs.html for a complete ary is $59,100. with a strong institutional commitment job description. (5) Assistant Adjunct Professorships to the achievement of diversity among its 000051 and Research Postdocs. Normally appoint- faculty and staff. ments are for one year, with the possibility All applications should include the fol- of renewal. Strong research and teaching lowing items: 3 Reference Letters (Writers Illinois background required. The salary range is should upload their reference letters to: $50,900-$55,400. Teaching load for Ad- mathjobs.org or send them under sepa- NORTHWESTERN UNIVERSITY juncts is five quarter courses per year. rate cover; at least one letter should ad- If you wish to be considered for any of dress teaching experience in some depth), Department of Mathematics these positions you must submit an ap- Cover Letter, Curriculum Vitae, Publica- 2033 Sheridan Road plication via http://www.mathjobs.org. tions List, Research Statement, Teaching Evanston, Illinois 60208-2730 Submit the AMS Cover Sheet and support- Statement, and optionally a statement Boas Assistant Professor ing documentation electronically. about contributions to diversity. 000061 For fullest consideration, an applica- Applications are solicited for up to three tion must be submitted on or before Ralph Boas assistant professorships of December 12, 2007. Ph.D. is required for three years each starting September 2008. all positions. UNIVERSITY OF CALIFORNIA, These are non-tenure-track positions with The University of California asks that SANTA CRUZ a teaching load of four quarter courses per applicants complete the Equal Opportu- Mathematics Department year. We invite applications from qualified nity Employer survey for Letters and Sci- mathematicians in all fields. ence at the following URL: http://cis. The Mathematics Department at the Uni- Applications should be made electroni- ucla.edu/facultysurvey/. versity of California, Santa Cruz, solicits cally at www.mathjobs.org and should applications for two tenure-track (as- Under Federal law, the University of include (1) the American Mathematical sistant professor) positions in the areas California may employ only individuals Society Cover Sheet for Academic Em- of low dimensional topology or alge- who are legally authorized to work in the ployment, (2) a curriculum vitae, (3) a braic geometry, pending administrative United States as established by providing research statement, and (4) three letters of approval. Duties include mathematical documents specified in the Immigration research, undergraduate and graduate recommendation, one of which discusses Reform and Control Act of 1986. teaching and departmental and univer- the candidate’s teaching qualifications. UCLA is an Equal Opportunity/Affirma- sity service. The standard teaching load Inquiries may be sent to: boas@math. tive Action Employer. is four one-quarter courses per year. The northwestern.edu. 000070 department invites applications from Applications are welcomed at any time, all qualified mathematicians. Colleagues but the review process starts December who can contribute to the diversity and 1, 2007. Northwestern University is an excellence of the academic community Affirmative Action, Equal Opportunity through their research, teaching, service Employer committed to fostering a diverse

1202 Notices of the AMS Volume 54, Number 9 Classified Advertisements faculty; women and minority candidates Applicants are strongly encouraged to in- Maryland are especially encouraged to apply. clude information related to their teaching 000065 experience, such as a teaching statement JOHNS HOPKINS UNIVERSITY or evaluations from courses previously Department of Mathematics taught, as well as an AMS cover sheet. If NORTHWESTERN UNIVERSITY you have applied for an NSF Mathematical Subject to availability of resources and Department of Mathematics Sciences Postdoctoral Fellowship, please administrative approval, the Department 2033 Sheridan Road, include that information in your applica- of Mathematics solicits applications for tion, and let us know how you plan to use Evanston, Illinois 60208-2730 two non-tenure-track J. J. Sylvester As- it if awarded. sistant Professors for the 2008-2009 Applications are invited for anticipated Applications must be submitted online academic year. The J. J. Sylvester Assistant tenured or tenure-track positions starting through http://www.mathjobs.org. Professorship is a three-year position of- September 2008. Priority will be given to Questions may be directed to: appt- fered to recent Ph.D.’s with outstanding exceptionally promising research math- [email protected]. We will begin research potential. Candidates in all areas ematicians. We invite applications from screening applications on December 3, of pure mathematics, including analysis, qualified mathematicians in all fields. 2007. Screening will continue until all mathematical physics, geometric analysis, Applications should be made electroni- available positions are filled. The Univer- complex and algebraic geometry, number cally at http://www.mathjobs.org and sity of Chicago is an Equal Opportunity/ theory, and topology are encouraged to should include (1) the American Math- Affirmative Action Employer. apply. The teaching load is three courses ematical Society Cover Sheet for Academic 000055 per academic year. To submit your ap- Employment, (2) a curriculum vitae, (3) a plications go to http://www.mathjobs. research statement, and (4) three letters of org/jobs/jhu. Applicants are strongly recommendation, one of which discusses Indiana advised to submit their other materials the candidate’s teaching qualifications. electronically at this site. If you do not Inquiries may be sent to: boas@math. UNIVERSITY OF NOTRE DAME have computer access, you may mail your application to: Appointments Commit- northwestern.edu. Department of Mathematics Applications are welcome at any time. tee, Department of Mathematics, Johns Notre Dame NSF-SUMR Hopkins University, 404 Krieger Hall, Northwestern University is an Affirma- Instructorship in Mathematics tive Action, Equal Opportunity Employer Baltimore, MD 21218, and should include a vita, at least four letters of recommen- committed to fostering a diverse faculty; The Department of Mathematics of the dation of which one concerns teaching, women and minority candidates are espe- University of Notre Dame invites applica- and a description of current and planned cially encouraged to apply. tions from recent doctorates (since 2005) research. Write to: [email protected] 000066 for the position of Notre Dame NSF-SUMR for questions concerning these positions. instructor in mathematics. Candidates in Applications received by November 16, any specialty compatible with the research 2007, will be given priority. The Johns UNIVERSITY OF CHICAGO interests of the department will be consid- Hopkins University is an Affirmative Ac- ered. The position is for a term of three Department of Mathematics tion/Equal Opportunity Employer. Minori- years beginning August 22, 2008; it is not ties and women candidates are encour- 1. L.E. Dickson Instructor: This is open renewable and is not tenure-track. The aged to apply. to mathematicians who have recently teaching load is one course per semester. 000052 completed or will soon complete a doc- Additional duties include mentoring of torate in mathematics or a closely related honors mathematics majors, and appli- field, and whose work shows remarkable cants should provide evidence of prior promise in mathematical research and experience mentoring undergraduates. JOHNS HOPKINS UNIVERSITY teaching. The appointment typically is for The salary will be competitive with those Department of Mathematics two years, with the possibility of renewal of distinguished instructorships at other for a third year. The teaching obligation AMS Group I universities, and the posi- Subject to availability of resources and is up to four one-quarter courses per tion includes $10,000 per year of summer administrative approval, the Department year. For applicants who are U.S. citizens research support for each of the first of Mathematics solicits applications for or permanent residents, there is the pos- two summers. The position is associated two tenure-track assistant professors for sibility of reduced teaching and resources with the department’s recent successful the 2008-2009 academic year. The assis- for summer support and travel from the five–year NSF grant in the program “Men- tant professorship is a three-year position. department’s VIGRE grant. toring Through Critical Transition Points”. Candidates in all areas of pure math- 2. Assistant Professor: This is open to Applications, including a curriculum vitae ematics, including analysis, mathematical mathematicians who are further along in and a completed AMS standard cover physics, geometric analysis, complex and their careers, typically two or three years sheet, should be filed through MathJobs algebraic geometry, number theory, and past the doctorate. These positions are (http://www.MathJobs.org). Applicants topology are encouraged to apply. The intended for mathematicians whose work should also arrange for at least three let- teaching load is three courses per aca- has been of outstandingly high caliber. ters of recommendation to be submitted demic year. To submit your applications Appointees are expected to have the po- through the MathJobs system. These go to http://www.mathjobs.org/jobs/ tential to become leading figures in their letters should address the applicant’s jhu. Applicants are strongly advised to fields. The appointment is generally for research accomplishments and supply submit their other materials electronically three years, with a teaching obligation of evidence that the applicant has the abil- at this site. If you do not have computer three one-quarter courses per year. ity to communicate articulately and teach access, you may mail your application to: Appointments Committee, Department of Applicants will be considered for any of effectively. Notre Dame is an Equal Op- Mathematics, Johns Hopkins University, the positions above which seem appropri- portunity Employer, and we particularly 404 Krieger Hall, Baltimore, MD 21218, ate. Complete applications consist of (a) a welcome applications from women and and should include a vita, at least four cover letter, (b) a curriculum vitae, (c) three minority candidates. The evaluation of letters of recommendation of which one or more letters of reference, at least one candidates will begin December 1, 2007. concerns teaching, and a description of of which addresses teaching ability, and Information about the department is avail- current and planned research. Write to: (d) a description of previous research and able at http://math.nd.edu. [email protected] for questions con- plans for future mathematical research. 000100 cerning these positions. Applications re-

October 2007 Notices of the AMS 1203 Classified Advertisements ceived by November 16, 2007, will be given email duplicates of items already submit- complete by January 1, 2008, to receive priority. The Johns Hopkins University is ted via mathjobs. full consideration. We request that your an Affirmative Action/Equal Opportunity MIT is an Equal Opportunity, Affirma- letters of reference be submitted by the re- Employer. Minorities and women candi- tive Action Employer. viewers online via mathjobs. We will also dates are encouraged to apply. 000083 accept recommendations either as PDF at- 000053 tachments sent to: [email protected], MASSACHUSETTS INSTITUTE OF or as paper copies mailed to: Committee TECHNOLOGY on Statistics, Room 2-263, Department of Massachusetts Department of Mathematics Mathematics, MIT, 77 Massachusetts Ave., Applied Mathematics Cambridge, MA 02139-4307. Please do not mail or email duplicates of items already MASSACHUSETTS INSTITUTE OF submitted via mathjobs. TECHNOLOGY The applied mathematics group at MIT is seeking to fill combined teaching and MIT is an Equal Opportunity, Affirma- Department of Mathematics research positions at the level of instruc- tive Action Employer. 000085 The Mathematics Department at MIT is tor, assistant professor or higher, begin- seeking to fill positions at the level of ning September 2008. Appointments are assistant professor or higher for Sep- mainly based on exceptional research tember 2008. Appointments are based qualifications. Candidates in all areas of Michigan on exceptional research contributions applied mathematics, including physi- in pure mathematics. Appointees will be cal applied mathematics, computational UNIVERSITY OF MICHIGAN, molecular biology, numerical analysis, expected to fulfill teaching duties and ANN ARBOR scientific computation, and theoretical pursue their own research program. We Department of Mathematics request that applications and other ma- computer science will be considered. Current activities of the group include: terials, including (a) curriculum vitae, (b) Pending authorization, the department combinatorics, operations research, the- research description, and (c) three letters invites applications for a Lecturer III in ory of algorithms, numerical analysis, of recommendation, be submitted online mathematics to begin September 2008. astrophysics, condensed matter physics, at: http://www.mathjobs.org. Applica- This is not a tenure-track position but may computational physics, fluid dynamics, tions should be complete by December be renewed, annually for up to the first geophysics, nonlinear waves, theoretical 1, 2007, to receive full consideration. four years, and thereafter for intervals of and computational molecular biology, We request that your letters of reference three to five years. Criteria for renewal material sciences, quantum computing be submitted by the reviewers online via are excellence in classroom teaching and and quantum field theory, but new hiring mathjobs. We will also accept recommen- participation in administration of the may involve other areas as well. dations either as PDF attachments sent to: department’s introductory program and [email protected], or as paper copies We request that applications and other instructor development. Interest and mailed to: Pure Mathematics Committee, materials, including (a) curriculum vitae, activity in pedagogical research is encour- Room 2-263, Department of Mathematics, (b) research description, and (c) three aged but not essential for reappointment. MIT, 77 Massachusetts Ave., Cambridge, letters of recommendation, be submitted The successful candidate is likely to have MA 02139-4307. Please do not mail or online at: http://www.mathjobs.org, both a doctorate and substantial experi- email duplicates of items already submit- and preferably well in advance of our ence in teaching mathematics. Please ted via mathjobs. deadline of January 1, 2008, since we submit a curriculum vitae, evidence of MIT is an Equal Opportunity, Affirma- will begin our deliberations in December. teaching excellence, and the names of at tive Action Employer. We request that your letters of reference least three references. Application ma- 000082 be submitted by the reviewers online via terials should preferably be submitted mathjobs. We will also accept recommen- electronically through the AMS website MASSACHUSETTS INSTITUTE OF dations either as PDF attachments sent MathJobs.Org. Alternatively, applications [email protected] TECHNOLOGY to: , or as paper may be sent to: Personnel Committee, copies mailed to: Applied Mathematics Department of Mathematics University of Michigan, Department of Committee, Room 2-345, Department of Mathematics, 2074 East Hall, 530 Church C. L. E. Moore Instructorships in Mathematics, MIT, 77 Massachusetts Ave., Mathematics Street, Ann Arbor MI 48109-1043. Ap- Cambridge, MA 02139-4307. Please do not plications are considered on a continuing mail or email duplicates of items already basis but candidates are urged to apply by These positions for September 2008 are submitted via mathjobs. open to mathematicians who show defi- November 1, 2007. Inquiries may be made MIT is an Equal Opportunity, Affirma- nite promise in research. Appointees will by email to math-fac-search@umich. tive Action Employer. be expected to fulfill teaching duties and edu. More detailed information regard- 000084 pursue their own research program. We ing the department may be found on our request that applications and other ma- website: http://www.math.lsa.umich. MASSACHUSETTS INSTITUTE OF terials, including (a) curriculum vitae, (b) edu. Women and minority candidates are research description, and (c) three letters TECHNOLOGY encouraged to apply. The University of of recommendation, be submitted online Department of Mathematics: Statistics Michigan is an Equal Opportunity/Affir- at: http://www.mathjobs.org. Applica- mative Action Employer . The Department of Mathematics at MIT tions should be complete by December 000059 is seeking to fill combined teaching and 1, 2007, to receive full consideration. research positions at the level of instruc- We request that your letters of reference tor, assistant professor or higher in STA- be submitted by the reviewers online via UNIVERSITY OF MICHIGAN TISTICS or APPLIED PROBABILITY begin- mathjobs. We will also accept recommen- Department of Mathematics ning September 2008. Appointments are dations either as PDF attachments sent to: [email protected], or as paper copies mainly based on exceptional research Pending authorization, the Department qualifications. We request that applica- mailed to: Pure Mathematics Committee, of Mathematics anticipates having one tions and other materials, including (a) Room 2-263, Department of Mathematics, or more openings at the tenure-track or curriculum vitae, (b) research description, MIT, 77 Massachusetts Ave., Cambridge, tenured-level. Candidates should hold a and (c) three letters of recommendations, MA 02139-4307. Please do not mail or Ph.D. in mathematics or a related field be submitted online at: http://www. and should show outstanding promise mathjobs.org. Applications should be

1204 Notices of the AMS Volume 54, Number 9 Classified Advertisements and/or accomplishments in both research Minneapolis, MN 55455 to submit their letters on line through and teaching. Applications are encouraged email: [email protected] http://mathjobs.org. If they are unable from any area of pure, applied, computa- Applicants must include the following: to do so, they may send their letters to the tional, or interdisciplinary mathematics. Cover letter, curriculum vitae, at least 4 above mentioned address. In addition to Salaries are competitive and are based on letters of recommendation, one of which your MathJobs application, the University credentials. Junior candidates should fur- should address teaching ability, descrip- of Minnesota requires all applicants to reg- nish a placement dossier consisting of a tion of research and a teaching statement. ister at the website http://employment. letter of application, curriculum vitae and Reference letter writers should be asked umn.edu. At this site you should first three letters of recommendation; senior to submit their letters online through click on the link “Search Positions”. Enter candidates should send a letter of applica- http://mathjobs.org. If they are un- tion, curriculum vitae, and names of three able to do so, they may send their letters Requisition Number 149255. When the suggested references. In all cases please to the above mentioned address. In ad- job listing appears click the “View” link provide a statement of teaching philoso- dition to your MathJobs application, the in the Position Title field and then the phy and experience, evidence of teaching University of Minnesota requires all ap- button “Apply for this Posting”. At this excellence, and a statement of current plicants to register at the website http:// point you will be prompted to “Fill out a and future research plans. Application employment.umn.edu. At this site you new Application”. In your application, you materials should preferably be submitted should first click on the link “Search Posi- should enter your name and optional de- electronically through the AMS website tions”. Enter Requisition Number 149251. mographic information. It is not necessary When the job listing appears click the MathJobs.Org. Alternatively, applications to fill out your complete contact informa- “‘View” link in the Position Title field and may be sent to: Personnel Committee, tion or to submit your other application University of Michigan, Department of then the button “Apply for this Posting”. At this point you will be prompted to “Fill material to this site. Mathematics, 2074 East Hall, 530 Church out a new Application”. In your applica- The University of Minnesota is an Equal Street, Ann Arbor MI 48109-1043. Ap- tion, you should enter your name and Opportunity Employer/Educator. plications are considered on a continuing optional demographic information. It is 000072 basis but candidates are urged to apply by not necessary to fill out your complete November 1, 2007. Inquiries may be made contact information or to submit your by email to math-fac-search@umich. other application material to this site. edu. More detailed information regard- UNIVERSITY OF MINNESOTA The University of Minnesota is an Equal ing the department may be found on our Opportunity Employer/Educator. School of Mathematics website: http://www.math.lsa.umich. 000071 edu. Women and minority candidates are The School of Mathematics of the Uni- encouraged to apply. The University of versity of Minnesota in conjunction with Michigan is supportive of the needs of the Institute for Mathematics and its UNIVERSITY OF MINNESOTA dual career couples and is an Equal Op- Applications (IMA) seeks an outstanding School of Mathematics portunity/Affirmative Action Employer. mathematical scientist with a record of 000060 The School of Mathematics of the Univer- interdisciplinary research for a faculty sity of Minnesota is seeking outstanding position, anticipated to be at the tenure candidates for 2-3 tenured or tenure-track or tenure-track level depending on quali- Minnesota faculty positions starting fall semester fications. The IMA is a partnership of the 2008. Particular attention will be given National Science Foundation, the Univer- UNIVERSITY OF MINNESOTA to applicants at the assistant or associate sity of Minnesota, and a consortium of professor level with strong interests in Dunham Jackson Assistant Professor affiliated institutions. Since its founding Geometry, Probability, and Scientific Com- in 1982, the IMA has established itself as a putation. Candidates should have a Ph.D. This is a three-year appointment from leading research institute for mathematics fall semester 2008, through spring se- or equivalent degree in mathematics or a and its applications, and the successful mester 2011, with a teaching load of 3 closely related field and excellent records candidate will enjoy the benefits of its one-semester courses per academic year. in both research and teaching. Outstanding research and teaching abili- For full consideration, applications and extraordinary scientific environment. In ties are required. Preference will be given all supporting materials must be submit- addition to faculty duties in the School of to applicants whose research interests ted electronically through: http://www. Mathematics, the successful candidate will are compatible with those of the school. mathjobs.org by December 1, 2007. support the activities of the IMA through Applicants should have received or expect Applications received after the deadline mentorship, program participation and to receive a Ph.D. in mathematics no ear- will be considered as positions remain. planning, and interaction with visitors, No paper submission is needed unless the lier than Jan. 1, 2007, and no later than and have teaching load set accordingly. candidate is unable to submit electroni- August 27, 2008. Salary is competitive. cally. In which case letters should be sent Candidates should have a Ph.D. or For full consideration, applications and to the following address: equivalent terminal degree in mathemat- all supporting materials must be submit- Lawrence F. Gray ics or closely related field and excellent ted electronically through: http://www. Professor and Head records in both research and teaching. mathjobs.org by December 1, 2007. For full consideration, applications and all Applications received after the deadline School of Mathematics supporting materials should be submitted will be considered as positions remain. University of Minnesota electronically through the AMS mathjobs No paper submission is needed unless the 127 Vincent Hall candidate is unable to submit electroni- 206 Church Street S. E. website at http://www.mathjobs.org cally. In which case letters may be sent to Minneapolis, MN 55455 by December 1, 2007. Applications will the following address: email: [email protected]. be reviewed from that date and continue Lawrence F. Gray Applicants must include the following: until the position is filled. No paper sub- Professor and Head Cover letter, Curriculum vitae, at least 4 mission is needed unless the candidate is School of Mathematics letters of recommendation, one of which unable to submit electronically. Reference University of Minnesota should address teaching ability, descrip- letter writers should be asked to submit 127 Vincent Hall, tion of research and a teaching statement. their letters online through http://www. 206 Church Street S.E. Reference letter writers should be asked mathjobs.org. If they are unable to do

October 2007 Notices of the AMS 1205 Classified Advertisements so, they may send their letters to the fol- Six of these fellowships will be available more half-time visiting positions (rank lowing address: for the 2008-09 academic year. To be eli- based on experience) for mathematics Lawrence F. Gray gible for the von Neumann Fellowships, professors on sabbatical/other leaves Professor and Head applicants should be at least 5 years from colleges, universities, and engineer- School of Mathematics following the receipt of their Ph.D. but ing schools for our Teaching Program Vis- not yet eligible to receive their first paid 127 Vincent Hall iting Faculty Positions beginning August sabbatical. 206 Church Street S. E. 16, 2008. Candidates with substantial The Veblen Research Instructorship is Minneapolis, MN 55455 experience teaching undergraduate math- a three-year position which the School of ematics, and with teaching and research Applicants must include the following: Mathematics and the Department of Math- Cover letter, curriculum vitae, at least 4 interests compatible with current faculty, ematics at Princeton University estab- are sought. Successful candidates are letters of recommendation, one of which lished in 1998. Three-year instructorships should address teaching ability, and de- expected to pursue a program of study will be offered each year to candidates in and/or research at Cornell. The normal scription of research. In addition to your pure and applied mathematics who have MathJobs application, the University of duties are to teach two identical courses received their Ph.D. within the last three each semester. The department actively Minnesota requires all applicants to reg- years. The first and third year of the ister at the website http://employment. encourages applications from women and instructorship will be spent at Princeton minority candidates. umn.edu. At this site you should first click University and will carry regular teaching Applicants are strongly encouraged on the link “Search Postings”. Enter the responsibilities. The second year will be http://www. Requisition Number 149253. When the spent at the Institute and dedicated to to apply electronically at: job listing appears click the “View” link independent research of the instructor’s mathjobs.org. in the Position Title field and then the choice. For information about these positions button “Apply for this Posting”. At this Application materials may be requested and application instructions, see: http:// point you will be prompted to “Fill out a from Applications, School of Mathemat- www.math.cornell.edu/Positions/ new Application”. In your application you ics, Institute for Advanced Study, Ein- facpositions.html. Deadline December should enter your name and optional de- stein Drive, Princeton, NJ 08540; email: 1, 2007. Cornell University is an Affirma- mographic information. It is not necessary [email protected]. Applica- tive Action/Equal Opportunity Employer to fill out your complete contact informa- tion forms may be downloaded via a Web and Educator. tion or to submit your other application connection to http://www.math.ias. 000087 materials to this site. edu. Application deadline is December 1. The University of Minnesota is an Equal The Institute for Advanced Study is CORNELL UNIVERSITY Opportunity Employer and Educator committed to diversity and strongly en- Department of Mathematics 000073 courages applications from women and minorities. The Department of Mathematics at Cornell 000068 University invites applications for possible New Jersey visiting positions, academic year or one- semester teaching positions (rank based on experience) beginning August 16, 2008. INSTITUTE FOR ADVANCED STUDY, New York We are seeking candidates who have excel- SCHOOL OF MATHEMATICS lent teaching skills. Teaching load varies Department of Mathematics CORNELL UNIVERSITY from 1-4 courses per year, depending Department of Mathematics The School of Mathematics has a limited on the individual and the availability of courses. Candidates with teaching and number of memberships, some with finan- The Department of Mathematics at Cornell cial support for research in mathematics research interests compatible with cur- University invites applications for two or rent faculty are sought. The department and computer science at the Institute more H. C. Wang Assistant Professors, during the 2008-09 academic year. Candi- actively encourages applications from non-renewable, 3-year term beginning women and minority candidates. dates must have given evidence of ability July 1, 2008. Successful candidates are Applicants are strongly encouraged in research comparable at least with that expected to pursue independent research to apply electronically at: http://www. expected for the Ph.D. degree. at Cornell and teach three courses per mathjobs.org. During the 2008-09 year, Alice Chang year. The department actively encourages of Princeton University will lead a special applications from women and minority For information about our positions program on geometric partial differential candidates. and application instructions, see: http:// equations. The emphasis will be on non- Applicants are strongly encouraged www.math.cornell.edu/Positions/ linear partial differential equations with to apply electronically at: http://www. facpositions.html. Applicants will be applications to problems in differential, mathjobs.org. automatically considered for all eligible positions. Deadline December 1, 2007. conformal and convex geometry. Top- For information about our positions Early applications will be regarded favor- ics covered will include Yamabe type and application instructions, see: http:// equations, Q-curvature equations, fully www.math.cornell.edu/Positions/ ably. Cornell University is an Affirmative non-linear equations in conformal and facpositions.html. Applicants will be Action/Equal Opportunity Employer and convex geometry, construction of confor- automatically considered for all eligible Educator. mal invariants and operators, problems positions. Deadline December 1, 2007. 000088 in conformally compact Einstein mani- Early applications will be regarded favor- folds, measure and probability theory ably. Cornell University is an Affirmative CORNELL UNIVERSITY approaches to the Ricci Tensor. Partial Action/Equal Opportunity Employer and Department of Mathematics differential equations continue to be one Educator. of the central tools for studying geomet- 000086 The Department of Mathematics at Cor- ric and even topological questions, and nell University invites applications for one goal of this program will be to bring CORNELL UNIVERSITY a tenure-track assistant professor posi- researchers in geometry and PDE together tion, or higher rank, pending adminis- Department of Mathematics to study problems of common interest in trative approval, starting July 1, 2008. areas such as those mentioned above. The Department of Mathematics at Cornell Applications in all areas of mathematics Recently the school has established the University invites applications for two or will be considered with a priority given von Neumann Early Career Fellowships. to probability. The department actively

1206 Notices of the AMS Volume 54, Number 9 Classified Advertisements encourages applications from women and than routine interest. Candidates are re- University is affiliated with the Baptist minority candidates. quired to have received a Ph.D. degree or General Convention of Texas. As an Af- Applicants are strongly encouraged equivalent by the start of their appoint- firmative Action/Equal Employment Op- to apply electronically at http://www. ment, and they may have up to three years portunity Employer, Baylor encourages mathjobs.org. of prior academic and/or postdoctoral minorities, women, veterans, and persons For information about our positions research experience. with disabilities to apply. Applicants are and application instructions, see: http:// Applicants should have strong research encouraged to submit all application www.math.cornell.edu/Positions/ potential and a commitment to teaching. materials online through MathJobs.org facpositions.html. Applicants will be Field of research should be consonant via the URL: http://www.mathjobs.org/ automatically considered for all eligible with the current research interests of jobs. Alternatively, send all materials to: positions. Deadline November 1, 2007. the department. For full consideration, a Mathematics Search Committee, Baylor Early applications will be regarded favor- curriculum vitae, an AMS Standard Cover University, One Bear Place #97328, Waco, ably. Cornell University is an Affirmative Sheet, and three letters of recommenda- TX 76798-7328; email: Math_Search@ Action/Equal Opportunity Employer and tion must be received by December 1, baylor.edu. Educator. 2007. All inquiries and materials should 000091 000089 be addressed to: Junior Search Committee, Department of Mathematics, Box 1917, Brown University, Providence, RI 02912. To BAYLOR UNIVERSITY access the AMS Standard Cover Sheet, visit Rhode Island our website: http://www.math.brown. Department of Mathematics edu/juniorsearch.html. Email inquiries BROWN UNIVERSITY The Department of Mathematics invites should be addressed to: juniorsearch@ applications for a postdoctoral position, Department of Mathematics math.brown.edu. Brown University is an starting in August 2008. This position Equal Opportunity/Affirmative Action may be renewable annually to a maximum The Mathematics Department at Brown Employer and encourages applications of three years and is not a tenure-track University invites applications for one from women and minorities. position. Customarily, the teaching load position at the level of tenured associate 000063 or full professor to begin July 1, 2008 in is two three-hour courses each semester. the area of analysis, broadly construed. Salary and benefits are competitive. Excel- [Exceptional candidates with less experi- lence in teaching and research is essential. ence may also be considered for a ten- Texas The department seeks candidates whose ure-track associate professor position.] research interests are compatible with Candidates should have a distinguished BAYLOR UNIVERSITY those of current faculty. Active research research record and a strong commit- Department of Mathematics areas in the department are in the general ment to excellence in undergraduate and areas of algebra, analysis, differential graduate teaching. Preference will be The Department of Mathematics invites equations, mathematical physics, numeri- given to applicants with research inter- applications for a tenure-track position cal analysis, representation theory, and ests consonant with those of the present at the assistant professor level, start- topology. An application must include members of the department. For more in- ing in August 2008. Salary and benefits a current curriculum vitae and state- formation see: http://www.math.brown. are competitive. Excellence in teaching ments describing interests and goals in edu/faculty/faculty.html. Qualified and research is essential. Strong poten- research and in teaching. In addition, individuals are invited to send a letter tial for obtaining extramural funding is at least three recent letters of reference desirable. Special consideration will be of application and a curriculum vitae to: must be made available on MathJobs. given to strong applicants with research Senior Search Committee, Department of org or be sent directly to the search com- interests in the general areas of analysis, Mathematics, Box 1917, Brown University, mittee. An applicant who has received topology, algebra, and numerical linear Providence, Rhode Island 02912. Appli- the doctoral degree within the last four algebra. Exceptional scholars in any area cants for full professor should include the years is encouraged to include a copy of names of five references who would be of specialization are strongly encouraged the doctoral transcript. Applications will contacted at the appropriate time by the to apply. An application must include a be reviewed beginning November 1, 2007. Search Committee. Applicants for associ- current curriculum vitae and statements To ensure full consideration, an applica- ate professor should have three letters of describing interests and goals in research tion should be received by November 15, reference sent at the time of application. and in teaching. In addition, at least three 2007, but applications will be accepted Applications received by November 15, recent letters of reference must be made 2007, will receive full consideration, but available on MathJobs.org or be sent until the position is filled or the search the search will remain open until the posi- directly to the search committee. An appli- is terminated. Baylor University has ap- tion is closed or filled. For further infor- cant who has received the doctoral degree proximately 14,000 students. The depart- mation or inquiries, write to: srsearch@ within the last four years is encouraged to ment has 30 faculty members and offers math.brown.edu. Brown University is an include a copy of the doctoral transcript. B.A., B.S., M.S., and Ph.D. degrees. Please Equal Opportunity/Affirmative Action Applications will be reviewed beginning visit the Baylor websites: http://www. Employer and encourages applications November 1, 2007. To ensure full consid- baylor.edu and http://www.baylor. from women and minorities. eration, an application should be received edu/math/ for further information about 000062 by November 15, 2007, but applications the university and the department. Baylor will be accepted until the position is University is affiliated with the Baptist filled or the search is terminated. Bay- General Convention of Texas. As an Af- BROWN UNIVERSITY lor University has approximately 14,000 firmative Action/Equal Employment Op- portunity Employer, Baylor encourages Department of Mathematics students. The department has 30 faculty members and offers B.A., B.S., M.S., and minorities, women, veterans, and persons J. D. Tamarkin Assistant Professorship: Ph.D. degrees. The university provides with disabilities to apply. Applicants are One or two three-year non-tenured non- generous benefits including tuition remis- encouraged to submit all application renewable appointments, beginning July sion for qualified family members. Please materials online through MathJobs.org 1, 2008. The teaching load is one course visit the Baylor websites: http://www. via the URL: http://www.mathjobs.org/ one semester, and two courses the other baylor.edu and http://www.baylor. jobs. Alternatively, send all materials to: semester and consists of courses of more edu/math/ for further information about Mathematics Search Committee, Baylor the university and the department. Baylor University, One Bear Place #97328, Waco,

October 2007 Notices of the AMS 1207 Classified Advertisements

TX 76798-7328; email: Math_Search@ interests are close to those of our regular Underrepresented groups are encouraged baylor.edu. faculty members. Senior Visiting Positions to apply. 000092 may be for a semester or one year period. UT Arlington is an EO/AA Employer. The complete dossier should be received 000069 by December 15, 2007. Early applications RICE UNIVERSITY are encouraged since the department will Mathematics Department start the review process in October, 2007. Applicants should send the completed Utah The Department of Mathematics invites “AMS Application Cover Sheet”, a vita, and UNIVERSITY OF UTAH applications for an anticipated position arrange to have letters of recommenda- at the rank of tenure-track assistant pro- tion sent to: Faculty Hiring, Department Department of Mathematics of Mathematics, Texas A&M University, fessor; candidates who could make an The Department of Mathematics at the College Station, Texas 77843-3368. Fur- extraordinary contribution to the depart- University of Utah invites applications for ther information can be obtained from: ment may be considered at other levels. the following positions: All applicants should have extremely http://www.math.tamu.edu/hiring. Full-time tenure-track or tenured ap- strong research potential and demon- Texas A&M University is an Equal Op- pointments at the level of assistant, as- strated success in the classroom. Send a portunity Employer. The university is ded- sociate, or full professor. Special consid- curriculum vitae to: icated to the goal of building a culturally eration will be given to candidates in the diverse and pluralistic faculty and staff Appointments Committee, area of statistics. Department of Mathematics, committed to teaching and working in a Three-year Scott, Wylie, Burgess, and Rice University, P. O. Box 1892, multicultural environment and strongly VIGRE Assistant Professorships, depend- Houston, TX 77251-1892. encourages applications from women, ing on funding availability. In addition, please provide evidence of minorities, individuals with disabilities, and veterans. The university is responsive IGERT and RTG Postdoctoral Fellow- teaching skills and solicit at least 3 let- ships. IGERT fellowship applicants should ters of reference, asking that they be sent to the needs of dual career couples. 000050 have a background in mathematical biol- directly to the address above. Submission ogy; while RTG fellowship applicants of the AMS Application Cover Sheet would should have a background in applied and be greatly appreciated. Applications which computational mathematics and have UNIVERSITY OF TEXAS AT ARLINGTON are complete by November 1, 2007, will be interests in working in mathematical assured consideration. Department of Mathematics biology. These postdoctoral fellowships Rice University is an Equal Opportunity/ are 3-year positions. See http://www. Affirmative Action Employer and strongly The Department of Mathematics at The University of Texas at Arlington invites math.utah.edu/research/mathbio/ encourages applications from women and opportunities.html. members of underrepresented minority applications for two tenure-track assistant professor positions beginning September Please see our website at http://www. groups. math.utah.edu/positions for infor- 000047 1, 2008, subject to available funding. Ten- ured appointments at the rank of associ- mation regarding available positions, ate or full professor may be considered application requirements and deadlines. Applications must be completed through TEXAS A&M UNIVERSITY for exceptional candidates with a strong record of external funding. The mini- the website http://www.mathjobs.org. The Department of Mathematics mum qualifications are an earned Ph.D. The University of Utah is an Equal Op- portunity, Affirmative Action Employer The Department of Mathematics antici- in mathematics, statistics, or mathematics education. At least two years of experience and encourages applications from women pates several openings for tenured, ten- and minorities, and provides reasonable ure-eligible, and visiting faculty positions beyond the Ph.D. is preferable. Demonstrated excellence in research accommodation to the known disabilities beginning fall 2008. The field is open, but of applicants and employees. we particularly seek applications from and teaching and a strong potential for The University of Utah values candidates individuals whose mathematical interests external funding are essential. While out- who have experience working in settings would augment and build upon existing standing applicants from all mathematical with students from diverse backgrounds, strengths both within the Mathematics research areas will be considered, prefer- and possess a strong commitment to Department as well as other departments ence will be given to those with significant improving access to higher education for in the university. Salary, teaching loads research and scholarly accomplishments historically underrepresented students. and start-up funds are competitive. For in statistics, operations research/com- 000067 a tenured-position the applicant should binatorics, algebra/algebraic geometry, have an outstanding research reputation or differential equations. For more de- and would be expected to fill a leadership tails, visit the department’s webpage role in the department. An established at: http://www.uta.edu/math/pages/ Wisconsin research program, including success in main/employment.htm. attracting external funding and supervi- Applicants should send a letter of ap- UNIVERSITY OF WISCONSIN - MADISON sion of graduate students, and a demon- plication plus a complete curriculum Department of Mathematics strated ability and interest in teaching are vitae, statement on research interests, required. Informal inquiries are welcome. statement of teaching philosophy, one The Department of Mathematics invites For an assistant professorship, we seek or two representative publications, and applications for Van Vleck Visiting Assis- strong research potential and evidence an AMS cover sheet to: Dr. Barbara Ship- tant Professorships to begin August 25, of excellence in teaching. Research pro- man, Chair, Faculty Recruiting Committee, 2008. Appointments are for a fixed term ductivity beyond the doctoral dissertation Department of Mathematics, The Univer- of two or three years. The usual teaching will normally be expected. We also have sity of Texas at Arlington, Arlington, TX load is two courses per semester. Candi- several visiting positions available. Our 76019. Applicants should also arrange to dates with interests overlapping those of Visiting Assistant Professor positions are have at least three letters of recommenda- specific faculty members may be offered for a three year period and carry a three tion sent to the above address. Inquiries support from sponsored research grants course per year teaching load. They are about the position may be directed to: together with a lower teaching load. Or- intended for those who have recently re- [email protected]. Review of applica- dinarily only those applicants who have ceived their Ph.D. and preference will be tions will begin on January 21, 2008, and received their doctorate since 2006 will given to mathematicians whose research will continue until the positions are filled. be considered. Promise of excellence in

1208 Notices of the AMS Volume 54, Number 9 Classified Advertisements research and teaching is important. Pref- will be commensurate with experience and more information about the department, erence will be given to candidates who are research record. please visit our website at http://www. likely to interact well with other members Applicants are strongly encouraged to math.ualberta.ca/. of the department. apply online as described at: http://www. Applications should include a curricu- Applicants should send a completed math.ubc.ca/Dept/jobs.htm#Apply. lum vitae, a research statement, a teach- AMS Standard Cover Sheet, a curriculum Alternatively, applicants may send a ing profile outlining experience and/or vitae which includes a publication list, and current CV including a list of publica- interests, and at least three confidential a brief statement of research plans to: tions, statement of research and teaching letters of reference. Hiring Committee interests, a teaching dossier or similar The closing date for applications is Dept. of Mathematics, Van Vleck Hall record of teaching experience, and should November 16, 2007, or until a suitable University of Wisconsin-Madison arrange for three letters of recommenda- candidate is found. Early applications are 480 Lincoln Drive tion to be sent directly to: encouraged. Madison, WI 53706-1388 Chair, Departmental Committee on Interested applicants may apply to: Appointments Arturo Pianzola, Chair Applicants should also arrange to have Department of Mathematics Department of Mathematical and Sta- sent to the above address, three to four #121-1984 Mathematics Road tistical Sciences letters of recommendation, at least one University of British Columbia University of Alberta of which must discuss the applicant’s Vancouver, B.C., Canada, V6T 1Z2 Edmonton, Alberta, Canada T6G 2G1 teaching experiences and capabilities. In order to ensure full consideration, ap- email: [email protected]. Other evidence of good teaching will be plications should be received by Novem- ca helpful. ber 20, 2007. All qualified candidates are encouraged to The Department of Mathematics is com- The department is one of the leading apply; however, Canadians and permanent mitted to increasing the number of women mathematics departments in Canada and residents will be given priority. and minority faculty. The University of has strong connections with other mathe- The University of Alberta hires on the Wisconsin is an Affirmative Action, Equal matical institutes, such as the Pacific Insti- basis of merit. We are committed to the Opportunity Employer and encourages tute for the Mathematical Sciences (PIMS), principle of equity in employment. We applications from women and minorities. Mathematics of Information Technology welcome diversity and encourage applica- Unless confidentiality is requested in writ- and Complex Systems (MITACS), Banff tions from all qualified women and men, ing, information regarding the applicants International Research Station (BIRS), and including persons with disabilities, mem- must be released upon request. Finalists the UBC Institute of Applied Mathematics bers of visible minorities, and Aboriginal cannot be guaranteed confidentiality. (IAM). For more information see http:// persons. For more information about the posi- www.math.ubc.ca. 000094 tion please consult: http://www.math. The University of British Columbia hires wisc.edu. on the basis of merit and is committed Deadline for Applications: December 10, to employment equity. We encourage all UNIVERSITY OF ALBERTA 2007, although applications will continue qualified persons to apply; however Ca- Department of Mathematics to be considered until all available posi- nadian citizens and permanent residents Tenure-Track Position, tions are filled. will be given priority. 000090 Geometrical Functional Analysis 000093 The Department of Mathematical and Statistical Sciences at the University of Canada UNIVERSITY OF ALBERTA Alberta invites applications for a tenure- Tenure-Track Position, track position in the area of geometrical Algebraic Geometry functional analysis. We primarily seek UNIVERSITY OF BRITISH COLUMBIA candidates at the assistant professor Department of Mathematics The Department of Mathematical and level, but exceptional candidates at a more Statistical Sciences at the University of senior level will be considered. The Mathematics Department at the Alberta invites applications for a tenure- The successful candidate will have es- University of British Columbia is seek- track position in the area of algebraic tablished accomplishments and outstand- ing outstanding candidates for at least geometry. We primarily seek candidates ing promise in research, as well as a strong three positions, subject to funding, at the at the assistant professor level, but excep- commitment to graduate and undergradu- tenure-track assistant professor level, with tional candidates at a more senior level ate teaching. Candidates must hold a Ph.D. a starting date of July 1, 2008. Exceptional will be considered. degree. We offer an excellent research en- candidates at the associate professor or The successful candidate will have es- vironment with a normal teaching load of full professor level may be considered. tablished accomplishments and outstand- three courses per year. A fit with some of Postdoctoral experience is normally ex- ing promise in research, as well as a strong the existing research being presently con- pected. Priority research areas are analy- commitment to graduate and undergradu- ducted in the department is an asset. For sis, combinatorics/discrete mathematics, ate teaching. Candidates must hold a Ph.D. more information about the department, mathematical finance, partial differential degree. We offer an excellent research please visit our website at http://www. equations, probability, and scientific com- environment with a normal teaching load math.ualberta.ca/. putation. More detail on hiring priorities of three courses per year. A close fit with We are looking for specialists in any of will be posted by September 1, 2007, at some of the existing research being pres- the areas of geometric functional analysis http://www.math.ubc.ca/priorities. ently conducted in the department is an including asymptotic theory of normed In any event, exceptional candidates in any asset. spaces and high-dimensional convex ge- area of mathematics may be considered. Alberta is one of the leading mathemat- ometry, related probabilistic methods, Joint positions with other departments ics departments in Canada and has strong geometric inequalities and concentra- may also be possible. connections with other mathematical tion inequalities, and related discrete The successful applicant is expected institutes, such as the Pacific Institute for mathematics aspects. Current research to work in an area of interest to current the Mathematical Sciences (PIMS), Math- strengths in the analysis group of the faculty, to interact with related groups in ematics of Information Technology and department include asymptotic geometric the department and to have demonstrated Complex Systems (MITACS), and the Banff analysis, abstract harmonic analysis, Ban- International Research Station (BIRS). For interest and ability in teaching. The salary ach spaces, Banach algebras and Banach

October 2007 Notices of the AMS 1209 Classified Advertisements lattices, operator theory, approximation areas such as regression, design, sampling of three courses per year. A close fit with theory, Fourier and wavelet analysis. and notions of robustness and of statisti- some of the existing research being pres- Alberta is one of the leading mathemat- cal learning as applied to these and other ently conducted in the department is an ics departments in Canada and has strong areas, and on to theoretical investigations asset. connections with other mathematical as embodied by mathematical statistics, Alberta is one of the leading mathemat- institutes, such as the Pacific Institute for probability, and stochastic processes. ics departments in Canada and has strong the Mathematical Sciences (PIMS), Math- Alberta is one of the leading mathemat- connections with other mathematical ematics of Information Technology and ics departments in Canada and has strong institutes, such as the Pacific Institute for Complex Systems (MITACS), and the Banff connections with other mathematical the Mathematical Sciences (PIMS), Math- International Research Station (BIRS). institutes, such as the Pacific Institute for ematics of Information Technology and Applications should include a curricu- the Mathematical Sciences (PIMS), Math- Complex Systems (MITACS), and the Banff lum vitae, a research statement, a teach- ematics of Information Technology and International Research Station (BIRS). For ing profile outlining experience and/or Complex Systems (MITACS), and the Banff more information about the department, International Research Station (BIRS). For interests, and at least three confidential please visit our website at http://www. more information about the department, letters of reference. math.ualberta.ca/. please visit our websites at http://www. The closing date for applications is Applications should include a curricu- November 16, 2007, or until a suitable mathstat.ualberta.ca/ and http:// lum vitae, a research statement, a teach- candidate is found. Early applications are www.stat.ualberta.ca/. ing profile outlining experience and/or encouraged. Applications should include a curricu- interests, and at least three confidential Interested applicants may apply to: lum vitae, a research statement, a teach- letters of reference. Arturo Pianzola, Chair ing profile outlining experience and/or The closing date for applications is Department of Mathematical and Sta- interests, and at least three confidential November 16, 2007, or until a suitable tistical Sciences letters of reference. candidate is found. Early applications are University of Alberta The closing date for applications is Edmonton, Alberta, Canada T6G 2G1 November 16, 2007, or until a suitable encouraged. email: [email protected]. candidate is found. Early applications are Interested applicants may apply to: ca encouraged. Arturo Pianzola, Chair All qualified candidates are encouraged to Interested applicants may apply to: Department of Mathematical and Sta- apply; however, Canadians and permanent Arturo Pianzola, Chair tistical Sciences residents will be given priority. If suitable Department of Mathematical and Sta- University of Alberta Canadian citizens or permanent residents tistical Sciences Edmonton, Alberta, Canada T6G 2G1 cannot be found, other individuals will be University of Alberta [email protected] considered. Edmonton, Alberta, Canada T6G 2G1 All qualified candidates are encouraged to The University of Alberta hires on the email: [email protected] apply; however, Canadians and permanent basis of merit. We are committed to the berta.ca residents will be given priority. If suitable principle of equity in employment. We All qualified candidates are encouraged to Canadian citizens or permanent residents welcome diversity and encourage applica- apply; however, Canadians and permanent cannot be found, other individuals will be tions from all qualified women and men, residents will be given priority. If suitable considered. including persons with disabilities, mem- Canadian citizens or permanent residents The University of Alberta hires on the cannot be found, other individuals will be bers of visible minorities, and Aboriginal basis of merit. We are committed to the considered. persons. principle of equity in employment. We 000095 The University of Alberta hires on the welcome diversity and encourage applica- basis of merit. We are committed to the tions from all qualified women and men, principle of equity in employment. We including persons with disabilities, mem- welcome diversity and encourage applica- UNIVERSITY OF ALBERTA bers of visible minorities, and Aboriginal tions from all qualified women and men, Department of Mathematics persons. including persons with disabilities, mem- Tenure-Track Position, 000097 bers of visible minorities, and Aboriginal Statistics and Probability persons. The Department of Mathematical and 000096 UNIVERSITY OF ALBERTA Statistical Sciences at the University of Alberta invites applications for a tenure- Department of Mathematics track position in the area of statistics and UNIVERSITY OF ALBERTA Tenure-Track Position, probability. We primarily seek candidates Department of Mathematics Partial Differential Equations at the assistant professor level, but excep- Tenure-Track Position, Representation tional candidates at a more senior level Theory The Department of Mathematical and will be considered. Statistical Sciences at the University of The successful candidate will have es- The Department of Mathematical and Alberta invites applications for a tenure- tablished accomplishments and outstand- Statistical Sciences at the University of track position in the area of partial differ- ing promise in research, as well as a strong Alberta invites applications for a tenure- ential equations. We primarily seek candi- commitment to graduate and undergradu- track position in the area of representa- dates at the assistant professor level, but ate teaching. Candidates must hold a Ph.D. tion theory. We primarily seek candidates exceptional candidates at a more senior degree. We offer an excellent research at the assistant professor level, but excep- level will be considered. environment with a normal teaching load tional candidates at a more senior level The successful candidate will have es- of three courses per year. A close fit will be considered. tablished accomplishments and outstand- with some of the existing research being The successful candidate will have es- ing promise in research, as well as a strong presently conducted in the department tablished accomplishments and outstand- commitment to graduate and undergradu- is an asset. Our statistics and probability ing promise in research, as well as a strong ate teaching. Candidates must hold a Ph.D. group encompasses a broad spectrum commitment to graduate and undergradu- degree. We offer an excellent research of research interests, ranging from such ate teaching. Candidates must hold a Ph.D. environment with a normal teaching load interdisciplinary areas as biostatistics and degree. We offer an excellent research of three courses per year. A close fit environmetrics, through core research environment with a normal teaching load with some of the existing research being

1210 Notices of the AMS Volume 54, Number 9 Classified Advertisements presently conducted in the department institutes, such as the Pacific Institute for Corduneanu (USA), Eduard Feireisl (Czech is an asset. the Mathematical Sciences (PIMS), Math- Republic), Peter D. Lax (USA). Alberta is one of the leading mathemat- ematics of Information Technology and The department will launch an inter- ics departments in Canada and has strong Complex Systems (MITACS), and the Banff national, two-year Master of Science (MS) connections with other mathematical International Research Station (BIRS). in applied mathematics program starting institutes, such as the Pacific Institute for Applications should include a curricu- academic year 2008/2009. Our MS pro- the Mathematical Sciences (PIMS), Math- lum vitae, research and teaching profiles gram will be focused on modern topics, ematics of Information Technology and outlining experience and/or interests, including analytical, statistical, numeri- Complex Systems (MITACS), and the Banff and at least three confidential letters of cal and computational methods, which International Research Station (BIRS). For reference. are essential in the employment market more information about the department, building strongly on cross-disciplinary The closing date for applications is please visit our website at http://www. practical skills. November 16, 2007, or until a suitable math.ualberta.ca/. For details see http://www.ceu.hu/ Applications should include a curricu- applicant is found. Early applications are encouraged. math or write to: G. Morosanu; email: lum vitae, a research statement, a teach- [email protected]. ing profile outlining experience and/or For more information about the depart- 000054 interests, and at least three confidential ment and the University of Alberta, please letters of reference. visit our webpage (http://www.math. The closing date for applications is ualberta.ca/). November 16, 2007, or until a suitable Interested applicants may apply to: Singapore candidate is found. Early applications are Arturo Pianzola, Chair NATIONAL UNIVERSITY OF SINGAPORE encouraged. Department of Mathematical and Sta- Interested applicants may apply to: tistical Sciences (NUS) Arturo Pianzola, Chair University of Alberta Department of Mathematics Department of Mathematical and Sta- Edmonton, Alberta, Canada T6G 2G1 The Department of Mathematics at the tistical Sciences email: [email protected]. National University of Singapore (NUS) University of Alberta ca invites applications for tenured, tenure- Edmonton, Alberta, Canada T6G 2G1 All qualified candidates are encouraged to track and visiting (including post- [email protected] apply; however, Canadians and permanent doctoral) positions at all levels, beginning All qualified candidates are encouraged to residents will be given priority. in August 2008. apply; however, Canadians and permanent The University of Alberta hires on the NUS is a research intensive university residents will be given priority. If suitable basis of merit. We are committed to the that provides quality undergraduate and Canadian citizens or permanent residents graduate education. The Department of cannot be found, other individuals will be principle of equity in employment. We Mathematics, which is one of the largest considered. welcome diversity and encourage applica- in the university, has about 70 faculty The University of Alberta hires on the tions from all qualified women and men, including persons with disabilities, mem- members and teaching staff whose exper- basis of merit. We are committed to the tise cover major areas of contemporary principle of equity in employment. We bers of visible minorities, and Aboriginal mathematical research. welcome diversity and encourage applica- persons. tions from all qualified women and men, 000099 We seek promising scholars and estab- including persons with disabilities, mem- lished mathematicians with outstanding bers of visible minorities, and Aboriginal track records in any field of pure and ap- persons. Hungary plied mathematics. The department offers 000098 internationally competitive salaries with start-up grants for research. The teach- CENTRAL EUROPEAN UNIVERSITY (CEU) ing load is particularly light for young Department of Mathematics scholars, in an environment conducive UNIVERSITY OF ALBERTA Study in the country of John von to research with ample opportunities for Department of Mathematics Neumann career development. Max Wyman Assistant Professorship and Peter Erdos! Research areas which the department in Number Theory plans to expand in the near future include The Department of Mathematics and Its (but are not limited to): All areas of pure The Department of Mathematical and mathematics (especially analysis) finan- Statistical Sciences at the University of Applications of Central European Uni- cial mathematics, mathematical imaging, Alberta invites applications for a Max versity (CEU), Budapest, Hungary, offers Wyman Assistant Professorship in Num- innovative programs at both Ph.D. and MS probability & stochastic analysis, scientific ber Theory. This is a three-year fixed-term levels. The language of instruction at CEU computing. position. The position offers an excel- is English. The Ph.D. program in math- Application materials should be sent lent research and teaching environment ematics and its applications is registered to: with a reduced teaching load (averaging by the board of regents of the University Search Committee two one-semester courses per year). A of the State of New York for, and on behalf Department of Mathematics startup research grant is included with of, the New York State Education Depart- National University of Singapore the position. ment. The program covers major branches 2 Science Drive 2, Singapore 117543 We are looking for a person with a Ph.D. in both mathematics and its applications. Republic of Singapore (or near completion), excellent research It is carried out jointly with the Renyi In addition, applicants should submit potential, and strong communication and Institute of Mathematics of the Hungar- electronically a PDF-file to search@math. teaching skills. Candidates are expected ian Academy. We further have partner- nus.edu.sg. Inquiries may also be sent to develop an independent research pro- ship agreements with other prominent to this link. gram, and will be eligible to apply for institutions from abroad. Outstanding Please include the following supporting federal research funds. foreign scholars are regularly invited to documentation in the application: Alberta is one of the leading mathemat- deliver lectures and teach our students, 1) an American Mathematical Society ics departments in Canada and has strong among whom were Haim Brezis (France), Standard Cover Sheet; 2) a detailed CV connections with other mathematical Carsten Carstensen (Germany), Constantin including publications list; 3) a statement

October 2007 Notices of the AMS 1211 Classified Advertisements of research accomplishments and plan; 4) a statement (max. of 2 pages) of teaching philosophy and methodology. Please at- tach evaluation on teaching from faculty members or students of your current institution, where applicable; 5) at least three letters of recommendation including one which indicates the candidate’s effec- tiveness and commitment in teaching. Heinz Hopf Lectureships Review process will begin at the end of November and will continue until po- The Department of Mathematics of the ETH Zurich invites appli- sitions are filled. For further informa- cations for several Heinz Hopf Lectureships beginning Septem- tion about the department, please visit ber 1st, 2008 or earlier. These positions are intended for young http://www.math.nus.edu.sg. scientists, after their Ph. D. up to five years. They are awarded for 000077 a period of 3 years, with the possibility of an extension by 1 year. Duties of Heinz Hopf lecturers include research and teaching in mathematics. Together with the other members of the depart- ment, the new lecturers will be responsible for undergraduate and graduate courses for students of mathematics, natural sciences, and engineering. The moderate teaching load leaves ample room for further professional development. Courses at Master level may be taught in English. Applicants should have proven excellence in research in any area of mathematics and possess potential for further outstanding achievements. Applications with curriculum vitae and a list of publications should be submitted to Prof. H.-R. Kuensch, [email protected], Department of Mathematics, ETH Zentrum, 8092 Zurich, Switzerland, by November 30th, 2007. Later applications can be considered for remaining positions. In addition, three letters of recommendation supporting the application should be sent directly to us. ETH Zurich specifically encourages female candi- dates to apply.

Prepared by Polaris Recruitment Communications The Ohio State University at Lima Date Created 01.26.0708.09.07 Last Modified 01.26.0708.09.07 Assistant Professor of Math The Ohio State University at Lima invites applications for a full-time, tenure-track Assistant Order Number cmh_14948OSU_18878 Professor of Mathematics. The appointment will be made in the Department of Mathematics at The Ohio State University and begin in September 2008. Ad Dimensions 2.253.25 x 494.25 agates The search committee seeks mathematicians who can make a strong commitment to the teaching, research, and outreach missions of The Ohio State University. The successful candidate Created by mllk will have the ability to teach the courses that the Department of Mathematics offers at Last modified by MLlk undergraduate level. The standard teaching load for the successful candidate will be six courses per academic year (Ohio State is on the quarter system), reduced to five courses for the first Art Links Verified? y three years of service. An ability to teach courses in Computer Science and/or Statistics, as well as remedial math courses will be desirable. The position will require a strong record/potential of service and scholarly research, and a demonstrated commitment to teaching excellence is essential. Preference will be given to hiring a tenure line faculty with specialization in Numerical Analysis/Integral Equations. We will also consider applicants in all other areas compatible with the rest of present faculty's research interests (Ring Theory, Representation Theory and Model Theory). Candidates must have a PhD in hand at the time of appointment. Salary is competitive. The Ohio State University at Lima is one of the five campuses of The Ohio State University. Current enrollment on the Lima campus is 1,200 students and there are approximately 100 full- and part-time faculty in all academic departments. Ohio State Lima offers the first two years of the Ohio State general education curriculum and nineprograms leading to baccalaureate degrees. Ohio State Lima also offers Master’s degree programs in Education and Social Work. The review of applications will begin November 20, 2007 and will continue until the position is filled. Please send a cover letter, a current curriculum vita, and three letters of recommendation to: Chair, Math Search Committee c/o HR Officer Kathy Baker Public Service Building The Ohio State University at Lima 4240 Campus Drive, Lima OH 45804 To build a diverse workforce, Ohio State encourages applications from individuals with disabilities, minorities, veterans, and women. EEO/AA employer.

1212 Notices of the AMS Volume 54, Number 9 Heinz Hopf Lectureships

The Department of Mathematics of the ETH Zurich invites appli- cations for several Heinz Hopf Lectureships beginning Septem- ber 1st, 2008 or earlier. These positions are intended for young scientists, after their Ph. D. up to five years. They are awarded for a period of 3 years, with the possibility of an extension by 1 year. Duties of Heinz Hopf lecturers include research and teaching in mathematics. Together with the other members of the depart- ment, the new lecturers will be responsible for undergraduate and graduate courses for students of mathematics, natural sciences, and engineering. The moderate teaching load leaves ample room for further professional development. Courses at Master level may be taught in English. Applicants should have proven excellence in research in any area of mathematics and possess potential for further outstanding achievements. Applications with curriculum vitae and a list of publications should be submitted to Prof. H.-R. Kuensch, [email protected], Department of Mathematics, ETH Zentrum, 8092 Zurich, Switzerland, by November 30th, 2007. Later applications can be considered for remaining positions. In addition, three letters of recommendation supporting the application should be sent directly to us. ETH Zurich specifically encourages female candi- dates to apply.

Prepared by Polaris Recruitment Communications The Ohio State University at Lima Date Created 01.26.0708.09.07 Last Modified 01.26.0708.09.07 Assistant Professor of Math The Ohio State University at Lima invites applications for a full-time, tenure-track Assistant Order Number cmh_14948OSU_18878 Professor of Mathematics. The appointment will be made in the Department of Mathematics at The Ohio State University and begin in September 2008. Ad Dimensions 2.253.25 x 494.25 agates The search committee seeks mathematicians who can make a strong commitment to the teaching, research, and outreach missions of The Ohio State University. The successful candidate Created by mllk will have the ability to teach the courses that the Department of Mathematics offers at Last modified by MLlk undergraduate level. The standard teaching load for the successful candidate will be six courses per academic year (Ohio State is on the quarter system), reduced to five courses for the first Art Links Verified? y three years of service. An ability to teach courses in Computer Science and/or Statistics, as well as remedial math courses will be desirable. The position will require a strong record/potential of service and scholarly research, and a demonstrated commitment to teaching excellence is essential. Preference will be given to hiring a tenure line faculty with specialization in Numerical Analysis/Integral Equations. We will also consider applicants in all other areas compatible with the rest of present faculty's research interests (Ring Theory, Representation Theory and Model Theory). Candidates must have a PhD in hand at the time of appointment. Salary is competitive. The Ohio State University at Lima is one of the five campuses of The Ohio State University. Current enrollment on the Lima campus is 1,200 students and there are approximately 100 full- and part-time faculty in all academic departments. Ohio State Lima offers the first two years of the Ohio State general education curriculum and nineprograms leading to baccalaureate degrees. Ohio State Lima also offers Master’s degree programs in Education and Social Work. The review of applications will begin November 20, 2007 and will continue until the position is filled. Please send a cover letter, a current curriculum vita, and three letters of recommendation to: Chair, Math Search Committee c/o HR Officer Kathy Baker Public Service Building The Ohio State University at Lima 4240 Campus Drive, Lima OH 45804 To build a diverse workforce, Ohio State encourages applications from individuals with disabilities, minorities, veterans, and women. EEO/AA employer.

1212 Notices of the AMS Volume 54, Number 9 Mathematical Sciences Employment Center San Diego Convention Center, San Diego, California January 6, 7, 8, and 9, 2008

2008 Employment Center Schedule Overview of the Employment Center October 24, 2007 Registration deadline for inclusion in Winter The Employment Center (formerly the Employment List books. Register) serves as a meeting place and information December 14, 2007 Advance registration deadline. After center for employers and Ph.D.-level job seekers this date, all registration activities will happen on site in San attending the Joint Mathematics Meetings. Most ap- Diego. plicants and employers began the search process in Sunday, January 6 the fall and are looking for an opportunity to meet 7:30 a.m.–4:00 p.m. Registration and materials pick-up. in person with those with whom they’ve already had 9:00 a.m.–9:30 a.m. Short (optional) orientation session. communication. Some, however, use the Employ- 9:30 a.m.–4:00 p.m. Submission of Scheduled Employment ment Center as a way to make some initial con- Register interview request forms for both Monday and tacts, gather information, and distribute their own Tuesday interviews. No request forms can be accepted information. This is a less effective, but common, use of after 4:00 p.m. Sunday. the program. The Employment Center allows everyone 9:30 a.m.–6:00 p.m. Interview Center open. to choose a comfortable level of participation by seeking No Scheduled Employment Register interviews are held on interviews for any of the open hours or by limiting Sunday. schedules to certain days or hours. Monday, January 7 7:00 a.m.–8:15 a.m. Distribution of interview schedules for The Employment Center is a four-day program both Monday and Tuesday for those participating in the which takes place on the Sunday, Monday, Tuesday, Scheduled Employment Register. Employers who have elected and Wednesday (morning only) of the Joint Meetings. the combination package will receive schedules for Monday Most participants register in advance (by the October only. 24 deadline), and their brief résumé or job description 8:15 a.m.–4:40 p.m. Scheduled Employment Register is printed in a booklet that is mailed to participants in interviews in 4 sessions: Session 1: 8:15 a.m.–9:50 a.m., advance. Session 2: 10:00 a.m.–11:35 a.m., Session 3: 1:00 p.m.– The Employment Center houses two services: the 2:35 p.m., Session 4: 3:00 p.m.–4:35 p.m. computer-scheduled interview tables (the Scheduled 8:00 a.m.–7:30 p.m. Interview Center open (doors open at 7:30 a.m.; do not schedule before 8:00 a.m.). Employment Register) and the employer-scheduled interview tables (the Interview Center). Following two Tuesday, January 8 8:15 a.m.–4:40 p.m. Scheduled Employment Register years of a job market favorable to employers, the Em- interviews in 4 sessions: Session 5: 8:15 a.m.–9:50 a.m., ployment Center applicant/employer ratio seems to Session 6: 10:00 a.m.–11:35 a.m., Session 7: 1:00 p.m.– be remaining stable. At the 2007 Employment Center, 2:35 p.m., Session 8: 3:00 p.m.–4:35 p.m. 638 candidates and 142 employers participated, giving 8:00 a.m.–7:30 p.m. Interview Center open (doors open an overall applicant-to-employer ratio of 4.4:1 (com- at 7:30 a.m.; do not schedule before 8:00 a.m.). Employers who pared with 554 applicants and 138 employers in 2006, a have elected the combination package will now be moved into ratio of 3.9:1). Those with the most interviews are those this section for interviews. requested most by employers, usually as a result of a Wednesday, January 9 careful application process during the months before 9:00 a.m.–12 noon Interview Center open. the Employment Center takes place. The total number Note: Any participant who plans to use the Scheduled Em- ployment Register must appear at the Employment Center of interviews arranged is dependent on the number of on Sunday by 4:00 p.m. to turn in the Interview Request/ participating employers. Fewer employers will mean Availability Form. Before traveling, please refer to the Employ- fewer interviews overall. ment Center Webpage for important phone numbers to contact At the January 2008 Employment Center, job can- in case of unexpected delays. didates will be able to choose how to participate. Two forms of participation will be available:

October 2007 Notices of the AMS 1213 Employment Center

All Employment Center services (computer- Schedules are distributed for all Monday and scheduling system, form posted in Winter List Tuesday interviews on Monday morning. Employers of Applicants, Winter List of Employers received who have elected the combination package will re- by mail, use of Employment Message Center, ceive schedules for Monday only. The schedule allows availability for employer-scheduled Interview 15-minute interviews, with 5 minutes between for note Center). taking. One or more interviewers for the same position(s) may interview at the table separately, together, or in Message Center and Winter Lists only (form shifts (however, no more than two may sit at the table at posted in Winter List of Applicants, Winter List one time). For follow-up interviews, the scheduled tables of Employers received by mail, use of Employ- will also be available for use until 7:30 p.m. on Monday ment Message Center, availability for employer- and Tuesday, and on Wednesday morning from 9:00 a.m. scheduled Interview Center, BUT NOT use of to noon. the computer-scheduling system). Participation in the scheduling program has become optional for applicants, so employers will notice some No matter which option is chosen, advance registration applicant résumés in the Winter List of Applicants with no works best so that the Applicant Form (received by Octo- applicant number. An employer can arrange to interview ber 24, 2007) can be printed in the Winter List distributed such an applicant outside of the scheduled interview to employers. sessions—for instance, between 4:40 p.m. and 7:30 p.m. Employer forms submitted by registered employers Monday or Tuesday, or on Wednesday morning—or during have no connection with the AMS online job ads (EIMS). sessions which they left unscheduled. Submitted forms are not available for browsing on the Employers who are interviewing for two distinct posi- Web. They are reproduced in the Winter List booklet for tions may wish to pay for two tables. See the instructions use by Employment Center participants. under “How to Register”. Employers should bring school The Mathematical Sciences Employment Center is catalogs, corporate reports, or more lengthy job descrip- sponsored by the American Mathematical Society, the tions to the Employment Center early on Sunday for pe- Mathematical Association of America, and the Society rusal by applicants prior to interviews. for Industrial and Applied Mathematics; it is managed by members of the AMS staff, with the general guid- The Employer-Scheduled Interview Center ance of the AMS-MAA-SIAM Committee on Employment The Interview Center allows any employer to reserve a table Opportunities. in an area adjacent to the Employment Center. Employers will arrange their own schedule of interviews, either in Employers: Choose one of these tables: advance or on site, by using the Employment Message Center. Employers who have never used the Employment Computer-scheduled Employment Register table Center before might want to try conducting interviews Employer-scheduled Interview Center table at this convenient location. Since they will be setting their own schedules, employers will have complete control over Combination Interview Table (split whom they’ll see, for how long, and when they’ll be inter- Computer-scheduled/Interview center) viewing. This allows employers to pursue other activities at the Joint Meetings. Please note: Employers who have The Employment Register Computer-Scheduling elected the combination package will be moved into this System area on Tuesday. The center will be open only during the following Employers register in advance by the October 24 deadline, hours: and their job listings (“Employer Forms”) are printed and distributed in mid-December to applicants. Employers Sunday, January 6, 2008, 9:30 a.m.–6:00 p.m. receive the book of brief, numbered applicant résumés Monday, January 7, 2008, 8:00 a.m.–7:30 p.m. in mid-December. Participants decide on Sunday, Tuesday, January 8, 2008, 8:00 a.m.–7:30 p.m. January 6, which of the eight sessions (of five interviews each) they Wednesday, January 9, 2008, 9:00 a.m.–noon will participate in and submit their Availability/Interview The fee for use of this area is the same as the normal Request Forms between 9:30 a.m. and 4:00 p.m. Sunday. employer fee, $245. It is requested that all employers fill Employers can reserve time for other Joint Meetings events out an Employer Form for inclusion in the Winter List. by marking “unavailable” for one or more of the eight ses- This should clarify to Employment Center applicants what sions. Employers can request ten specific applicants per type of position is being filled. If an employer is unable day, assuming they are available for all four sessions that to accept new applicants because the deadline has passed, day. Usually those requests will be filled by the scheduling that should be stated on the form. algorithm, provided the applicants are present, except in The Winter List of Applicants, containing information the case of the few most-requested applicants. The rest of about the candidates present at the Employment Center, their interviews will be with applicants who ask to see them. will be mailed to all employers in advance of the meet- Employers should be specific about their requirements on ing. the Employer Form to avoid interviews with inappropriate Employers scheduling interviews in advance should tell candidates. applicants to find the table with the institution’s name

1214 Notices of the AMS Volume 54, Number 9 Employment Center in the Interview Center (not the numbered-table area). Submit an Employer (job listing) Form elec- Employers can schedule any time during the open tronically at www.ams.org/emp-reg. Be sure hours listed above. To schedule interviews after arriving the form indicates which type or types of tables in San Diego, leave messages for Employment Center will be used. This form will be printed in the applicants in the Employment Message Center. Paper Winter List of Employers. forms will be provided to help speed the invitation pro- It is important to register by the October 24 deadline cess. Each employer will be provided with a box in the in order for your form to be included in the Winter List Message Center where applicants can leave items. of Employers. However, registration will be accepted Employers should have at most two interviewers per up to December 14 for the normal fees or on site in table at any time due to space limitations. There will be no San Diego at the on-site rates. Call 800-321-4267, outlets or electricity available at the interviewing tables. ext. 4113, with any questions or deadline problems. Only banners that can be draped over the four-foot table Any representatives of the institution can sit at the can be accommodated. table together or working in shifts (however, the limit is two at one time). If possible, their names should be listed Combination Interview Table on the Employer Form as a reference point for the appli- This year, employers may opt to pay one table fee and cants. Employment Center fees should be paid only for experience both settings. The combination table will be each table required, not for each person. located in the computer-scheduled area for one full day In a few unusual cases, an institution will be conduct- of interviews, and then in the Interview Center for the last ing interviews in the Employment Center for two or more day and a half. distinct positions and will not want to conduct these inter- views at one table. In that case, two or more Employer Forms About the Winter List of Applicants should be submitted, and separate tables and employer This booklet contains hundreds of résumés of applicants numbers will be provided. Applicants will then be able to request interviews for the appropriate job by employer who registered by October 24 for the Employment Center. number. First and second table fees should be paid. It will be mailed in December to all employers who register The fee for all employers to register in advance is by October 24 and indicate on their Joint Meetings regis- $245 for the first table and $95 for each additional tration form that they would like their materials mailed. table. On-site registration fees (any registrations after Employers should be aware that there will be hundreds of December 14, 2007) are $325 for the first table and $125 brief résumés to look through and should be sure to obtain for each additional table. Employers must also register the Winter List of Applicants as early as possible. for the Joint Meetings and pay the appropriate Joint Meetings fee. Employers Not Planning to Interview Employers who do not plan to participate in the Employ- Employers: Registration on Site ment Center at all may place a job description in the book Employers who do not register for the Joint Mathematics of employers. This description must be submitted on Meetings and the Employment Center by December 14 the Employer Form, which is located on the Web at www. may register on site in San Diego at the Joint Meetings ams.org/emp-reg, with the appropriate box checked, registration desk. They must bring their receipt to the indicating that no interviews will take place. A fee of $50 Employment Center desk between 7:30 a.m. and 4:00 is charged for this service (paid through the Joint Meet- p.m. on Sunday, January 6, to receive their materials. If ings registration form). The form must be received in registering for the employer-scheduled Interview Center the Providence office (with payment or purchase order only, registration on Monday is possible. sent separately) by the October 24 deadline to appear in the Winter List of Employers. Forms received in the Provi- Applicants: Use of the computer-scheduled dence office after that deadline will be displayed at the program is now optional. meeting. Those wishing to bring a one-page job descrip- tion to the Employment Center desk for display during the meetings may do so at no charge. In 2008 applicants will be given flexibility in deciding how to participate in the Employment Center. There are two Employers: How to Register options: The interviewer should register and pay for the Joint All Employment Center services (computer- Mathematics Meetings. They should register for the Em- scheduling system, form posted in Winter List ployment Center by completing the following steps: of Applicants, Winter List of Employers received Indicate on the Joint Meetings registration by mail, use of Employment Message Center, form (available electronically in early September availability for employer-scheduled Interview 2007 at www.ams.org/amsmtgs/2109_intro. Center). html that you are also paying the Employment Center employer fee. Indicate your choice of Message Center and Winter Lists only (form tables. Mark all that apply. posted in Winter List of Applicants, Winter List

October 2007 Notices of the AMS 1215 Employment Center

of Employers received by mail, use of Employ- Interviews ment Message Center, availability for employer- Applicants should understand that the Employment Center scheduled Interview Center, BUT NOT use of provides no guarantees of interviews or jobs. It is simply the computer-scheduling system). This option a convenient meeting place for candidates and employers is available at a slightly lower price. who are attending the Joint Meetings. Those who have not Applicants who participate in the 2008 Employment yet begun their job search efforts may go unnoticed at Center will find themselves talking with employers in two the Employment Center (although applicants will likely different settings: receive between one and three interviews in the scheduled 1. A computer-scheduling program sets 15-minute program). Attention generally goes to candidates who interviews at the Employment Register numbered tables. already have applied for open positions or to those who are This is the choice that has now become optional for well suited for teaching positions at bachelor’s-granting applicants. Applicants do not have to hand in a computer- colleges. scheduling form at all. Data from recent Employment Centers show that women 2. There is also an Interview Center, where employers represent about half of the most sought-after applicants, set their own schedules. These employers do not par- although they make up less than half of the total Employ- ment Center applicant pool. Those without permanent au- ticipate in the scheduling program, so applicants have no thorization to work in the United States will find themselves automatic access to interviews with them. They determine far less requested than U.S. citizens or permanent residents. their own schedules and make their own appointments Newer Ph.D.’s tend to be invited for more interviews than privately, either in advance or on site using the Employ- those who have been working longer. Most jobs listed ment Message Center. These interviews have always been require a doctorate. Approximately 32 percent of appli- “optional” for applicants, since they may turn down any cants responding to a recent survey report having between written invitation they receive. Applicants are reminded zero and two interviews in the Interview Center. The rest to respond to all invitations promptly. Many applicants reported higher numbers. Most of the applicants reported prefer the interviews they are invited for in this setting, that at least some of the Interview Center appointments had since it is more relaxed and interviews tend to last lon- been arranged in advance of the meetings. ger. Overall, many applicants report being disappointed Preparations that there are not more research-oriented jobs being Candidates just beginning a job search should realize interviewed for at the Employment Center. The best way that employers have no method to judge their credentials to predict what type of employers will interview at the other than the brief résumé form, and they should make Employment Center is to peruse a list of institutions from an effort to make it distinct and interesting. the previous year, available at www.ams.org/emp-reg. Applicants who register in advance will receive the Win- Applicants should expect that many of the jobs are best ter List of Employers in mid-December. If time permits, they suited to enthusiastic and well-qualified candidates who should apply for suitable open positions they notice in the can contribute on many levels in an academic setting. Winter List of Employers after they receive it. Applicants are advised to bring a number of copies of their brief vita The Schedule or résumé so that they may leave them with prospective For applicants using all services there is a certain sched- employers. It is a good idea in the fall for applicants to uling burden placed on them to juggle these simultane- alert any employer to whom applications are made that ous services. However, computer-scheduled sessions they plan to be present at the Joint Meetings. Also, they are in small blocks, for a total of eight sessions over the should bring enough materials with them to accompany two days of interviews (Monday and Tuesday). This allows requests for interviews they may want to leave in the applicants, once they receive invitations to interview in Message Center boxes of the Interview Center employ- the Interview Center, to accept, knowing that when they ers. submit the computer schedule request on Sunday, they can Applicants are also encouraged to leave some extra mark that they are unavailable for one or more of these copies of their résumés in their own message folders sessions without seriously jeopardizing their chances of so that interested employers may find them there. Photo- obtaining scheduled interviews. Likewise, applicants who copying costs at a convention/hotel are high, so applicants are scheduled to give a talk can avoid interviews for that should come prepared with a reasonably large number time. Applicants are encouraged to schedule their time of copies. A brightly colored form in each folder gives in advance in this manner and not wait for the computer applicants an opportunity to present for public perusal schedule to be distributed Monday morning. some information about their availability during the Applicants are advised to place as many selections meetings. as possible on their scannable request sheets; however, The Winter List of Applicants is mailed to all employers be advised that this may result in interviews with less- in advance, so it is vital that the Joint Meetings registration preferred employers. Applicants should be aware that each form, applicant résumé form, and payments be received year approximately 10 percent of applicants signing up for by the October 24 deadline so the Applicant Form can be all services fail to submit a schedule request sheet. This is printed in the book. This greatly increases an applicant’s often due to having too many schedule conflicts. chances of being invited to the Interview Center.

1216 Notices of the AMS Volume 54, Number 9 Employment Center

Applicants should keep in mind that interviews arranged publishing may allow your late form to get into the book. by the Employment Center represent only an initial con- At the very least, your printed-out form will be brought tact with the employers and that hiring decisions are not to the meetings by staff and displayed there (after all the ordinarily made during or immediately following such fees have been paid). interviews. When to Arrive All participants in the scheduled section of the Em- Results ployment Center must submit their Interview Request/ In a recent survey, 63 percent of applicants responding Availability Forms in person between 9:30 a.m. and reported being invited for at least one on-campus visit to 4:00 p.m. on Sunday, January 6, 2008, or they will not be an employer they had interviewed with during the Employ- included when the interview-scheduling program runs ment Center; 44 percent reported receiving at least one Sunday night. Before traveing, please refer to the Em- job offer in the months following the interview. Overall, ployment Center webpage for important phone num- 30 percent reported accepting a position with an employer bers to contact in case of unexpected delays. Be they spoke with during the Employment Center. Another sure to keep Employment Center materials with you, 56 percent reported (in May) having no new job offers. The because in an emergency you can report your interview rest accepted positions with employers they met through requests over the phone. other means. Applicants: Registering on Site Applicants: Register Early Feel free to enter the Employment Center area first to Applicants need to complete the following steps by the consult staff about the decision to register on site and advance deadline of October 24, 2007. to check on which employers are participating. Full reg- 1. Pay fees istration on site early Sunday is allowed for a higher fee Register for the Joint Mathematics Meetings (the elec- but is severely discouraged. Most employers will not no- tronic information available in early September 2007 at tice an Applicant Form that arrives on Sunday. Therefore, www.ams.org/amsmtgs/2109_intro.html). You cannot these individuals will receive only a couple of computer- participate in the Employment Center unless you are a scheduled interviews. Registration on site is advisable Meetings participant. Mark one of the two “Employment only for those who know they will be interviewed in the Center Applicant Fee” boxes on the Joint Meetings regis- Interview Center and would like a Message Center folder tration form and make payments. The fee in advance for for employers to leave messages in. Registering on site applicants is $44; “Message Center and Winter List ONLY” for a mailbox only is possible, at the $22 rate, on Sunday registration is $22. and Monday. Pay the fees at the Joint Meetings registra- 2. Send form tion area and then bring your receipt to the Employment Submit the Applicant Form (a brief résumé form) Center desk to register yourself. electronically at www.ams.org/emp-reg/. After Registration Submission of the Applicant Form electronically will result in an email acknowledgement almost immediately. For registration and payments, the Meetings Service Bu- reau acknowledges all payments. When payments AND the Applicant Form have been received, another acknowl- edgement will go out by email, if possible, or by mail. Please allow a week or so for processing, but after that contact staff (AMS 800-321-4267, ext. 4113) if you do not receive acknowledgement from the Employment Center. Around December 15 the Winter List of Employers will be mailed to all registered applicants unless they request otherwise. Registering after the Deadline After October 24 applicants can still register for the Employment Center at the same prices until the final deadline of December 14. However, the Applicant Form will NOT be included in the Winter List of Applicants, but will be posted on site at the Employment Center (a serious disadvantage). Those who do not register by December 14 must register on site at the Joint Meetings registration desk and pay higher fees ($82 Employment Center fee; however, the “Message Center and Winter List ONLY” fee is always just $22). It is worthwhile to submit the applicant form even if you miss the October 24 deadline. An unexpected delay in

October 2007 Notices of the AMS 1217 AMS Short Course

Applications of Knot Theory tangles, Ernst and Sumners developed a tangle model of recombination to make predictions—later experimentally San Diego, California, January 4–5, 2008 verified—about how a particular protein interacts with DNA. Modified versions of the tangle model have since Organized by been used to determine various features of protein-DNA Dorothy Buck, Imperial College of London interactions for a number of specific proteins. Erica Flapan, Pomona College Similarly, in chemistry, Pasteur began the study of Over the past twenty years, knot theory has rekindled its molecular chirality. Since two enantiomers of the same historic ties with biology, chemistry, and physics. While drug can interact with a host’s metabolism very differ- the original motiviation for understanding and classify- ently, pharmaceutical companies are particularly inter- ing knots—Lord Kelvin’s correlation of chemical elements ested in topological stereochemistry. Thus, knot theory with particular knotted configurations in the “ether”— techniques have been used to understand whether—and proved erroneous, mathematicians continued to develop if so how intrinsically—a number of synthetic compounds the theory of knots, and until the 1980s this remained a are chiral. primarily pure field of mathematics. In addition to the examples described above, there are At this time, chemists (most notably Ned Seeman and many other deep interactions of knot theory with biology, Kurt Mislow), biologists (most notably Nick Cozzarelli and chemistry and physics. While this Short Course can not Andrzej Stasiak), and physicists began searching for more cover all aspects of applied knot theory, the organizers’ sophisticated descriptions of the entanglements of natural goal is to provide the participants with an appetizer—both phenomena—from strings to small organic compounds to, as a small taste and to stimulate the (mathematical) ap- most famously, DNA. petite. Since their discovery in the late 1960s, DNA knots It is planned that lecture notes will be available to those and links have been implicated in a number of cellular who register for this course. Advance registration fees processes. In particular, they have been found during are: member of the AMS—US$94; nonmember—US$125; replication and recombination and as the products of pro- student, unemployed, emeritus—US$42. On-site fees are: tein actions, notably with topoisomerases, recombinases, member of the AMS—US$125; nonmember—US$155; and transposases. The variety of DNA knots and links student, unemployed, emeritus—US$63. Registration observed made biologically separating and distinguishing and housing information can be found in this issue of these molecules a critical issue. While DNA knots and links the Notices; see the section “Registering in Advance and can be visualized via electron microscopy, this process Hotel Accommodations” in the announcement for the can be both difficult and time-consuming. So topological meetings in San Diego. The registration form is at the methods of characterizing and predicting their behavior back of this issue. can be helpful. Format of the Short Course: Topological techniques (notably the node number for This AMS Short Course will introduce knots, and some knots, the Jones polynomial for catenanes/links, and the of their recent applications in molecular biology, chemis- work of Schubert for 4-plats) played a significant role in try, and physics. characterizing knotted and linked DNA that arises from No prior knowledge of knots, biology, or physics is the biochemical process of site-specific recombination. assumed. In particular, the first day of the Short Course Additionally, building on the experimental work of Was- will include introductory lectures by Colin Adams on serman and Cozzarelli as well as Conway’s theory of knot theory, Dorothy Buck on DNA and knots, and Erica

1218 Notices of the AMS Volume 54, Number 9 Conferences

Flapan on topological stereochemistry. The second day will developed a course entitled “Problem Solving in the Sci- include lectures on particular aspects of these subjects: ences”, to help students with weak math skills succeed in Lou Kauffman on applications of knot theory to physics; general chemistry. Together with an organic chemist, she Ned Seeman, who uses topology for DNA nanotechnology; also developed an interdisciplinary upper division course and Jon Simon on the statistical and energetic properties on Symmetry and Chirality. of knots and their relation to molecular biology. Speakers will highlight both their own motivation and Introduction to Knots and DNA projects, as well as describing new avenues for interested Dorothy Buck, Imperial College London researchers (and their students) to explore. Abstract: This talk will introduce DNA, and explain The Short Course will conclude with a panel discussion why knot theorists are interested in this molecule. We will of the putative trajectories of these applications of knot explore the topological techniques used to understand theory, and summarize the major open problems and both DNA itself and how it interacts with proteins in the challenges. cell. As an extended example, we will give an overview In addition to the formal activities led by the speakers of the tangle model and its variations to understand the and organizers, the organizers will ensure that the par- molecular process of site-specific recombination. We will ticipants themselves have adequate time to discuss topics also discuss mathematicians’ contributions to several of mutual interest—during the panel discussion, during open questions involving DNA, including how a protein smaller group discussions at the end of the first day, and unknots DNA effectively and how complicated linked DNA at a dinner organized for the first evening. is copied accurately. Dorothy Buck is a mathematical biologist at Imperial Introduction to Knot Theory College London in the Department of Mathematics and Colin Adams, Williams College Centre for Bioinformatics. She specializes in 3-manifold Abstract: This talk will be an introduction to the math- topology and its applications to mathematical biology. Her ematical theory of knots, including Reidemeister moves, training is in both mathematics and microbiology—she surfaces, types of knots, and various invariants associated spent six years, both at University of Texas-Austin and to knots. We will also touch on the stick number for knots Johns Hopkins Medical School, working in molecular and its implications for chemistry. biology labs. Before joining the faculty at Imperial, she Colin Adams is the the Francis Christopher Oakley was an NSF Postdoctoral Fellow with Craig Benham at the Third Century Professor of Mathematics at Williams Col- University of California Davis Genome Center, and an as- lege. He authored the now-standard undergraduate knot sistant professor in the Applied Mathematics Department theory text, “The Knot Book”, and is renowned for his witty at Brown University. and deceptively sophisticated introductory geometry and topology talks. His own research focuses on hyperbolic Knots and Physics knots and 3-manifolds, and he has involved numerous Lou Kauffman, University of Illinois–Chicago undergraduates in annual summer research projects at Abstract: Knots are mathematical abstractions of the Williams. He is a recipient of the Deborah and Franklin topological properties of rope in physical space. As such, Tepper Haimo Distinguished Teaching Award from the there are immediate relationships of knots with the phys- MAA, a Polya Lecturer for the MAA, and a Sigma Xi Dis- ics of ropes, weaves, long-chain molecules, and other tinguished Lecturer. knotting phenomena in Nature. There are also beautiful and surprising relationships of knot theory with the struc- Introduction to Topological Chirality tures and methods of statistical mechanics and quantum Erica Flapan, Pomona College theory. This talk will survey some of the speaker’s favorite Abstract: Symmetry plays an important role in pre- interactions between knots and physics. dicting the behavior of molecules. A particular type of Louis Kauffman is professor of mathematics at Univer- symmetry that is chemically important is mirror image sity of Illinois–Chicago. He authored the interdisciplinary symmetry. A molecule is said to be chiral if it cannot text “Knots and Physics”. He discovered the bracket poly- change into its mirror image. In this talk we will explain nomial state model for the Jones polnomial and the first why chirality is important; discuss the differences between direct relationship between statistical mechanics models chemical, geometric, topological, and intrinsic chirality; and knot invariants. As a topologist, he is omnivorous, and introduce various techniques to show that a molecule working in knot theory and its relationships with statisti- is topologically chiral. cal mechanics, quantum theory, algebra, combinatorics, Erica Flapan is the Lingurn H. Burkhead Professor and more recently, biology. He is editor of the Journal of of Mathematics at Pomona College. Her research is in Knot Theory and its Ramifications. 3-dimensional topology and applications of topology to chemistry. Her book “When Topology Meets Chemistry”, Single-Stranded DNA Topology was jointly published by the Mathematical Association of Ned Seeman, New York University America and Cambridge University Press. From 2000 to Abstract: The double helical nature of the DNA mol- 2004, she was the principle investigator of an NSF-CCLI ecule has a wide variety of topological implications. Most grant entitled “Enhancing the mathematical understand- biologists are familiar with the notion that circular DNA ing of students in chemistry”. As part of this grant, she molecules are catenanes/links, so that the strands are

October 2007 Notices of the AMS 1219 Conferences linked about once every 10 nucleotides. Consequently, Jon Simon is professor of mathematics at the Uni- biological systems contain topoisomerases which change versity of Iowa. He, along with the chemist Kurt Mislow, the linking topology of the molecule, thereby solving pioneered the rigorous application of knot theory to a variety of problems in the metabolism of the genetic chemistry, in particular by determining chirality of syn- material. Today, the realm of DNA extends beyond its thetic compounds. He codeveloped the idea of Möbius biological role as a molecule with an unbranched helix energy of thick knots. His current research also includes axis. Branched DNA molecules exist as intermediates in particular knotting and tangling of filaments; “energy” of genetic recombination, but for twenty-five years synthetic knots; and applications to molecular biology, e.g., knotted branched DNA molecules have been built for a variety of DNA loops. purposes that are important for nanotechnology and for References molecular computation. The ability to assemble branched DNA backbones has enabled the deliberate construc- [1] The Knot Book, by Colin Adams, American Mathematical Soci- ety (2004). tion of single-stranded knots, polyhedral catenanes and [2] Knots and Physics, by L. Kauffman, World Scientific, Third Borromean rings. New branched DNA motifs have been Edition (2001). derived by using techniques from knot theory. Branched [3] http://www.math.uic/kauffman/Alex.pdf (Alexander’s DNA molecules have enabled the deliberate construction original paper on the Alexander polynomial). of periodic and aperiodic DNA crystals. The applications [4] http://www.math.uic/kauffman/QuickTrip.pdf (Fox’s of these systems include analysis of biological systems, Quick Trip through Knot Theory). nanoelectronics and nanorobotics. [5] arXiv Math 0410329 (Kauffman’s paper on Knot Diagrammat- ics). Ned Seeman is professor of chemistry at New York [6] DNA Topology, by A. Maxwell and A. Bates, Cambridge Univer- University. He founded the field of single-stranded Nucleic sity Press, Second Edition (2005). Acid Topology. Among other work, his lab has character- [7] When Topology Meets Chemistry: A Topological Look at Mo- ized the interactions of synthetic DNA knots with topo- lecular Chirality, by E. Flapan, Cambridge University Press and isomerases, developed a general algorithm for the con- Mathematical Association of America (2000). struction of any DNA knot, synthesized a DNA molecule [8] Thickness of knots, by R. Litherland, J. Simon, E. Rawdon, that can be built to yield four different topological species, and O. Durumeric, Topology and its Applications 91 (1999), and discovered an RNA topoisomerase. For his innovation, 233–244. [9] Physical models for exploring DNA topology, by N. C. Seeman, he was awarded the Feynman Prize in Nanotechnology, Journal of Biomolecular Structure and Dynamics 5 (1988), the Emerging Technology Award from Discover Magazine, 997–1004. and elected Fellow of the Royal Society of Chemistry. He [10] DNA nicks and nodes and nanotechnology, by N. C. Seeman, is the founding president of the International Society for NanoLetters 1 (2001), 22–26. Nanoscale Science, Computation and Engineering. [11] Models of entanglement, by G. Buck and J. Simon, Knot The- ory for Scientific Objects, OCAMI Studies 1 (2007), 51–74. Long Tangled Filaments [12] Total curvature and packing of knots, by G. Buck and J. Simon, Topology and its applications 154 (2007), 192–204. Jon Simon, University of Iowa [13] Thickness and crossing number of knots, by G. Buck and J. Abstract: We are interested in filaments, from rope and Simon, Topology and its Applications 91 (1999), 245–257. string and hair to DNA and proteins, anything that might be understood as one-dimensional strands wiggling and tangling in three-dimensional space. If the filaments are short, we can try to describe the exact geometric shape and understand how the shape relates to physical behavior. If the filaments are some- what long and flexible, then topological knot type can be very useful, as evidenced by the success of topological methods for studying the actions of DNA enzymes. But if the filaments are very long (think of a complicated 3-dimensional scribble) or somehow random (think of a lot of complicated 3-dimensional scribbles) then it may be impractical to try describe the exact shapes or even knot types. We need to develop a vocabulary of ideas and models that describe physically important geometric/to- pological properties of long tangled things. In this talk, we will consider ideas, experiments, and theorems dealing with packing, curvature, tangling, and knotting of individual complicated filaments as well as statistical ensembles. We will explore some of the work that has been done, some open research problems, and some topics that seem well-suited for undergraduate research activities.

1220 Notices of the AMS Volume 54, Number 9 Meetings & Conferences of the AMS

IMPORTANT information regarding meetings programs: AMS Sectional Meeting programs do not appear in the print version of the Notices. However, comprehensive and continually updated meeting and program information with links to the abstract for each talk can be found on the AMS website. See http://www.ams.org/meetings/. Final programs for Sectional Meetings will be archived on the AMS website accessible from the stated URL and in an electronic issue of the Notices as noted below for each meeting.

Alex Iosevich, University of Missouri, Incidence theory, Chicago, Illinois Fourier analysis and applications to geometric combinator- ics and additive number theory. DePaul University (Loop Campus) David E. Radford, University of Illinois at Chicago, Representations of pointed Hopf algebras. October 5–6, 2007 Friday – Saturday Special Sessions Algebraic Coding Theory (in honor of Harold N. Ward’s Meeting #1030 retirement), Jay A. Wood, Western Michigan University. Central Section Algebraic Combinatorics: Association Schemes and Associate secretary: Susan J. Friedlander Related Topics, Sung Y. Song, Iowa State University, and Announcement issue of Notices: August 2007 Paul Terwilliger, University of Wisconsin. Program first available on AMS website: August 16, 2007 Algebraic Geometry, Lawrence Man Hou Ein and Ana- Program issue of electronic Notices: October 2007 toly S. Libgober, University of Illinois at Chicago. Issue of Abstracts: Volume 28, Issue 3 Algorithmic Probability and Combinatorics, Manuel Lladser, University of Colorado, and Robert S. Maier, Deadlines University of Arizona. For organizers: Expired Analysis and CR Geometry, Song-Ying Li, University For consideration of contributed papers in Special Ses- of California Irvine, and Stephen S-T Yau, University of sions: Expired Illinois at Chicago. For abstracts: Expired Applied Harmonic Analysis, Jonathan Cohen and Ahmed I. Zayed, DePaul University. The scientific information listed below may be dated. Automorphic Forms: Representation Theory of p-adic For the latest information, see www.ams.org/amsmtgs/ and Adelic Groups, Mahdi Asgari and Anantharam Ra- sectional.html. ghuram, Oklahoma State University. Differential Geometry and Its Applications, Jianguo Cao, Invited Addresses University of Notre Dame. Martin Golubitsky, University of Houston, Symmetry Ergodic Theory and Symbolic Dynamical Systems, Ayse breaking and synchrony breaking. A. Sahin and Ilie D. Ugarcovici, DePaul University. Matthew J. Gursky, University of Notre Dame, Origins Extremal and Probabilistic Combinatorics, Jozsef Ba- and applications of some nonlinear equations in conformal logh, University of Illinois at Urbana-Champaign, and geometry. Dhruv Mubayi, University of Illinois at Chicago.

October 2007 Notices of the AMS 1221 Meetings & Conferences

Free Resolutions, Noam Horwitz and Irena Peeva, Cor- Program first available on AMS website: August 16, 2007 nell University. Program issue of electronic Notices: October 2007 Geometric Combinatorics, Caroline J. Klivans, Univer- Issue of Abstracts: Volume 28, Issue 3 sity of Chicago, and Kathryn Nyman, Loyola University Chicago. Deadlines Graph Theory, Hemanshu Kaul and Michael J. Pelsma- For organizers: Expired jer, Illinois Institute of Technology. For consideration of contributed papers in Special Ses- Hopf Algebras and Related Areas, Yevgenia Kashina sions: Expired and Leonid Krop, DePaul University, M. Susan Mont- For abstracts: Expired gomery, University of Southern California, and David E. Radford, University of Illinois at Chicago. The scientific information listed below may be dated. Mathematical Modeling and Numerical Methods, Atife Caglar, University of Wisconsin-Green Bay. For the latest information, see www.ams.org/amsmtgs/ Model Theory of Non-elementary Classes, John T. Bald- sectional.html. win, University of Illinois at Chicago, David W. Kueker, University of Maryland, and Rami Grossberg, Carnegie Invited Addresses Mellon University. Satyan L. Devadoss, Williams College, The topology of Networks, Martin Golubitsky, University of Houston, particle collisions. and Mary Silber, Northwestern University. Tara S. Holm, Cornell University, Act globally, compute Nonlinear Conservation Laws and Related Problems, locally: Localization in symplectic geometry. Cleopatra Christoforou and Gui-Qiang Chen, Northwest- Sir Roger Penrose, University of Oxford, Spacetime con- ern University. formal geometry, and a new extended cosmology (Einstein Numerical and Symbolic Techniques in Algebraic Geom- Public Lecture in Mathematics). etry and Its Applications, Gian Mario Besana, DePaul Uni- Scott Sheffield, Courant Institute and Institute for versity, Jan Verschelde, University of Illinois at Chicago, Advanced Study, Random metrics and geometries in two and Zhonggang Zeng, Northeastern Illinois University. dimensions. Sequence Spaces and Transformations, Constantine Mu-Tao Wang, Columbia University, Isometric embed- Georgakis, DePaul University, and Martin Buntinas, Loyola dings and quasi-local mass. University of Chicago. Singular Integrals and Related Problems, Laura De Special Sessions Carli, Florida International University, and A. M. Stokolos, DePaul University. Commutative Algebra, Jooyoun Hong, University of Smooth Dynamical Systems, Marian Gidea, Northeast- California Riverside, and Wolmer V. Vasconcelos, Rutgers ern Illinois University, and Ilie D. Ugarcovici, DePaul University. University. Geometric Analysis of Complex Laplacians, Siqi Fu, The Euler and Navier-Stokes Equations, Alexey Cheski- Rutgers University, Camden, Xiaojun Huang, Rutgers dov, University of Michigan, and Susan J. Friedlander and University, New Brunswick, and Howard J. Jacobowitz, Roman Shvydkoy, University of Illinois at Chicago. Rutgers University, Camden. Wave Propagation from Mathematical and Numerical Invariants of Lie Group Actions and Their Quotients, Viewpoints, Gabriel Koch, University of Chicago, Catalin Tara S. Holm, Cornell University, and Rebecca F. Goldin, Constantin Turc, Caltech and University of North Caro- George Mason University. lina at Charlotte, and Nicolae Tarfulea, Purdue University Mathematical and Physical Problems in the Foundations Calumet. of Quantum Mechanics (in honor of Shelly Goldstein’s 60th birthday), Roderich Tumulka and Detlef Dürr, München University, and Nino Zanghi, University of Genova. New Brunswick, New Noncommutative Geometry and Arithmetic Geometry, Caterina Consani, Johns Hopkins University, and Li Guo, Jersey Rutgers University. Rutgers University-New Brunswick, College Partial Differential Equations of Mathematical Physics, Avenue Campus Sagun Chanillo, Michael K.-H. Kiessling, and Avy Soffer, Rutgers University. October 6–7, 2007 Probability and Combinatorics, Jeffry N. Kahn and Van Saturday – Sunday Ha Vu, Rutgers University. Set Theory of the Continuum, Simon R. Thomas, Rut- Meeting #1031 gers University. Eastern Section Toric Varieties, Milena S. Hering, Institute for Math- Associate secretary: Lesley M. Sibner ematics and Its Applications, and Diane Maclagan, Rutgers Announcement issue of Notices: August 2007 University.

1222 Notices of the AMS Volume 54, Number 9 Meetings & Conferences

Harmonic Analysis and Operator Theory, Maria C. Albuquerque, New Pereyra and Wilfredo O. Urbina, University of New Mexico. Mexico Mathematical and Computational Aspects of Compress- ible Flow Problems, Jens Lorenz and Thomas M. Hag- University of New Mexico strom, University of New Mexico. Methods of Heterogeneous Data Analysis, Hanna Ewa October 13–14, 2007 Makaruk, Los Alamos National Laboratory, and Nikita A. Saturday – Sunday Sakhanenko, University of New Mexico. Nonlinear Waves in Optics, Hydrodynamics and Plasmas, Meeting #1032 Alejandro Aceves and Pavel Lushnikov, University of Western Section New Mexico. Associate secretary: Michel L. Lapidus Recent Developments in 2-D Turbulence, Michael S. Announcement issue of Notices: August 2007 Jolly, Indiana University, and Greg Eyink, Johns Hopkins Program first available on AMS website: August 30, 2007 University. Program issue of electronic Notices: October 2007 Topics in Mathematical Physics, Rafal Komendarczyk, Issue of Abstracts: Volume 28, Issue 4 University of Pennsylvania, and Robert Michal Owczarek, Los Alamos National Laboratory. Deadlines Variational Problems in Condensed Matter, Lia Bron- For organizers: Expired sard, McMaster University, and Tiziana Giorgi, New Mexico For consideration of contributed papers in Special Ses- State University. sions: Expired For abstracts: Expired

The scientific information listed below may be dated. Murfreesboro, For the latest information, see www.ams.org/amsmtgs/ sectional.html. Tennessee

Invited Addresses Middle Tennessee State University Emmanuel J. Candes, California Institute of Technol- November 3–4, 2007 ogy, The role of probability in compressed sensing. Alexander Polischuk, University of Oregon, A-infinity Saturday – Sunday structures and theta series. Meeting #1033 Eric Rains, California Institute of Technology, Elliptic hypergeometric integrals. Southeastern Section William E. Stein, University of California San Diego, Associate secretary: Matthew Miller SAGE: Open source mathematics software. Announcement issue of Notices: September 2007 Program first available on AMS website: September 20, Special Sessions 2007 Affine Algebraic Geometry, David Robert Finston, New Program issue of electronic Notices: November 2007 Mexico State University. Issue of Abstracts: Volume 28, Issue 4 Arithmetic and Algebraic Geometry, Alexandru Buium Deadlines and Michael J. Nakamaye, University of New Mexico. Computational Applications of Algebraic Topology, Ross For organizers: Expired Staffeldt, New Mexico State University. For consideration of contributed papers in Special Ses- Computational Methods in Harmonic Analysis and Sig- sions: Expired nal Processing, Emmanuel Candes, California Institute For abstracts: September 11, 2007 of Technology, and Joseph D. Lakey, New Mexico State University. The scientific information listed below may be dated. Financial Mathematics: The Mathematics of Financial For the latest information, see www.ams.org/amsmtgs/ Markets and Structures, Cristina Mariani and Kenneth sectional.html. Martin, New Mexico State University. Geometric Structures on Manifolds, Charles Boyer and Invited Addresses Krzysztof Galicki, University of New Mexico. Sergey Gavrilets, University of Tennessee, Mathemati- Harmonic Analysis Applied to Partial Differential Equa- cal models of speciation. tions, Justin Holmer, University of California Berkeley, Daniel K. Nakano, University of Georgia, Bridging al- Changxing Miao, Institute of Applied Physics and Com- gebra and geometry via cohomology. putational Mathematics, and Jiaong Wu, Oklahoma State Carla D. Savage, North Carolina State University, The University. mathematics of lecture hall partitions.

October 2007 Notices of the AMS 1223 Meetings & Conferences

Sergei Tabachnikov, Pennsylvania State University, State University, and Judith H. Hector, Walters State Com- Ubiquitous billiards. munity College. Special Sessions Advances in Algorithmic Methods for Algebraic Struc- Wellington, New tures (Code: SS 3A), James B. Hart, Middle Tennessee State University. Applied Partial Differential Equations (Code: SS 4A), Yuri Zealand A. Melnikov, Middle Tennessee State University, and Alain Victoria University of Wellington J. Kassab, University of Central Florida. Billiards and Related Topics (Code: SS 6A), Sergei December 12–15, 2007 Tabachnikov, Pennsylvania State University, and Richard Schwartz, Brown University. Wednesday – Saturday Combinatorial Enumeration, Optimization, Geometry, Meeting #1034 and Statistics (Code: SS 13A), Nicholas A. Loehr, College of William and Mary, Gabor Pataki, University of North First Joint International Meeting between the AMS and the Carolina, Chapel Hill, Margaret A. Readdy, University of New Zealand Mathematical Society (NZMS). Kentucky and M.I.T., Carla D. Savage, North Carolina State Associate secretary: Matthew Miller University, and Ruriko Yoshida, University of Kentucky. Announcement issue of Notices: June 2007 Combinatorial Methods in Continuum Theory (dedicated Program first available on AMS website: Not applicable to Jo Heath, Auburn University, on the occasion of her Program issue of electronic Notices: Not applicable retirement) (Code: SS 8A), Judy A. Kennedy, University Issue of Abstracts: Not applicable of Delaware and Lamar University, Krystyna M. Kuper- berg, Auburn University, and Van C. Nall, University of Deadlines Richmond. For organizers: Expired Differential Equations and Dynamical Systems (Code: SS For consideration of contributed papers in Special Ses- 1A), Wenzhang Huang and Jia Li, University of Alabama, sions: To be announced Huntsville, and Zachariah Sinkala, Middle Tennessee State For abstracts: October 31, 2007 University. Financial Mathematics (Code: SS 16A), Abdul Khaliq, The scientific information listed below may be dated. Middle Tennessee State University. For the latest information, see www.ams.org/amsmtgs/ Graph Theory (Code: SS 2A), Rong Luo, Don Nelson, Chris Stephens, and Xiaoya Zha, Middle Tennessee State internmtgs.html. University. AMS Invited Addresses Lie and Representation Theory (Code: SS 11A), Terrell L. Hodge, Western Michigan University, Daniel K. Nakano, Marston Conder, University of Auckland, Chirality. University of Georgia, and Brian J. Parshall, University of Rodney G. Downey, Victoria University of Wellington, Virginia. Practical FPT and foundations of kernelization. Mathematical Modeling in Biological Systems (Code: SS Michael H. Freedman, Microsoft Research, Physically 9A), Terrence J. Quinn, Middle Tennessee State Univer- motivated questions in topology: Manifold pairings. sity. Bruce J. Kleiner, Yale University, Title to be an- Mathematical Tools for Survival Analysis and Medical nounced. Data Analysis (Code: SS 7A), Curtis Church, Middle Ten- Gaven J. Martin, Massey University, Curvature and nessee State University, Chang Yu, Vanderbilt University, dynamics. and Ping Zhang, Middle Tennessee State University. Assaf Naor, Microsoft Research/Courant Institute, Title Nonlinear Partial Differential Equations and Applica- to be announced. tions (Code: SS 14A), Emmanuele DiBenedetto, Mikhail Theodore A. Slaman, University of California Berkeley, Perepelitsa, and Gieri Simonett, Vanderbilt University. Title to be announced. Physical Knots and Links (Code: SS 10A), Yuanan Diao, Matthew J. Visser, Victoria University of Wellington, University of North Carolina at Charlotte, and Claus Ernst, Emergent spacetimes, rainbow geometries, and pseudo- Western Kentucky University. Recent Advances in Algebraic Topology (Code: SS 12A), Finsler geometries. Mark W. Johnson, Pennsylvania State University, Altoona, AMS Special Sessions and Donald Yau, The Ohio State University at Newark. Splines and Wavelets with Applications (Code: SS 5A), Computability Theory, Rodney G. Downey and Noam Don Hong, Middle Tennessee State University, and Qing- Greenberg, Victoria University of Wellington, and Theo- tang Jiang, University of Missouri-St. Louis. dore A. Slaman, University of California Berkeley. Using National Assessment of Educational Progress Dynamical Systems and Ergodic Theory, Arno Berger, (NAEP) Data to Enhance Assessment and Inform Instruction University of Canterbury, Rua Murray, University of (Code: SS 15A), Michaele F. Chappell, Middle Tennessee Waikato, and Matthew J. Nicol, University of Houston.

1224 Notices of the AMS Volume 54, Number 9 Meetings & Conferences

Geometric Numerical Integration, Laurent O. Jay, The Associate secretary: Michel L. Lapidus University of Iowa, and Robert McLachlan, Massey Uni- Announcement issue of Notices: October 2007 versity. Program first available on AMS website: November 1, Group Theory, Actions, and Computation, Marston 2007 Conder, University of Auckland, and Russell Blyth, Saint Program issue of electronic Notices: January 2008 Louis University. Issue of Abstracts: Volume 29, Issue 1 History and Philosophy of Mathematics, James J. Tat- tersall, Providence College, Ken Pledger, Victoria Univer- Deadlines sity of Wellington, and Clemency Williams, University of For organizers: Expired Canterbury. For consideration of contributed papers in Special Ses- Hopf Algebras and Quantum Groups, M. Susan Mont- sions: Expired gomery, University of Southern California, and Yinhuo For abstracts: September 20, 2007 Zhang, Victoria University of Wellington. Infinite-Dimensional Groups and Their Actions, Chris- The scientific information listed below may be dated. topher Atkin, Victoria University of Wellington, Greg For the latest information, see www.ams.org/amsmtgs/ Hjorth, University of California Los Angeles/University national.html. of Melbourne, Alica Miller, University of Louisville, and Vladimir Pestov, University of Ottawa. AMS-MAA Joint Invited Addresses Integrability of Continuous and Discrete Evolution Sys- Fan Chung, University of California San Diego, The tems, Mark Hickman, University of Canterbury, and Willy mathematics of PageRank, 11:10 a.m. on Tuesday. A. Hereman, Colorado School of Mines. Terence Tao, University of California Los Angeles, Mathematical Models in Biomedicine, Ami Radunskaya, Structure and randomness in the prime numbers, 11:10 Pomona College, James Sneyd, University of Auckland, a.m. on Sunday. Urszula Ledzewicz, University of Southern Illinois at AMS Committee on Science Policy-MAA Science Policy Edwardsville, and Heinz Schaettler, Washington Univer- Committee Government Speaker, speaker and title to be sity. announced, 4:20 p.m. on Tuesday. Matroids, Graphs, and Complexity, Dillon Mayhew, Victoria University of Wellington, and James G. Oxley, Joint Prize Session Louisiana State University. Prize Session and Reception: In order to showcase New Trends in Spectral Analysis and Partial Differential the achievements of the recipients of various prizes, the Equations, Boris P. Belinskiy, University of Tennessee, AMS and MAA are cosponsoring this event at 4:25 p.m. Chattanooga, Anjan Biswas, Delaware State University, on Monday. A cash bar reception will immediately follow. and Boris Pavlov, University of Auckland. All participants are invited to attend. The AMS, MAA, and Quantum Topology, David B. Gauld, University of SIAM will award the Frank and Brennie Morgan Prize for Auckland, and Scott E. Morrison, University of California Outstanding Research in Mathematics by an Undergradu- Berkeley. ate Student. The AMS will announce the winners of the Special Functions and Orthogonal Polynomials, Shaun Award for Distinguished Public Service, Bôcher Memorial Cooper, Massey University, Diego Dominici, SUNY New Prize, Frank Nelson Cole Prize in Number Theory, Levi Paltz, and Sven Ole Warnaar, University of Melbourne. L. Conant Prize, Joseph L. Doob Prize, Leonard Eisenbud Water-Wave Scattering Focusing on Wave-Ice Interac- Prize for Mathematics and Physics, JPBM Communica- tions, Michael H. Meylan, Massey University, and Malte tions Award, and the Leroy P. Steele Prizes. The MAA will Peter, University of Bremen. award the Beckenbach Book Prize, Chauvenet Prize, Euler Book Prize, Yueh-Gin Gung and Dr. Charles Y. Hu Award for Distinguished Service to Mathematics, Deborah and San Diego, California Franklin Tepper Haimo Awards for Distinguished Col- lege or University Teaching of Mathematics, Certificates San Diego Convention Center of Meritorious Service, and the David P. Robbins Prize. January 6–9, 2008 The AWM will present the Alice T. Schafer Prize for Excel- lence in Mathematics by an Undergraduate Woman and Sunday – Wednesday the Louise Hay Award for Contributions to Mathematics Meeting #1035 Education. Joint Mathematics Meetings, including the 114th Annual Meeting of the AMS, 91st Annual Meeting of the Mathemati- cal Association of America (MAA), annual meetings of the 114th Meeting of the AMS Association for Women in Mathematics (AWM) and the AMS Invited Addresses National Association of Mathematicians (NAM), and the winter meeting of the Association for Symbolic Logic (ASL), James G. Arthur, University of Toronto, Semisimple groups with sessions contributed by the Society for Industrial and as universal examples, 3:20 p.m. on Monday. (AMS Retiring Applied Mathematics (SIAM). Presidential Address)

October 2007 Notices of the AMS 1225 Meetings & Conferences

Constantine M. Dafermos, Brown University, Progress in Conformally Flat Lorentzian Manifolds, Virginie Cha- hyperbolic conservation laws, 9:00 a.m. on Wednesday. rette, Université de Sherbrooke, William M. Goldman, Wen-Ching Winnie Li, National Tsing Hua University and University of Maryland, Karin H. Melnick, Yale University, Pennsylvania State University, Combinatorics and number and Kevin Scannel, Saint Louis University; Monday morn- theory, 10:05 a.m. on Sunday. ing and afternoon. Dynamics and Stability of Coherent Structures, Ricardo Donald G. Saari, University of California Irvine, A new Carretero and Jennifer M. Gorsky, University of San mathematical frontier: The social and behavioral sciences, Diego; Tuesday morning and afternoon. 10:05 on Tuesday. E-Theory, Extensions, and Elliptic Operators, Constantin Peter Teichner, University of California Berkeley, Quan- D. Dumitrascu, University of Arizona, and John D. Trout, tum field theory and generalized cohomology, 2:15 p.m. Dartmouth College; Wednesday morning and afternoon. on Wednesday. Environmental Mathematics: Some Mathematical Prob- Wendelin Werner, University of Paris-Sud, Random con- lems on Climate Change and Geophysical Fluid Dynamics, formally invariant pictures, 1:00 p.m. on Sunday, Monday, Samuel S. Shen, San Diego State University, and Gerald and Tuesday. (AMS Colloquium Lectures) R. North, Texas A&M University (AMS-SIAM); Wednesday morning. Avi Wigderson, Institute for Advanced Study, Random- Expanders and Ramanujan Graphs: Construction and ness—A computational complexity view, 8:30 p.m. on Applications, Michael T. Krebs and Anthony M. Shaheen, Sunday. (AMS Josiah Willard Gibbs Lecture) California State University, Los Angeles, and Audrey A. AMS Special Sessions Terras, University of California San Diego; Tuesday and Wednesday afternoons and Wednesday morning. Some sessions are cosponsored with other organiza- Feynman Integral in Mathematics and Physics, Lance tions. These are noted within the parentheses at the end W. Nielsen, Creighton University; Wednesday morning of each listing, where applicable. and afternoon. Abstracts for all Special Sessions must be submitted Financial Mathematics, Jean-Pierre Fouque, Univer- through the meeting website at www.ams.org/cgi-bin/ sity of California Santa Barbara; Kay Giesecke, Stanford abstracts/abstract.pl. No speaker will be scheduled University; Ronnie Sircar, Princeton University; and unless an abstract is submitted by the deadline for perusal Knut Solna, University of California Irvine; Tuesday and by the Program Committee. Wednesday, mornings and afternoons. Algebraic Dynamics, Diana M. Thomas, Montclair State Global Optimization and Operations Research Ap- University, Lennard F. Bakker, Brigham Young University, plications, Ram U. Verma, University of Central Florida; and Donald Mills, Rose-Hulman Institute of Technology; Wednesday morning and afternoon. Tuesday morning and afternoon. Graph Theory, Andre Kundgen and K. Brooks Reid, Algebraic Topology, Nitu Kitchloo, University of Cali- California State University, San Marcos; Monday and Tues- fornia San Diego; Ralph L. Cohen, Stanford University; day mornings and Monday afternoon. James P. Lin and Justin Robert, University of California Groups, Representations, and Character Theory, Ma- San Diego; and Peter Teichner, University of California nouchehr Misaghian, Johnson C. Smith University, and Berkeley; Sunday and Monday mornings and Sunday Mohammad Reza Darafsheh, University of Tehran; Sun- afternoon. day morning and afternoon. Algebraic and Geometric Aspects of Integrable Systems, Heegaard Splittings, Bridge Positions, and Low Dimen- Baofeng Feng, University of Texas-Pan American; Wenxiu sional Topology, Jesse Johnson, Yale University; Abigail Ma, University of South Florida; Kenichi Maruno and Zhi- A. Thompson, University of California Davis; and Robin jun Qiao, University of Texas-Pan American; and Taixi Xu, Wilson, University of California Santa Barbara; Wednesday Southern Polytechnic State University; Wednesday morn- morning and afternoon. ing and afternoon. History of Mathematics, Joseph W. Dauben, Lehman Applications of Computer Algebra in Enumerative and College, CUNY; Patti Hunter, Westmont College; Victor Algebraic Combinatorics, Akalu Tefera, Massachusetts J. Katz, University of District of Columbia; and Karen H. Institute of Technology and Grand Valley State University, Parshall, University of Virginia; Tuesday and Wednesday, and Moa Apagodu, Virginia Commonwealth University; mornings and afternoons. (AMS-MAA) Tuesday afternoon. Hyperbolic Dynamical Systems, Todd L. Fisher, Univer- Asymptotic Methods in Analysis with Applications, Diego sity of Maryland, and Boris Hasselblatt, Tufts University; Dominici, SUNY New Platz, and Peter A. McCoy, U.S. Naval Sunday morning and afternoon. Academy; Sunday morning and afternoon. (AMS-SIAM) Interactions Between Noncommutative Alge- Automorphic Forms and Related Topics, Olav K. Richter, bra and Algebraic Geometry, Daniel S. Rogalski and University of North Texas; Kathrin Bringmann, University Lance W. Small, University of California San Diego, of Minnesota; and Harold M. Stark, University of California and James J. Zhang, University of Washington; San Diego; Sunday morning and afternoon. Sunday morning and afternoon. Biomathematical Modeling, Olcay Akman, Illinois State Inverse Problems in Geometry, Peter A. Perry, Uni- University, and Timothy D. Comar, Benedictine University; versity of Kentucky, and Carolyn S. Gordon, Dartmouth Tuesday afternoon. College; Tuesday morning and afternoon.

1226 Notices of the AMS Volume 54, Number 9 Meetings & Conferences

Learning and Math Graduate Students in K–12 Class- sity; and Tamas Wiandt, Rochester Institute of Technol- room, Richard S. Millman, University of Kentucky, Loyce ogy; Tuesday and Wednesday mornings and Monday and M. Adams, University of Washington; Overtoun M. Jenda, Wednesday afternoons. (AMS-MAA-SIAM) Auburn University; and M. Helena Noronha, California Scholarship of Teaching and Learning in Mathemat- State University, Northridge; Tuesday afternoon. ics, Curtis D. Bennett and Jacqueline M. Dewar, Loyola Linear Diophantine Problem of Frobenius, Matthias Marymount University; Sunday morning and afternoon Beck, San Francisco State University; Stanley Wagon, (AMS-MAA) Macalester College; and Kevin M. Woods, Oberlin College; Secant Varieties and Related Topics, Christopher S. Wednesday afternoon. Peterson, Colorado State University; Hirotachi Abo, Low Genus Curves and Applications, Kristin E. Lauter, University of Idaho; and Anthony V. Geramita, Queen’s Microsoft Research, and Peter Stevenhagen, Leiden Uni- University and University of Genoa; Tuesday morning and versity; Monday and Tuesday afternoons and Tuesday afternoon. morning. Set Theory and Banach Spaces, Christian Rosendal, Mathematical Problems in Biological Formations, Yu- University of Illinois at Urbana-Champaign, and Stevo B. anwei Qi, University of Central Florida; Wednesday af- Todorcevic, University of Toronto and CNRS, Université ternoon. Paris 7; Sunday and Monday mornings and Sunday after- Mathematics and Education Reform, Bonnie S. Saun- noon. (AMS-ASL) ders, University of Illinois, Chicago; William H. Barker, Stochastic, Large-Scale, and Hybrid Systems with Ap- Bowdoin College; Dale R. Oliver, Humboldt State Univer- plications, Aghalaya S. Vatsala, University of Louisiana at sity; and Michael Starbird, University of Texas, Austin; Lafayette, and G. S. Ladde, University of Texas at Arling- Wednesday morning and afternoon. (AMS-MAA-MER) ton; Monday morning and afternoon. Mathematics for Teaching: Educating Elementary and Structure, Geometry, and Symbolic Computation of Middle School Teachers for Success, Babette M. Benken, Algebraic Groups and Symmetric Spaces, Jennifer R. Dan- Lynn C. California State University, Long Beach, and iel, Lamar University, and Aloysius G. Helminck, North McGrath and Perla L. Myers, University of San Diego; Carolina State University; Monday and Tuesday mornings Monday morning and afternoon. and Monday afternoon. Mathematics of Information and Knowledge, Peter W. Time-Frequency Analysis: Hilbert Huang Transform Jones, Yale University; James G. Glimm, SUNY at Stony and Wavelet Analysis, Yuesheng Xu, Syracuse University; Brook; Steve Smale, Toyota Institute of Technology at Sherman D. Riemenschneider, West Virginia University; Chicago; Sunday and Monday, mornings and afternoons. and Samuel S. Shen, San Diego State University; Monday Modular Forms and Modularity, Ling Long, Iowa State morning and afternoon. University; Wen-Ching Winnie Li, Pennsylvania State Uni- Voting Theory, Michael A. Jones, Montclair State Univer- versity; and Tong Liu, University of Pennsylvania; Monday sity; Eric I. Gottlieb, Rhodes College; and Brian P. Hopkins, and Tuesday mornings and Monday afternoon. Saint Peter's College; Monday morning and afternoon. Monotone Discrete Dynamical Systems with Applica- n tions, M. R. S. Kulenovic and Orlando Merino, University Wavelet Sets and Tilings of R , Kathy D. Merrill, Colo- of Rhode Island, and Hal L. Smith, Arizona State Univer- rado College, and Lawrence W. Baggett and Judith A. sity; Monday morning and afternoon. Packer, University of Colorado, Boulder; Tuesday morning Probability Theory and Statistical Mechanics, Itai Ben- and afternoon. jamini, Weizmann Institute and Microsoft Research, and Zeta Functions of Graphs, Ramanujan Graphs, and Re- Wendelin Werner, University of Paris-Sud; Wednesday lated Topics, Audrey A. Terras, University of California morning and afternoon. San Diego, and Matthew Horton, Wellesley College; Sunday Progress in Commutative Algebra, Janet Striuli, Univer- morning and afternoon. (AMS-AWM) sity of Nebraska, Lincoln; Sean M. Sather-Wagstaff, North Contributed Paper Sessions Dakota State University; and Lars Winther Christensen, Texas Tech University; Sunday and Monday mornings and There will be sessions for contributed papers of ten Monday afternoon. minutes’ duration. Contributed papers will be grouped by Recent Advances in Mathematical Biology, Ecology, and related Mathematics Subject Classification into sessions Epidemiology, Linda J. S. Allen, Texas Tech University; insofar as possible. The author(s) and their affiliation(s) Sophia R. Jang, University of Louisiana at Lafayette; and and the title of each paper accepted will be listed in the Lih-Ing W. Roeger, Texas Tech University; Sunday and program along with the date and time of presentation. Monday mornings and Sunday afternoon. Although an individual may present only one contributed Representation Theory and Nonassociative Algebras, paper at a meeting, any combination of joint authorship Murray R. Bremner, University of Saskatchewan; Irvin R. may be accepted, provided no individual speaks more than Hentzel, Iowa State University; and Luiz A. Peresi, Uni- once. Abstracts will be published in Abstracts Presented to versity of Sao Paulo; Tuesday afternoon. the American Mathematical Society and should be submitted Research in Mathematics by Undergraduates, Darren electronically. See www.ams.org/cgi-bin/abstracts/ A. Narayan and Bernard Brooks, Rochester Institute of abstract.pl for the form. Select AMS CP 1 as the event Technology; Jacqueline A. Jensen, Sam Houston State code. See the beginning of this announcement for perti- University; Vadim Ponomarenko, San Diego State Univer- nent deadlines, which are strictly enforced.

October 2007 Notices of the AMS 1227 Meetings & Conferences

Other AMS Sessions Wikipedia, since mathematical facts are ... well ... facts, and there ought to be little room for disagreement. How Grant Writing in the Mathematical Sciences, Sunday, 8:00 does this work out in practice? The session will offer an a.m. to 10:55 a.m. and 2:15 p.m. to 5:30 p.m., organized by anecdotal survey, exhibiting some of the best as well as Michelle Wagner, National Security Agency, and Deborah some of the worst. We hope also to discuss how perhaps F. Lockhart, National Science Foundation. The goals of it should deal with mathematics. this workshop are to inform the community about ongo- ing and new funding opportunities in the mathematical Committee on Science Policy Panel Discussion: Tues- sciences, provide grant writing guidance from program day, 2:30 p.m. to 4:00 p.m. managers and successful proposal writers, and provide Committee on Education Panel Discussion: Wednes- a hands-on opportunity for participants to write mock day, 8:30 a.m. to 10:00 a.m. proposals and have their work critiqued by their peers and other experts. The first part of the program will Other AMS Events feature presentations by program managers of several Council: Saturday, 1:30 p.m. agencies that provide funding in the mathematical sci- Business Meeting: Wednesday, 11:45 a.m. ences. Program managers will provide an overview of The secretary notes the following resolution of the the kinds of funding opportunities that exist within their Council: Each person who attends a business meeting of organizations, and will also describe proposal submis- the Society shall be willing and able to identify himself as sion processes, evaluation criteria, and funding rates and a member of the Society. In further explanation, it is noted statistics. In the next segment of the session, a panel of that each person who is to vote at a meeting is thereby program managers and successful proposal writers will identifying himself as and claiming to be a member of talk about the “dos and don’ts” of proposal writing. Suc- the American Mathematical Society. The Society has a cessful proposal writers will share their experiences of Committee on the Agenda for Business Meetings. The navigating the proposal submission and review process; purpose is to make business meetings orderly and effec- program managers will talk more in depth about review tive. The committee does not have legal or administrative processes, and will present specific strategies for writing power. It is intended that the committee consider what sound proposals of different types (research, conference, may be called “quasipolitical” motions. The committee has REU, etc). The workshop will culminate with a hands-on several possible courses of action on a proposed motion, opportunity for participants to write short sections of including but not restricted to: mock proposals and have them critiqued by other session (a) doing nothing, participants and the session leader. Please be sure to check (b) conferring with supporters and opponents to arrive the appropriate box on the registration form. at a mutually accepted amended version to be circulated Congressional Fellowship Session, Sunday, 4:30 p.m. in advance of the meeting, to 5:50 p.m., organized by Samuel M. Rankin, III, AMS. (c) recommending and planning a format for debate to This program is administered by the American Association suggest to a business meeting, for the Advancement of Science (AAAS). The fellowship (d) recommending referral to a committee, and is designed to provide a unique public policy learning (e) recommending debate followed by referral to a experience, to demonstrate the value of science/govern- committee. ment interaction, and to bring a technical background There is no mechanism that requires automatic sub- and external perspective to the decision-making process mission of a motion to the committee. However, if a in Congress. We intend to have the three AMS-sponsored motion has not been submitted through the committee, it Congressional Fellows give their perspective on the fel- may be thought reasonable by a business meeting to refer lowship to interested meeting participants to encourage it rather than to act on it without benefit of the advice of applications for future fellowships. the committee. Who Wants to Be a Mathematician, Tuesday, 10:00 a.m. In order that a motion for this business meeting to 10:55 a.m., organized by Michael A. Breen, AMS, and receive the service offered by the committee in the most William T. Butterworth, DePaul University. Come watch effective manner, it should be in the hands of the AMS eight of the area’s top high school students compete for Secretary by December 7, 2007. cash and prizes by answering questions about mathemat- ics. You are invited to come and take part in this educa- AMS Short Course tional and fun presentation. This two-day course on Applications of Knot Theory is or- Current Events Bulletin, Tuesday, 1:00 p.m. to 6:00 ganized by Dorothy Buck, Imperial College London, and p.m., organized by David Eisenbud, Mathematical Sciences Erica L. Flapan, Pomona College, and takes place on Friday Research Institute. This session follows the model of the and Saturday, January 4 and 5. Over the past twenty years Bourbaki Seminars in that mathematicians with strong knot theory has rekindled its historic ties with biology, expository skills speak on work not their own. Written chemistry, and physics. While the original motivation for versions of the talks will be distributed at the session. understanding and classifying knots came from chemistry, Wiki Math, Tuesday, 1:00 p.m. to 2:15 p.m., organized knot theory remained a primarily pure field of mathemat- by William Casselman, University of British Columbia. ics until the 1980s, when chemists, biologists, and physi- Nominally, mathematics should be an ideal subject for cists began searching for more sophisticated descriptions

1228 Notices of the AMS Volume 54, Number 9 Meetings & Conferences of entanglements of natural phenomena—from strings to Paul H. Edelman, Vanderbilt University, Mathematics and small organic compounds to DNA. the law: The apportionment of the House of Representa- This course will introduce knot theory and some of tives, 3:20 p.m. on Sunday. its recent applications in molecular biology, chemistry, Karen H. Parshall, University of Virginia, 4000 years of and physics. No prior knowledge of knot theory, biology, algebra: An historical tour from BM 13901 to Moderne chemistry, or physics is assumed—there will be introduc- Algebra, 9:00 a.m. on Monday. tory talks on the first day. Speakers will survey their own work in these areas, as well as describing new avenues Carl Pomerance, Dartmouth College, The covering con- for interested researchers (and their students) to explore. gruences of Paul Erdo˝s, 9:00 a.m. on Tuesday. The course will conclude with a panel discussion of the Presentations by Teaching Award Recipients putative trajectories of these applications of knot theory, Tuesday, 2:30 p.m.–4:00 p.m., organized by MAA and summarize the major open problems and challenges. secretary, Martha Siegel, Towson University, and moder- References will be available in advance and lecture notes ated by MAA president, Joseph A. Gallian, University of published afterwards. Minnesota-Duluth. Winners of the Deborah and Franklin Speakers are Colin C. Adams, Williams College; Doro- Tepper Haimo Awards for Distinguished College or Uni- thy Buck; Erica L. Flapan; Louis H. Kauffman, University versity Teaching will give presentations on the secrets of of Illinois at Chicago; Nadrian C. Seeman, Department of their success. Chemistry, New York University; and Jonathan Simon, University of Iowa. Please see the complete article on MAA Minicourses page 1218 or at www.ams.org/meetings/shcourse.html. Minicourses are open only to persons who register for There are separate registration fees to participate. See the Joint Meetings and pay the Joint Meetings registration the fee schedule on the registration form at the back of fee in addition to the appropriate minicourse registra- this issue or visit www.ams.org/amsmtgs/2109_ tion fee of US$60. The MAA reserves the right to cancel registration.html. any minicourse that is undersubscribed. Participants in Minicourses #1–#6 are required to come with a laptop Department Chairs Workshop computer equipped with appropriate software. Instruc- This annual one-day workshop for chairs and leaders of tions to download any data files needed for those courses departments of mathematical sciences will be held a day will be provided by the organizers. before the start of the Joint Meetings on Saturday, 8:00 a.m. Minicourse #1: Teaching a Galois theory course for to 6:30 p.m. The workshop format is intended to stimulate undergraduates, organized by John R. Swallow, Davidson discussion among attending chairs and workshop leaders. College; Part 1: Sunday, 9:00 a.m.–11:00 a.m., and Part Sharing ideas and experiences with peers provides a form 2: Tuesday, 9:00 a.m.–11:00 a.m. Participants explore of department chair therapy, creating an environment that Galois theory from an undergraduate perspective, gain- enables attending chairs to address departmental matters ing materials and technological tools for use teaching from new perspectives. an undergraduate course. The course outlines the theory Past workshop sessions have focused on a range of is- from a concrete, computational point of view, assuming sues facing departments today, including personnel issues only one semester of abstract algebra. The course also (staff and faculty), long-range planning, hiring, promotion introduces AlgFields, a package for use with Maple or and tenure, budget management, assessments, outreach, Mathematica, to facilitate computation in number fields. stewardship, junior faculty development, communication, Participants study examples, solve exercises, and pose and departmental leadership. new problems, all built around the concept of an algebraic There is a registration fee for the workshop, which number with complex approximation. Handouts and web is in addition to and separate from the Joint Meetings links to the freely available package will be distributed. registration. An invitation to attend the workshop will be Laptops should be equipped with either Maple (version sent to department chairs this fall. Information will also 9 or later) or Mathematica (version 4.2 or later), but no be posted on the AMS website. For further information, prior experience with Mathematica or Maple is required. please contact the AMS Washington Office at 202-588-1100 Enrollment limit is 30. or [email protected]. Minicourse #2: Some deterministic models in mathemati- cal biology and their simulations, organized by Cammey Cole Manning, Meredith College; Huseyin Kocak, Univer- 91st Meeting of the MAA sity of Miami; and James F. Selgrade, North Carolina State University; Part 1: Sunday, 2:15 p.m.–4:15 p.m., and Part 2: MAA Invited Addresses Tuesday, 1:00 p.m.–3:00 p.m. This minicourse will present and analyze discrete and continuous models from physi- John H. Conway, Princeton University, Title to be an- ology (e.g., the Hodgkin-Huxley model), pharmacokinetics, nounced, 2:15 p.m. on Sunday. and population biology (e.g., the chemostat model). The Carl C. Cowen, Indiana University-Purdue University In- class will be conducted in a computer lab where participants dianapolis, The teaching-technology linkage in mathemat- will use the software Phaser to simulate model behavior. ics, 10:05 a.m. on Wednesday. (MAA Retiring Presidential Each of the four topics will be discussed for 30 minutes Address) followed by 30 minutes of computer experimentation. The

Ocotber 2007 Notices of the AMS 1229 Meetings & Conferences participants will be provided electronic copies of the web- can be used to offer the course at their home institution. based notes, simulations, and the software. Familiarity Participants are expected to have one of Mathematica, with the material in undergraduate courses in ordinary Matlab, or Maple installed on their laptop as well as differential equations and linear algebra will be helpful. Adobe Acrobat Reader. For those interested in attend- Participants for this minicourse will be required to bring ing the workshop but who do not have a CAS on their a laptop equipped with at least 100MB of available disk laptop, please contact the organizers. For more informa- space, 512MB RAM, with a CDROM drive and with one of tion, please visit http://cam.mathlab.stthomas.edu/ the three operating systems: Windows 2000/XP/Vista, wavelets. Enrollment limit is 30. Mac OS X (10.4.5 or later, with Java 5 or greater installed) Minicourse #5: Visualizing abstract mathematics with or Linux. A free and fully functional evaluation copy of cellular automata, organized by Michael J. Bardzell and Phaser 3.0 may be downloaded at http:www.phaser. Donald E. Spickler, Salisbury University; Part 1: Mon- com/. Each prospective registrant should download and day, 10:30 a.m.–12:30 p.m., and Part 2: Wednesday, 1:00 install a copy of Phaser on his/her laptop to prepare for p.m.–3:00 p.m. Many undergraduate students are familiar the minicourse. Technical support for any installation with Pascal’s triangle and, in some cases, Pascal’s triangle related issues should be addressed to Jason Glick at mod n. This later construction is a type of infinite one- [email protected]. Each registrant of the minicourse dimensional cellular automata generated over a finite will be provided a license activation key for the copy of group. Cellular automata, both finite and infinite, can Phaser downloaded at no additional charge. Enrollment be generated over other groups as well. Studying these limit is 30. dynamical systems necessitates simple techniques from Minicourse #3: Introduction to the mathematics of mod- abstract algebra, discrete mathematics, number theory, ern cryptography, organized by Jeffrey Ehme and Colm K. fractal geometry, and computer graphics. We present Mulcahy, Spelman College; Part 1: Sunday, 4:45 p.m.–6:45 innovative classroom activities and undergraduate re- p.m., and Part 2: Tuesday, 3:30 p.m.–5:30 p.m. The math- search projects that have evolved from this project. The ematics of modern cryptography is for anyone with an in- supporting computer software PascGaloisJE will be intro- terest in mathematics today, especially if that person also duced. A basic knowledge of group theory is sufficient registers for classes (or submits grades) on line, or pays for the course. We will provide copies of the software bills or shops on the Internet. Since that includes most at the workshop but it can take some time to install the of our students and most of us, it is a perfect subject for package, although Windows users can run the software adding to the standard undergraduate curriculum, either right from a provided CD. So we ask that the other par- in a regular or special topics course, or as a subject for di- ticipants download and install the software before the rected research. There can be no better way of illustrating beginning of the workshop. You can get the software from the application to everyday life of abstract mathematics http://pascgalois.org/and follow the “A download and clever modern ideas. This minicourse will focus on site for PascGaloisJE, ...” link at the bottom of the page the basics, assuming only a rudimentary knowledge of or go directly to the download site at http://faculty. number theory and abstract algebra (e.g., Fermat’s Little salisbury.edu/~despickler/PascGaloisJE.htm. En- Theorem and the concept of an abelian group), and cover rollment limit is 30. topics ranging from 1970s breakthroughs such as Dif- Minicourse #6: Sonification for mathematics instruc- fie Hellman key exchange and the RSA cryptography, to tion, organized by Steven M. Hetzler and Robert M. Tar- the more recent methods of ElGamal, elliptic curves and diff, Salisbury University; Part 1: Monday, 1:00 p.m.–3:00 Groebner bases. Participants are expected to bring laptops p.m., and Part 2: Wednesday, 3:30 p.m.–5:30 p.m. Some equipped with Maple, Adobe Acrobat Reader, and a CD students struggle to interpret standard graphic and sym- drive. Enrollment limit is 30. bolic representations of mathematics, and many of these Minicourse #4: Wavelets and applications: A multi- students are primarily auditory learners. At http:// disciplinary undergraduate course with an emphasis on faculty.salisbury.edu/~smhetzler/ scientific computing, organized by Patrick J. Van Fleet, Minicourse2008/, there are illustrations of how auditory University of St. Thomas, and David K. Ruch, Metropolitan graphs can be used with spreadsheets to enhance calculus State College of Denver; Part 1: Monday, 8:00 a.m.–10:00 instruction. This minicourse is designed to teach par- a.m., and Part 2: Wednesday, 9:00 a.m.–11:00 a.m. This ticipants how to use nonspeech audio to improve student minicourse provides a basic introduction to wavelets and learning. Participants work together to create an activity applications. The wavelet transform is developed in an ad that uses sound to teach interpretation of horizontal hoc manner. It is then used in applications such as data asymptotes. Then, working individually or in pairs, par- compression. Participants develop the necessary software ticipants will develop another activity in their own area of and are encouraged to bring their own digital images or interest. The minicourse will conclude with a discussion of audio files to use. Our construction is easy to understand the potential of sound for representing other mathematical but is limited in applications. Thus we have the motiva- concepts, and participants will receive a copy of all materi- tion for developing wavelets in a general context. The als created in the sessions. Participants’ laptops will need minicourse content provides an excellent template for to be running Windows XP and Microsoft Excel 2003 or an undergraduate class in wavelets and applications. We higher, with a headphone jack for the soundcard and either discuss how the course can be offered to undergraduates. a CD-RW drive or USB port. Partial support for this work Participants receive software and lecture materials that was provided by the National Science Foundation–Course,

1230 Notices of the AMS Volume 54, Number 9 Meetings & Conferences

Curriculum, and Laboratory Improvement program under number theory, tilings, permutations, chemistry, optics, grant 0442450. Enrollment limit is 30. electrostatics, probability, and graph theory. Enrollment Minicourse #7: Directing undergraduate research, limit is 50. organized by Aparna W. Higgins, University of Dayton; Minicourse #11: More music and mathematics, orga- Part 1; Sunday, 9:00 a.m.–11:00 a.m., and Part 2: Tuesday, nized by Leon Harkleroad, Wilton, Maine; Part 1: Monday, January 8, 1:00 p.m.–3:00 p.m. This course will cover 1:00 p.m.–3:00 p.m., and Part 2: Wednesday, 1:00 p.m.–3:00 many aspects of facilitating research by undergraduates, p.m. This session will focus on an all new set of topics from such as getting students involved in research, finding ap- the interface of math and music. We will explore subjects propriate problems, deciding how much help to provide, such as historical geometric methods to approximate and presenting and publishing the results. Similarities and equal tempering in instrument design, group theory in differences between research conducted during summer contradancing, and music from space-filling curves and programs and research that can be conducted during the fractals. This minicourse will not repeat material from academic year will be discussed. Although the examples the original minicourse (given in Atlanta, GA, in January used will be primarily in the area of discrete mathemat- 2005), and it will not assume that participants attended ics, the strategies discussed can be applied to any area of that earlier installment. Enrollment limit is 50. mathematics. Enrollment limit is 50. Minicourse #12: Developing department self-studies, or- Minicourse #8: Mathematics and geometry of voting, ganized by Donna L. Beers, Simmons College, and Richard organized by Donald G. Saari, University of California Alan Gillman, Valparaiso University; Part 1: Sunday, 9:00 Irvine; Part 1: Sunday, 4:45 p.m.–6:45 p.m, and Part 2: a.m.–11:00 a.m., and Part 2: Tuesday, 9:00 a.m.–11:00 a.m. Tuesday, 3:30 p.m.–5:30 p.m. By now, most of us know The self-study process and report are critical components that voting rules can cause unexpected outcomes and deli- of a departmental program review. They are retrospective, cious paradoxes. It is possible for the standard plurality engaging department members and other interested par- ranking, for instance, to be Alice > Barb > Connie while ties (e.g., other departments and the administration) in the “vote for two” outcome is precisely the opposite. The examining the current status of all aspects of departmen- mathematical issues—which constitute the theme of this tal programs. They are also forward-looking, anticipating course—are to identify everything that can possibly hap- new areas for growth and contribution to the institutional pen and why, how to construct any number of illustrating mission. Since the self-study entails honest discussion examples, to identify which voting rule is the “best”, and of issues confronting a department, it is both a process to learn how to convert portions of this recent research of reflection and a report. This minicourse enables par- into rich course offerings for our undergraduates. Enroll- ticipants to determine how a self-study, which is usually ment limit is 50. conducted in response to an administrative mandate, Minicourse #9: Classroom response systems: Teaching can be a positive opportunity for departmental renewal. with clickers, organized by Derek Bruff, Vanderbilt Uni- Enrollment limit is 50. versity; Matthew Leingang, Harvard University; and Kelly Minicourse #13: Teaching and the philosophy of math- Cline, Mark R. Parker, and Holly S. Zullo, Carroll College; ematics, organized by Martin E. Flashman, Humboldt State Part 1: Sunday, 2:15 p.m.–4:15 p.m., and Part 2: Tuesday, University; Part 1: Sunday, 2:15 p.m.–4:15 p.m., and Part 2: 1:00 p.m.–3:00 p.m. Classroom response systems, or Tuesday, 1:00 p.m.–3:00 p.m. The goal of this minicourse “clickers”, are instructional technologies that enable teach- is to introduce participants to issues in the philosophy ers to rapidly collect and analyze students’ responses to of mathematics that can be used to illuminate classroom multiple-choice questions. In this minicourse, participants topics in undergraduate courses at a variety of levels and will learn how to use clickers to transform the way they provide a foundation for organizing an undergraduate use class time—promoting active participation, engage- course in the philosophy of mathematics for mathematics ment, and discussion among students; assessing student and philosophy students. The course will focus primarily learning in real-time during class; and adapting lessons on issues related to i) the nature of the objects studied to respond to the particular learning needs of one’s stu- in mathematics (ontology) and ii) the knowledge of the dents. This minicourse will also feature a question-writing truth of assertions about these objects (epistemology). “workshop” and a mock clicker class as ways to explore Responses ascribed to many views such as platonism, the kinds of questions and activities that make the most formalism, intuitionism, constructivism, logicism, struc- of teaching with clickers. Enrollment limit is 50. turalism, and empiricism will be outlined. Enrollment Minicourse #10: The Fibonacci and Catalan numbers, limit is 50. organized by Ralph P. Grimaldi, Rose-Hulman Institute Minicourse #14: Beyond formulas and algorithms: of Technology; Part 1: Monday, 9:00 a.m.–11:00 a.m., Teaching a conceptual/thematics single variable calculus and Part 2: Wednesday, 9:00 a.m.–11:00 a.m. In many course, organized by Shahriar Shahriari, Pomona College; introductory courses in discrete mathematics or combi- Part 1: Sunday, 4:45 p.m.–6:45 p.m., and Part 2: Tuesday, natorics, one often encounters the sequences of numbers 3:30 p.m.–5:30 p.m. Many students enter college having called the Fibonacci numbers and the Catalan numbers. seen the main ideas of calculus and knowing how to do This minicourse is designed to demonstrate how certain routine calculus problems but without a firm grasp of the properties of these sequences come about and to examine concepts underlying calculus. In this hands-on course, where ideas related to these sequences arise in applica- the participants will be introduced and will have a chance tions dealing with geometry, trigonometry, set theory, to explore an honors calculus class where the theme is

October 2007 Notices of the AMS 1231 Meetings & Conferences approximations and one of the test cases is approximating Boston. The SIGMAA-QL and Project SAUM are sponsors of the number of primes up to x. In this alternative calcu- this event. lus class, the students take an active role in formulating Biomathematics in the Undergraduate Curriculum, questions, and in developing the material. A thematic/ Wednesday morning and afternoon, organized by Timothy conceptual approach using open-ended problems that D. Comar and Lisa G. Townsley, Benedictine University; incorporates some unusual mathematics (in this case, Glenn W. Ledder, University of Nebraska; and Olcay analytic number theory) allows us to take advantage of the Akman, Illinois State University. This session is sponsored students’ prior experience with calculus to get a deeper by the SIGMAA on Mathematical and Computational Biol- understanding of the subject. Enrollment limit is 50. ogy (BIO). Minicourse #15: Evaluating student presentations in Building Diversity in Advanced Mathematics: Models that mathematics, organized by Suzanne Dorée, Augsburg Col- Work, Wednesday morning, organized by Abbe H. Herzig, lege; Richard Jardine, Keene State College; and Thomas University at Albany, State University of New York, and Linton, Central College; Part 1: Monday, 9:00 a.m.–11:00 Patricia L. Hale, California State Polytechnic University, a.m., and Part 2: Wednesday, 9:00 a.m.–11:00 a.m. Do Pomona. The session is cosponsored by the MAA Commit- your students give in-class presentations? Present their tee on the Participation of Women, the MAA Committee undergraduate research project at a conference or senior on the Participation of Minorities, and the AMS-ASA-AWM- seminar? While most mathematics professors can tell a IMS-MAA-NCTM-SIAM Joint Committee on Women. great mathematics talk from a truly horrible one, when College Algebra: Concepts, Data, and Models, Monday it comes to grading student presentations we are often morning, organized by Florence S. Gordon, New York In- at a loss. In this mini-course we’ll examine what makes stitute of Technology, Laurette Foster, Prairie View A&M a good student mathematics talk, offer concrete advice University, Mary R. Robinson, University of New Mexico on helping students prepare to speak, discuss the use of Valencia Campus, and Yajun Yang, Farmingdale State Col- rubrics for evaluating presentations, and explore the role lege of New York. This session is cosponsored by CRAFTY of presentations in departmental curriculum and assess- and the Committee on Two Year Colleges (CTYC). Countering “I Can’t Do Math”: Strategies for Teach- ment. Participants will practice using rubrics to evaluate ing Under-Prepared Math-Anxious Students Interested in presentations on video and at the meetings themselves. Business and the Sciences, Tuesday morning, organized Enrollment limit is 50. by Kimberly J. Presser and J. Winston Crawley, Ship- Minicourse #16: A beginner’s guide to the scholarship of pensburg University. teaching and learning in mathematics, organized by Curtis Crossing the “Bridge to Higher Mathematics”: What Works D. Bennett and Jacqueline M. Dewar, Loyola Marymount and Why, Sunday morning, organized by George J. Davis, University; Part 1: Monday, 1:00 p.m.–3:00 p.m. and Part 2: Georgia State University. Wednesday, 1:00 p.m.–3:00 p.m. This course will introduce Cryptology for Undergraduates, Wednesday morning, participants to the scholarship of teaching and learning in organized by Chris Christensen, Northern Kentucky Uni- mathematics (SoTL). We will present a framework that il- versity, and Robert E. Lewand, Goucher College. lustrates the similarities between disciplinary research and Curriculum Materials for Preservice Middle School SoTL work, offer examples of SoTL projects in mathemat- Mathematics Teachers, Monday afternoon, organized by ics at varying stages of development, discuss methods for Laurie J. Burton, Maria G. Fung, and Klay T. Kruczek, investigation, and help participants begin projects of their Western Oregon University. This session is sponsored by own. Participants will be guided in transforming a teaching the Committee on the Mathematical Education of Teach- problem of their own into a problem for scholarly investi- ers (COMET). gation. Suggestions for how to make this work public will Demos and Strategies with Technology that Enhance also be given. Enrollment limit is 50. Teaching and Learning Mathematics, Monday morn- ing and afternoon, organized by David R. Hill, Temple MAA Contributed Paper Sessions University; Scott Greenleaf, University of New England; The MAA Committee on Contributed Paper Sessions so- Mary L. Platt, Salem State College; and Lila F. Roberts, licits contributed papers pertinent to the sessions listed Georgia College & State University. below. Contributed paper session organizers generally Ethnomathematics and Its Uses in Teaching, Sunday limit presentations to ten or fifteen minutes. Each ses- morning, organized by Dorothee J. Blum and Ximena P. Cat- sion room contains a computer projector, an overhead epillan, Millersville University; Robert E. Jamison, Clemson projector, and one screen. Please note that the dates University; Shemsi I. Alhaddad, University of South Caro- and times scheduled for these sessions remain tentative. lina; and Amy Shell-Gellasch, Pacific Lutheran University. Full descriptions of these sessions may be found in the This contributed paper session is sponsored by the SIG- August issue of the Notices, p. 939, or see www.ams.org/ MAA on the History of Mathematics. amsmtgs/2109_maacontrib.html. Great Activities for an Introductory Statistics Class, Assessment of Student Learning in Undergraduate Math- Sunday morning, organized by Patricia B. Humphrey, ematics, Monday afternoon, organized by William O. Martin, Georgia Southern University; Christopher J. Lacke, Rowan North Dakota State University; Bernard L. Madison, Univer- University; and Ginger Holmes-Rowell, Middle Tennessee sity of Arkansas; Kimberly M. Vincent, Washington State State University. The session is sponsored by the SIGMAA University; and Maura B. Mast, University of Massachusetts- on Statistics Education. In order to be considered for this

1232 Notices of the AMS Volume 54, Number 9 Meetings & Conferences session applicants should submit a one-page summary Michelle J. Zandieh, Arizona State University; and Chris of the presentation to Pat Humphrey at phumphre@ Rasmussen, San Diego State University. georgiasouthern.edu along with the abstract to the Serving Students Who Have Taken Calculus in High meeting website. Presenters in the session will be con- School, Sunday afternoon, organized by Ann E. Watkins, sidered for the SIGMAA on Statistics Education’s Best California State University, Northridge, and Daniel J. Contributed Presentation Award. Teague, North Carolina School of Science and Mathemat- Guided Discovery in Mathematics Education, Tuesday ics. This session is sponsored by the MAA-NCTM Commit- afternoon, organized by Jerome S. Epstein, Polytechnic tee on Mutual Concerns. University, and Chris Rasmussen, San Diego State Univer- Topics and Techniques for Real Analysis, Monday morn- sity. This session is sponsored by the SIGMAA on Research ing, organized by Erik O. Talvila, University College of the in Undergraduate Mathematics Education. Fraser Valley; Robert W. Vallin, Slippery Rock University; Innovative and Effective Ways to Teach Linear Algebra, and James E. Peterson, Benedictine College. Tuesday morning, organized by David M. Strong, Pep- Using Ideas from Asian Mathematics in the Classroom, perdine University, and Gilbert Strang, Massachusetts Sunday afternoon, organized by Victor J. Katz, University Institute of Technology. of the District of Columbia, Kim L. Plofker, Brown Uni- Mathematics and the Arts, Monday afternoon, organized versity, and Frank Swetz, Pennsylvania State University, by Douglas E. Norton, Villanova University. This session Harrisburg. This session is sponsored by the SIGMAA on is sponsored by the SIGMAA-ARTS. the History of Mathematics. Mathematics Experiences in Business, Industry, and Using Innovative Technologies to Implement Active Government, Tuesday morning, organized by Philip Gus- Learning in Mathematics (and in other STEM disciplines), tafson, Mesa State College, and Michael G. Monticino, Wednesday morning, organized by Marilyn A. Reba, Clem- University of North Texas. This session is sponsored by the son University, and Beth Simon, University of California MAA Business, Industry and Government Special Interest San Diego. Group (BIG SIGMAA). General Session, Sunday, Monday, Tuesday, and Wednes- Mathlets and Web Resources for Mathematics and Statis- day mornings and afternoons; organized by Sarah L. tics Education, Wednesday morning, organized by Thomas Mabrouk, Framingham State University. Papers may be E. Leathrum, Jacksonville State University; Patricia B. presented on any mathematical topic. Papers that fit into Humphrey, Georgia Southern University; Christopher J. one of the other sessions should be sent to that organizer, Lacke, Rowan University; David M. Strong, Pepperdine not to this session. University; and Joe Yanik, Emporia State University. The session is jointly sponsored by the SIGMAA on Statistics Submission Procedures for MAA Contributed Education and MAA CTiME (Committee on Technology in Papers Math Education). Presentations related to statistics will Send your abstract directly to the meeting website (ab- be considered for the SIGMAA on Statistics Education’s stracts should not be sent to the organizer(s) who will Best Contributed Presentation Award. Presenters who automatically receive a copy). Please read the session wish to be considered for the award should also send descriptions thoroughly as some organizers require an a one-page summary of their presentation to Patricia additional summary of your proposal be sent to them Humphrey, [email protected], by the directly. Participants may speak in at most two MAA abstracts deadline. contributed paper sessions. If your paper cannot be ac- Philosophy of Mathematics, Monday morning, organized commodated in the session for which it was submitted, it by Kevin M. Iga, Pepperdine University, and Bonnie Gold, will be automatically considered for the general session. Monmouth University. This session is sponsored by the Speakers in the general session will be limited to one talk SIGMAA for the Philosophy of Mathematics. because of time constraints. Abstracts must be submitted The Power of Inductive and Recursive Thinking, Sunday by Thursday, September 20, 2007. afternoon, organized by William A. Marion, Valparaiso All accepted abstracts will be published in a book avail- University. able at the meeting to all registered participants. Abstracts Preparing Faculty for Success in a Problem-Solving and must be submitted electronically. While no knowledge of a a a Technology-Rich Curriculum, Sunday morning, organized L TEX is necessary for submission, L TEX and AMS-L TEX by Alex J. Heidenberg, Gerald C. Kobylski, Barbra Melen- are the only typesetting systems that can be used if math- dez, and Rodney Sturdivant, U.S. Military Academy. ematics or any text markup (e.g., accent marks) is included. Research and Professional Development Activities for The abstracts submissions page is at http://www.ams. Math Majors, Monday afternoon, organized by Suzanne M. org/cgi-bin/abstracts/abstract.pl. Simply select Lenhart, University of Tennessee; Mike O’Leary, Towson the San Diego meeting, fill in the number of authors, and University; and Margaret M. Robinson, Mount Holyoke proceed with the step-by-step instructions. Submitters College. The session is sponsored by MAA CUPM Subcom- will be able to view their abstracts before final submis- mittee on Research by Undergraduates. sion. Upon completion of your submission, your unique Research on the Teaching and Learning of Under- abstract number will immediately be sent to you. All ques- graduate Mathematics, Wednesday afternoon, orga- tions concerning the submission of abstracts should be nized by David E. Meel, Bowling Green State University; addressed to [email protected].

October 2007 Notices of the AMS 1233 Meetings & Conferences

MAA Panels, Posters, and Other Sessions tions should be submitted to Kevin Charlwood, kevin. National Science Foundation Programs Supporting [email protected], or Mike Axtell axtellm@ Learning and Teaching in the Mathematical Sciences, wabash.edu, by Friday, December 7, 2007. Sunday, 9:00 a.m.–10:20 a.m., Lloyd E. Douglas, Division Mathematics and Hollywood: A Conversation with of Mathematical Sciences, National Science Foundation; Mathematical Hollywood Writers and Mathematics and Daniel P. Maki, Elizabeth J. Teles, and Lee L. Zia, Faculty, Sunday, 2:15 p.m.–3:35 p.m., Christopher Goff, Division of Undergraduate Education, National Science University of the Pacific, and Sarah J. Greenwald, Appala- Foundation. A number of NSF divisions offer a variety of chian State University. Recently, Hollywood has expanded its use of mathematical themes. A parallel trend involves grant programs that support innovations in learning and linking these “mathematical moments” to educational teaching in the mathematical sciences. These programs initiatives. Our panel will furnish insiders’ perspectives will be discussed along with examples of successful proj- on the effect of mathematical training on the creative pro- ects. Anticipated budget highlights and other new initia- cess and the challenges of representing mathematics and tives for the next fiscal year will also be presented. mathematicians in Hollywood. We will also begin a criti- Making the Connection Between Research and Teach- cal discussion about how Hollywood affects mathematics ing in Undergraduate Mathematics Education, Sunday, education and public perceptions. As schedules allow, 9:00 p.m.–10:20 p.m., Chris Rasmussen, San Diego State planned panel members include mathematical writers as University; Marilyn P. Carlson, Arizona State University; well as mathematical consultants: David M. Bressoud, and David E. Meel, Bowling Green State University. This Macalester College, is a NUMB3RS worksheet author; Ken session of invited speakers will discuss several chapters Keeler has a doctorate in applied mathematics and has from a forthcoming MAA Notes volume on research in un- won Writer’s Guild and Emmy Awards for his work on The dergraduate mathematics education, edited by Carlson and Simpsons and Futurama, Twentieth Century Fox; Alice Rasmussen. Chapters from the forthcoming book include Silverberg, University of California Irvine, has consulted papers written by mathematics education researchers and for film and television; Eric Weisstein, Wolfram Research, by mathematicians discussing topics in the undergraduate consults for NUMB3RS; and Jeff Westbrook has a doctor- curriculum as well as overarching issues in undergraduate ate in computer science and is currently a writer for The mathematics education, with emphasis on the implica- Simpsons, Twentieth Century Fox. The panel is sponsored tions of that research in the teaching of undergraduate by SIGMAA on Mathematics and the Arts. mathematics courses. The panel session will feature the What Every Chair Should Know About NSF Fund- following three presentations, followed by discussion and ing, Sunday, 2:15 p.m.–3:35 p.m., Catherine M. Murphy, questions from the audience: Guershon Harel, University Purdue University Calumet, and Daniel P. Maki, Indiana of California San Diego, and Stacy Brown, University of University. Dan Maki will speak about curriculum funding Illinois at Chicago, Mathematical induction: Cognitive and through DUE and a yet-to-be-named representative from instructional considerations; Annie and John Selden, New DMS will speak about research funding in this session for Mexico State University, Overcoming students’ difficulties chairs. There will time available for questions and conver- in learning to understand and construct proofs; and Keith sation with the presenters. H. Weber, Rutgers University and Sean P. Larsen, Portland How to Interview for a Job in the Mathematical Sci- State University, Teaching and learning group theory. The ences, Sunday, 2:15 p.m.–3:35 p.m., organized by David C. session is sponsored by SIGMAA on Research in Under- Manderscheid, University of Iowa. This session is aimed graduate Mathematics Education. at Ph.D. students and at recent graduates. An overview Tenure (and Promotion)—You Know You Want It, of the employment process will be given with ample op- Sunday, 9:00 a.m.–10:20 a.m., James E. Hamblin, Shippens- portunity for participants to ask questions. The emphasis burg University, and Kimberly A. Roth, Juniata College. will be on the portion of the employment process from Once you get your tenure-track job, the next step is to get interviewing through accepting an offer. Questions that tenure and promotion. Tenure and promotion policies, of will be addressed include: How do employers conduct in- course, vary from institution to institution, but there are terviews? How can you best prepare for these interviews? some general things you can do to help the process go How do employers choose to whom they will make offers? smoothly. Panelists will discuss their advice for people on How do you negotiate once you have an offer? How do the tenure-track and their experiences on it. The session you choose among competing offers? The panelists are is co-sponsored by the Young Mathematician’s Network Allen Butler, Daniel H. Wagner Associates, Inc.; Sharon and Project NExT. M. Clarke, Pepperdine University; James H. Freeman, Project NExT/Young Mathematicians’ Network Poster Cornell College; Sarah Ann Stewart, Belmont University; Session, Sunday, 2:15 p.m.–4:15 p.m., organized by Kevin and David C. Manderscheid. The session is cosponsored E. Charlwood, Washburn University, and Michael C. Ax- by the MAA Committee on Graduate Students and The tell, Wabash College. Junior mathematicians who are no Young Mathematicians Network. more than five years beyond their Ph.D. are invited by Engaging Students in College Mathematics Courses, Project NExT and the Young Mathematicians’ Network to Sunday, 3:50 p.m.–5:10 p.m., Juli D’Ann Ratheal, West submit abstracts for the session. The poster size will be Texas A&M University. Most colleges and universities en- 48” (length) by 36” (height). Posters and materials for post- counter problems associated with retention and passing ing pages on the posters will be provided onsite. Applica- rates in mathematics courses, especially core courses.

1234 Notices of the AMS Volume 54, Number 9 Meetings & Conferences

The emphasis of this panel discussion will be how to en- to undergraduates. It is expected that posters represent- gage students and enhance their learning experience in ing a wide variety of programs will be displayed. Possible mathematics courses. Instructional strategies designed programming formats include after school clubs, special to increase the level of student engagement and concep- conferences, mentoring programs, and summer camps. tual understanding by establishing learning communities Those who are in the process of constructing an outreach through collaborative activities and projects will be ex- program are especially encouraged to attend this session plored. Data which measured students’ attitudes toward to acquire valuable insights and tips for designing and specific pedagogical methods used in college algebra implementing a mathematics outreach project. We solicit classes were collected over a three-year period. These data abstracts from all those involved with such outreach will be reviewed and discussed by the panelists, who have work. For example, successful grant awardees from both worked collaboratively for a number of years to reform the Tensor Foundation and Summa Programs might be mathematics courses by implementing instructional strat- particularly interested in participating. The session is egies which increase student engagement and make course sponsored by the Women and Mathematics Network. The content more meaningful. Panelists will include James A. deadline for submissions is Friday, December 7, 2007. Ap- M. Epperson, Unversity of Texas-Arlington; Winifred A. plications should be submitted to Betsy Yanik, eyanik@ Mallam, Texas Woman’s University; Kimberly M. Childs, emporia.edu. Stephen F. Austin State University; Bowen Brawner, Tar- Exciting, Surprising, and Satisfying: Why and How leton State University; Rebecca Walls, West Texas A&M to Teach Proof, Monday, 9:00 a.m.–10:20 a.m., Carol S. University; and Juli D’Ann Ratheal. Schumacher, Kenyon College, and Diane Herrmann, Uni- Tracking Our Students from College Algebra to versity of Chicago. CUPM has been considering the tricky Calculus: Where They Come From, Where They Go, and point in the early to middle of the undergraduate math- Where They Don’t, Sunday, 3:50 p.m.–5:50 p.m., organized ematics curriculum where students first encounter proof by Sheldon P. Gordon, Farmingdale State College. A growing in a serious way. There are issues of both “salesmanship” body of evidence shows that only a very small percentage (This is hard. Is really necessary? Is it worthwhile?) and of the approximately 1,000,000 students who take college tactics (how do we help our students to learn to engage the algebra and related courses each year ever go on to start mathematics on their own?) Panelists will discuss various calculus, which is the focus of most of these courses. In successful strategies for helping students through this this session, the panelists will discuss the results of stu- difficult phase. Panelists include T. Christine Stevens, dent tracking studies and their implications, including Saint Louis University, and Susanna S. Epps, DePaul Uni- comparisons of students who have taken prerequisite versity. courses in high school or in college, what courses students Research and Outreach Focusing on the Mathemat- take after taking college algebra or precalculus courses, ics Education of K–8 Latino/a Students, Monday, 9:00 and where the students who take calculus have come from. a.m.–10:20 a.m., Taliesin Sutton, University of Arizona and Panelists include Barbara E. Edwards, Oregon State Laura Kondek McLeman, University of Arizona. Interest in University; Steven R. Dunbar, University of Nebraska; the mathematics education for underrepresented groups Aimee Ellington, Virginia Commonwealth University; Scott has grown in recent years, due in part to the discourag- Herriott, Maharishi International University; Mercedes ing results in national tests at the K–12 level (e.g., NAEP) McGowen, William Rainey Harper College; and William as well as the lack of minority groups choosing to major A. Waller, University of Houston–Downtown. The panel is in mathematics at the college level. Researchers from the sponsored by the MAA committee on Curriculum Renewal Center for the Mathematics Education of Latino/as pro- Across the First Two Years (CRAFTY). vide some insight into these issues as they investigate the Proposal Writing Workshop for Grant Applications to teaching and learning of mathematics to Latino/as at the the NSF Division of Undergraduate Education, Monday, elementary and middle school level. This work focuses 9:00 a.m.–10:30 a.m., Daniel P. Maki, Elizabeth J. Teles, not only on student understanding, but also on what roles and Lee L. Zia, Division of Undergraduate Education, parents and teachers play in furthering Latino/a students’ National Science Foundation. Presenters will describe the mathematics education. The panelists will discuss their general NSF grant proposal process and consider particu- work with preservice and inservice teachers, parents, lar details relevant to programs in the Division of Under- and students, focusing specifically on how language and graduate Education. This interactive session will feature a culture impacts the mathematics education of Latino/a series of “read/think/share/report” exercises built around students. The panel includes Richard Kitchen, Univer- a series of short excerpts from sample proposals. sity of New Mexico; and Virginia Horak, Laura Kondek Outreach Programs For Underrepresented Popula- McLeman, José María Menéndez, and Taliesin Sutton tions in Mathematics, Monday, 9:00 a.m.–11:00 a.m., from the University of Arizona. Elizabeth Yanik, Emporia State University; Jennifer Using the New Technologies in Teaching Mathematics Hontz, Meredith College; and Kathleen Sullivan, Seattle Invited Paper Session, Monday, 9:00 a.m.–noon, Lawrence University. This poster session is designed to showcase C. Moore, Duke University, and Bruce W. Yoshiwara, Los successful outreach mathematics programs that encour- Angeles Pierce College. age students from underrepresented populations to con- Classroom Voting Comes to the Mathematics Class- tinue their study of mathematics. The participants in such room, Monday, 10:45 a.m.–12:05 p.m., Mark R. Parker, programs range in grade level from elementary students Carroll College, and Cheryl L. Olsen, Nebraska Wesleyan

October 2007 Notices of the AMS 1235 Meetings & Conferences

University. This session is dedicated to examining the and social realities and ramifications of conducting and pedagogy behind the popular new technology, to sharing communicating research in ethnomathematics. Panelists lessons learned from practitioners, and to spotlighting and their topics include Ubiratan D’Ambrosio, Univer- another tool for engaging students in all levels of mathe- sidade Estadual de Campinas, Brazil, Social justice and matics classrooms. We will start with a series of classroom ethnomathematics; Ana Lúcia Braz Dias, Central Michigan voting questions to demonstrate different techniques: (1) University, The role of ethnomathematics in refuting deficit vote with no discussion, (2) vote, peer discussion, revote explanations for the achievement gap; and Arthur B. Pow- and (3) peer discussion, vote. Voting will be accomplished ell, Rutgers University, Ethnomathematics: Traversing the via both colored paper as well as electronic personal re- ‘digital divide’. The panel is sponsored by the SIGMAA on sponse systems. Panelists will discuss their use of, and History of Mathematics. student responses to, classroom voting. The session will Projects Supported by the NSF Division of Under- conclude with a question and answer period from the graduate Education, Monday, 2:00 p.m.–4:00 p.m., Jon audience. The panelists have a depth of experience with W. Scott, Montgomery Community College. This poster the pedagogy of classroom voting. Kelly Cline, Carrroll session will feature principal investigators (PIs) present- College, is co-PI on the NSF-funded MathQUEST project ing progress and outcomes from various NSF funded to develop classroom voting questions for linear algebra projects in the Division of Undergraduate Education and and differential equations. David O. Lomen, University of other NSF divisions supporting opportunities to improve Arizona, was part of the ConceptTests development team undergraduate education. The poster session format will for the Harvard Calculus Consortium. Maria S. Terrell, permit ample opportunity for attendees to engage in small Cornell University, was the PI of the NSF-funded Good- group discussions with the PIs and to network with each Questions project to develop classroom voting questions other. Information about presenters and their projects will for calculus. This session is sponsored by the Committee appear in the program. on the Teaching of Undergraduate Mathematics. Dueling Platforms: Java vs. Flash, Monday, 2:30 Creating and Implementing a Capstone Course in p.m.–3:50 p.m., Mary L. Platt, Salem State College, and Mathematics for Preservice Secondary Teachers, Mon- Lawrence C. Moore, Duke University. Trying to decide day, 1:00 p.m.–2:20 p.m., David W. Dempsey, Jackson- between learning Java and learning Flash? In this panel ville State University, and Matthew Winsor, University presentation a team of two representing Java and a cor- of Texas at El Paso. Reports from the MAA and NCTM responding team representing Flash will present work indicate that as a result of changes in the way mathemat- on a common assigned task. Each team will demonstrate ics is being taught in secondary schools, teachers need a their completed mathlet(s) and will describe the process of more thorough preparation in mathematics (Conference creating the mathlet(s) from scratch using their tool. Their Board of Mathematical Sciences (CBMS), 2001; Leitzel, accounts will include the time spent on the task, advan- 1991; NCTM, 1991, 2000). In response to the need for tages of their approach, and problems encountered. Teams improving preservice teachers’ content knowledge, The will also describe collections of programs that could be Mathematical Education of Teachers (MET) publication used as building blocks in larger collections. Each team charges mathematics departments with supporting the will have a chance to comment on the other team’s work. development of “a capstone course sequence for teach- Time will be reserved for questions and comments from ers in which conceptual difficulties, fundamental ideas, the audience. The session will be moderated by Mary L. and techniques of high school mathematics are examined Platt. Panelists include Thomas E. Leathrum, Jacksonville from an advanced standpoint” (CBMS, 2001, p. 39). This State University; Kyle T. Siegrist, University of Alabama, panel session will present several examples of capstone Huntsville; Doug Ensley, Shippensburg University; and courses that have been implemented at different universi- Barbara Kaskosz, University of Rhode Island. ties around the nation. Panel members will discuss how The Proof is in the Pudding: Humorous Theater of they created and implemented a capstone course, give the Mathematical Variety, Monday, 6:00 p.m.–7:30 p.m., examples of mathematics from capstone courses, and Colin C. Adams et al, Williams College. With several short present research based on their capstone course. Time theatrical pieces, A Difficult Delivery, Trial and Error, and will be allowed for discussion. Panelists include Edward A Killer Theorem, we will attempt a proof of the following E. Aboufadel and Rebecca Walker, Grand Valley State proposition: Theorem. Math can be funny. University; Gail Burrill, Michigan State; Henry S. Kepner, A Quick Introduction to WeBWorK, a Web-Based Inter- University of Wisconsin-Milwaukee, David W. Dempsey, active Homework System, Tuesday, 1:00 p.m.–2:20 p.m., and Matthew Winsor. Michael E. Gage, Arnold K. Pizer, and Vicki Roth, Uni- The Political Dimension of Ethnomathematics, Mon- versity of Rochester. WeBWorK is a program which allows day, 1:00 p.m.–3:00 p.m., Amy Shell-Gellasch, Pacific students to do their mathematical homework interactively Lutheran University, and Janet L. Beery, University of over the Web. It is currently being used by over 100 col- Redlands. Ethnomathematics is a growing area of both leges, universities, and high schools in courses such as research and educational ideas. With its emphasis on college algebra, pre-calculus to vector calculus, differential cultural contexts for mathematical ideas, the study of eth- equations, linear algebra, complex variables, and statistics. nomathematics draws on diverse disciplines and has the WeBWorK can handle most homework problems typically potential to influence education and society in meaningful used in such courses and is distributed with an extensive and even radical ways. Panelists will address the political library of problems. With WeBWorK students get immediate

1236 Notices of the AMS Volume 54, Number 9 Meetings & Conferences feedback on the validity of their answers and have the op- these exhibit mathematics in dance, along with the perfor- portunity to correct mistakes while they are still thinking mance of three very short mathematical dances we have about the problem. Students receive individualized ver- created together (including at least one proof!). sions of problems so instructors can encourage students So You Want to Teach Environmental Math, Do You? A to work together yet each student must develop an answer skit portraying the efforts to implement an environmen- to their own version of the problem. Further WeBWorK tal mathematics course at a mathematics department provides automatic scoring of assignments. The session meeting, Tuesday, 7:00 p.m.–8:00 p.m. Texts are appearing will provide an interactive introduction to WeBWorK. We which attempt to teach mathematics in an environmental will demonstrate how students use WeBWorK, how profes- context, using mathematics to understand some of the sors administer WeBWorK and will also discuss various most important problems facing us today—and hopefully assessment issues. Further information on WeBWorK and contributing to solutions. In this one-act skit, the pros and this session can be found at www.maa.org/webwork/. cons of introducing an “Environmental Math” class are Summer Research Programs, Tuesday, 2:30 p.m.–3:50 presented in a humorous fashion at a meeting of the math- p.m., William A. Hawkins Jr, MAA, and Robert E. Meggin- ematics faculty at Bogus U, revealing personalities that son, University of Michigan. The MAA has sponsored Sum- most of us will recognize. The skit is authored by Martin mer Research Programs since 2003 with funding from NSF, E. Walter, University of Colorado at Boulder, directed by NSA, and the Moody’s Foundation. Each program consists Patricia Clark Kenschaft, Bloomfield College, and spon- of a small research group of four minority undergradu- sored by the Environmental Mathematics SIGMAA. ates mentored by a faculty member. Thirty-three sites had been funded as of summer 2006 and 12–13 were funded Special Interest Groups of the MAA (SIGMAAs) in summer 2007. Panelists include Tuncay Aktosun and SIGMAAs will be hosting a number of interesting ac- Minerva Cordero, University of Texas at Arlington, and tivities, sessions, and guest lecturers. There are currently Monica Stephens, Spelman College. These site directors nine such focus groups offering members opportunities to will discuss their programs. There will be ample time for interact not only at meetings but throughout the year via questions and discussion. Funding will be available for newsletters and email-based communications. For more summer 2008. Additional information can be found on information visit www.maa.org/SIGMAA/SIGMAA.html. the NREUP website at www.maa.org/nreup. The session is sponsored by CMPM, SUMMA (Strengthening Under- SIGMAA on Mathematical and Computational Biology represented Minority Mathematics Achievement), and the Biomathematics in the Undergraduate Curriculum, Office of Minority Participation. Wednesday morning and afternoon (See the “MAA Con- Current Issues in Actuarial Science Education, Tues- tributed Paper Sessions” section). day, 5:00 p.m.–7:00 p.m. Robert E. Buck, Slippery Rock University; Bettye Anne Case, Florida State University; SIGMAA on Business, Industry, and Government Matthew J. Hassett, Arizona State University; and Steve Guest Lecturer, Monday, 3:00 p.m.–3:45 p.m. Robert Paris, Florida State University. A diverse group of work- J. Lang, Alamo, California, will speak on From flapping ing actuaries, publishers, and actuarial educators bring birds to space telescopes: The art, math, and science of new information from professional society committees, origami. specialized publications initiatives, and academic depart- ment experience. The pace of change is faster than in most SIGMAA on Environmental Mathematics academic areas, and the session helps faculty adjust as Guest Lecture and Business Meeting, Sunday, 4:00 quickly as possible not only to educate their students p.m.–5:30 p.m. generally, but give the students good professional infor- So You Want to Teach Environmental Math, Do You? A mation and to determine upcoming curriculum change skit portraying the efforts to implement an environmen- that may be necessary. tal mathematics course at a mathematics department Hard Problems, Tuesday, 6:00 p.m.–7:30 p.m., George meeting, Tuesday, 7:00 p.m.–8:00 p.m. (See the “MAA P. Csicsery, Zala Films. The world premiere of a 90-minute Panels, Posters, and Other Sessions” section). documentary about the USA team’s participation in the 2006 International Mathematical Olympiad in Slovenia will SIGMAA on the History of Mathematics be shown. A question and answer session with Csicsery Business Meeting, Reception, and Guest Lecturer, and a reception will follow the film presentation. Other Sunday, 5:30 p.m.–7:30 p.m. films by Csicsery are N is a Number: A Portrait of Paul The Political Dimension of Ethnomathematics, Mon- Erdo˝s, porridge pulleys and Pi, and Invitation to Discover. day, 1:00 p.m.–3:00 p.m. (See the MAA Panels, Posters and Dancing Mathematics and the Mathematics of Dance, Other Sessions” section). Tuesday 6:45 p.m.–7:45 p.m., presented by Sarah-Marie Belcastro, Smith College, Karl Schaffer, DeAnza College. SIGMAA on Mathematics and the Arts This session will be a lecture/demonstration/performance Mathematics and Hollywood: A Conversation with Math- that will consist of brief introductions of our mathematical ematical Hollywood Writers and Mathematics Faculty, Sun- and dance backgrounds, descriptions of the connections day, 2:15 p.m.–3:35 p.m. (See the “MAA Panel and Poster we see between mathematics and dance, and video clips Sessions” section). of our separate choreography giving explanations of how

October 2007 Notices of the AMS 1237 Meetings & Conferences

SIGMAA on the Philosophy of Mathematics real mathematical research experience. This session is Business Meeting, Reception, and Guest Lecturer, designed to help faculty recognize and find appropriate Monday, 5:45 p.m.–7:15 pm. The featured speaker is problems that can be tackled in a single semester, match Penelope Maddy, University of California Irvine, How ap- problems to students, and mentor these young researchers plied mathematics became pure. A reception will follow throughout the research experience from initial approach the lecture. to final product, a paper and/or presentation. Panelists include William E. Fenton, Bellarmine University; Steven SIGMAA on Quantitative Literacy W. Morics; and Barbara Reynolds, Cardinal Stritch Uni- Business Meeting and Reception, Monday, 5:45 p.m.– versity. 6:45 p.m. New Technologies for Faculty: Wikis, Discussion Assessment of Student Learning in Undergraduate Boards, and Clickers, Wednesday, 9:30 a.m.–11 a.m., Mathematics, Monday afternoon (See the “MAA Contrib- organized by Mason A. Porter, University of Oxford, and uted Paper Sessions” section). Holly S. Zullo, Carroll College. Technology changes rap- idly, leading to an inevitable influx of new innovations SIGMAA on Research in Undergraduate Mathematics in teaching and research. This can feel overwhelming, Making the Connection Between Research and Teach- but many of your colleagues have found exciting ways ing in Undergraduate Mathematics Education, Sunday, to improve their pedagogy with cutting-edge technology. 9:00 p.m.–10:20 p.m. (See the “MAA Panels, Posters and Come learn how you too can enhance your teaching with Other Sessions” section). these easy-to-learn technologies. Among other topics the Business Meeting, Tuesday, 6:00 p.m. - 7:00 p.m. panelists will discuss how to use wikis and clickers to increase student communication both in and out of class. SIGMAA on Statistics Education Panelists will give short presentations describing the way Business Meeting, Monday, 5:45 p.m.–7:15 p.m. they use technology, and there will be an open discussion Project NExT Sessions at the end. Panelists include Joy L. Becker, University Project NExT (New Experiences in Teaching) is the of Wisconsin, Stout; Kris Green, St. John Fisher College; MAA’s professional development program for new and Jean McGivney-Burelle, University of Hartford; Steven W. recent Ph.D.'s in the mathematical sciences. Each year, Morics, University of the Redlands; and Reva Narasimhan, about sixty new faculty are selected as Project NExT Fel- Kean University. lows; application materials for 2008–09 are available at the Project NExT booth in the exhibit area. Project NExT has MAA Sessions for Students organized several sessions to which it invites all meeting Help for Undergraduates: Negotiating the Joint Meetings, participants. Sunday, 5:00 p.m.–6:30 p.m., Elizabeth Mayfield, Hood The following sessions were organized by Project NExT Fellows to address the concerns of faculty who have four College, How do you make sense of a 200-page program to ten years of teaching experience. book? What is the difference between a contributed talk Making the Math Major Work for the Under-Prepared and an invited talk—and how can you tell which of those Student, Monday, 2:30 p.m.–4:00 p.m., organized by Linda might be accessible to undergraduates? Which social Braddy, East Central University, and Pamela B. Pierce, The events are you allowed to attend? What’s up with the ex- College of Wooster. Wouldn’t it be great if all students con- hibits? What special events are planned for students at the sidering a major in mathematics were adequately prepared Joint Meetings? This informal panel will help undergradu- to succeed in the major? Of course, the reality is that many ate students find their way through the Joint Mathematics of our students need additional motivation, guidance, and Meetings and make this a successful experience for them. assistance with the material in order to make it through Panelists include Dan Kalman, American University, Jac- the major. Our panelists will give brief presentations on queline A. Jensen, Sam Houston State University, and an some strategies that have proven successful at helping undergraduate student. The session is sponsored by the such students to succeed without compromising learning MAA Committee on Undergraduate Student Activities and in the major. We plan to conclude this session by solicit- Chapters. ing ideas, concerns, and success stories from members Undergraduate Career Paths in Math: What Can You of the audience. Panelist include Bonnie Gold, Monmouth Do with a Math Degree?, Monday, 10:45 a.m.–12:05 p.m., University; John Ramsay, The College of Wooster; Laura Vanessa Garcia, Texas State University–San Marcos, and Taalman, James Madison University. Dov N. Chelst, DeVry University. A myriad of choices Capstone and One-Semester Research Projects for a are available for students who major in mathematics. Variety of Students, Tuesday, 1:00 p.m.–2:30 p.m., orga- This panel showcases a selection of career choices from nized by Steven W. Morics, University of Redlands, and industry, government, and education. Come to learn Mary D. Shepherd, Northwest Missouri State University. more about your options with an undergraduate degree Creating a true mathematical research experience for all in mathematics. students can be a challenge. Students have varying abili- J. Brian Conrey, The American Institute of Mathemat- ties and interests. Mathematics majors, even those not ics, The Riemann Hypothesis, Tuesday, 1:00 p.m. (Student destined for mathematical stardom, can benefit from a Lecture)

1238 Notices of the AMS Volume 54, Number 9 Meetings & Conferences

Undergraduate Student Poster Session, Tuesday, knew her; Bjarne Toft, Southern Denmark University, The 3:00 p.m.–5:30 p.m., organized by Diana M. Thomas, game of Hex: History, results and problems; Montclair State University. The session is reserved for un- Toward the Future: Ronald L. Graham, University of dergraduates and first-year graduate students submitting California, San Diego, Combinatorics: The future and posters on work done while undergraduates. Abstracts beyond. are accepted on a first come basis. Space is limited and There are separate registration fees to participate. See students are encouraged to apply early. Beginning August the fee schedule on the registration form at the back of 1, 2007 students can submit abstracts online at http:// this issue or visit www.ams.org/amsmtgs/2109_ www.maa.org/students/undergrad/poster08.htm. registration.html. Students are encouraged to apply early. Examples of poster topics include a new result, a different proof of Other MAA Events a known theorem, an innovative solution of a Putnam Board of Governors, Saturday, 8:30 a.m.–4:00 p.m. problem, a new mathematical model or method of solution Section Officers, Sunday, 2:30 p.m.–5:00 p.m. an applied problem. Purely expository posters cannot be Joint PME and MAA Student Chapter Advisors’ Meet- accepted. Prizes will be awarded to the top rated post- ing, Sunday, 3:00 p.m. to 3:50 p.m. ers with money provided by the AMS, MAA, AWM, CUR, SIGMAA Officers Meeting, Monday 8:00 a.m.–10:00 PME and by the Moore Foundation. Trifold, self-standing a.m., chaired by Amy Shell-Gellasch, Pacific Lutheran 48” by 36” tabletop posters will be provided. Additional University. material or equipment is the responsibility of the present- Business Meeting, Wednesday, 11:10 a.m.–11:40 p.m., ers. Questions regarding the session may be directed to organized by MAA secretary, Martha J. Siegel, Towson Diana Thomas at [email protected]. The University, and moderated by MAA president, Joseph A. deadline for proposals is Friday, November 2, 2007. The Gallian, University of Minnesota-Duluth. session is sponsored by the MAA-CUPM Subcommittee Department Liaisons Meeting, day and time to be on Undergraduate Research and the MAA Committee on determined. Minority Chairs Breakfast Meeting, day and time to Undergraduate Student Activities and Chapters (CUSAC). be determined. Also see the “Social Events” section for the open hours See the listings for various receptions in the “Social of the Student Hospitality Center and the Reception for Events” section. Undergraduates.

MAA Short Course Activities of Other Organizations Several organizations or special groups are having recep- This two-day Short Course on Combinatorics: Past, Pres- tions or other social events. Please see the “Social Events” ent, and Future is organized by Robin Wilson, The Open section of this announcement for details. University, and will take place on Friday and Saturday, January 4 and 5. Association for Symbolic Logic (ASL) The object of this short course is to learn about the This two-day program on Tuesday and Wednesday will development of a wide range of combinatorial topics, include sessions of contributed papers and Invited Ad- from earliest times up to the present day and beyond. dresses. The topics presented will include early combinatorics See also the Special Session cosponsored by the ASL on from China and the Islamic and Hebrew traditions, Euro- Set Theory and Banach Spaces on Sunday and Monday in pean combinatorics during the Renaissance, the legacy of the “AMS Special Sessions” listings. Leonhard Euler, and combinatorial topics in the modern era. Speakers and their topics include: Association for Women in Mathematics (AWM) Early Combinatorics (up to the 17th century): Andrea Twenty-Ninth Annual Emmy Noether Lecture, Monday, Breard, Université des Sciences et Technologies de Lille, 10:05 a.m., will be given by Audrey Terras, University of France, China; Victor Katz, University of the District of California San Diego, title to be announced. A luncheon Columbia, Combinatorics in the Islamic and Hebrew tradi- will be given in her honor; see the “Social Events” section tions; for details. Also see the related Special Session on Zeta Europe: Eberhard Knobloch, Technical University of Functions of Graphs, Ramanujan Graphs, and Related Top- Berlin, European combinatorics, 1200–1700; ics jointly sponsored by the AWM listed under the “AMS Euler’s Legacy: Robin Wilson, Early graph theory and Special Sessions” heading. Cayley’s work on trees, to the early attempts to solve map- Panel Discussion, Sunday, 2:15 p.m.–3:40 p.m. Topic coloring problems; George Andrews, Pennsylvania State and panelists to be announced. Just before the panel dis- University, Euler’s “De Partitio Numerorum”; Lars Ander- cussion, AWM will recognize the Alice T. Schafer award sen, University of Aalborg, Latin squares; Robin Wilson, honorees. Note that formal prizewinner announcements Triple systems, schoolgirls, and designs; are made at the Joint Prize Session on Monday after- Combinatorics Comes of Age: Lowell Beineke, Indiana noon. University–Purdue University at Fort Wayne, 20th-century Business Meeting, Sunday, 3:45 p.m.–4:15 p.m. graph theory; Herb Wilf, University of Pennsylvania, Phila- Workshop, Wednesday, 8:20 a.m.–4:20 p.m. With fund- delphia, and Lily Yen, Capilano College, Sister Celine as I ing from the Office of Naval Research and the National

October 2007 Notices of the AMS 1239 Meetings & Conferences

Security Agency, AWM will conduct its workshop for women Education and Applied Mathematics, William L. Briggs, graduate students and women who have received the Ph.D. University of Colorado at Denver (Sunday morning); within the last five years. Twenty women mathematicians Analysis and Computation of Stochastic Equations, Jack are selected in advance of this workshop to present their Xin, University of California Irvine (Sunday afternoon); research; graduate students will present posters, and the re- From Global Predictions to Local Action, Inez Fung, cent Ph.D.’s will give 20-minute talks. The workshop opens Christopher K. Jones, University of North Carolina, and with a dinner on a previous evening to introduce workshop- Mary Lou Zeeman, Bowdoin College (Monday morning and pers and mentors, and includes a panel discussion on career afternoon); issues. All mathematicians (female and male) are invited to Environmental Mathematics: Some Mathematical Prob- attend the entire program. Departments are urged to help lems on Climate Change and Geophysical Fluid Dynamics, graduate students and recent Ph.D.’s who do not receive Samuel S. Shen, San Diego State University, and Gerald R. funding to obtain some institutional support to attend the North, Department of Meteorology, Texas A&M University workshop and other meeting sessions. The deadline for (Tuesday morning and afternoon); applications for presenting and funding has expired. Up- Graph Coloring and Partitioning, Andre Kundgen and dated information about the Workshop is available at www. Radhika Ramamurthi, California State University-San awm-math.org/workshops.html. AWM seeks volunteers to Marcos, (Wednesday morning and afternoon). lead discussion groups and to act as mentors for workshop participants. If you are interested, please contact the AWM Young Mathematicians Network (YMN) office; inquiries regarding future workshops may be made Concerns of Young Mathematicians: A Town Meeting to the office at [email protected]. , Reception, Sunday, 9:30 p.m.–11:00 p.m. See the listing Tuesday, 7:30 p.m.–8:30 p.m., organized by David T. Kung, in the “Social Events” section of this announcement. St. Mary’s College of Maryland. This panel discussion will focus on the current primary concerns of young National Association of Mathematicians (NAM) mathematicians, from undergraduates to newly-tenured Granville-Brown-Haynes Session of Presentations by professors, with emphasis on audience participation. Recent Doctoral Recipients in the Mathematical Sciences, Also see details about the events cosponsored by the Tuesday, 2:15 p.m.–4:00 p.m. YMN under the “MAA Panels, Posters, and Other Sessions” Cox-Talbot Address, to be given Tuesday after the section. banquet; speaker and title to be announced. Panel Discussion, Wednesday, 9:00 a.m.–9:50 a.m. Others Business Meeting, Wednesday, 10:00 a.m.–10:50 a.m. Math on the Web, Sunday–Wednesday, various times. Claytor-Woodard Lecture: Wednesday, 1:00 p.m., The problem of communicating math on the Web is really speaker and title to be announced. no different than communicating math via other media. See details about the banquet on Tuesday in the “Social Namely, authoring and displaying mathematical notation Events” section. is difficult. On top of that, the Web is a dynamic medium, where users can interact with rich media documents in National Science Foundation (NSF) sophisticated ways. This introduces a whole new layer of The NSF will be represented at a booth in the exhibit challenges and possibilities for engaging, interactive com- area. NSF staff members will be available to provide munication between authors and readers. There will be counsel and information on NSF programs of interest to several presentations on the exhibit hall floor throughout mathematicians. The booth is open the same days and the meeting. hours as the exhibits. Times that staff will be available Mathematical Art Exhibit, organized by Robert will be posted at the booth. Fathauer, Tesselations Company, Nathaniel A. Fried- Pi Mu Epsilon (PME) man, ISAMA and SUNY Albany, and Reza Sarhangi, Bridges Conference, Towson University. A popular feature at the Council Meeting, Tuesday, 8:00 a.m.–11:00 a.m. last Joint Mathematics Meetings in New Orleans, this ex- Rocky Mountain Mathematics Consortium hibit provides a break in your day. On display are works in (RMMC) various media by artists who are inspired by mathematics Board of Directors Meeting, Tuesday, 2:15 p.m.–4:10 and by mathematicians who use visual art to express their p.m. findings. Fractals, symmetry, and tiling are some of the ideas at play here. Don’t miss this unique opportunity for Society for Industrial and Applied Mathematics a different perspective on mathematics. The exhibit will (SIAM) be open during the regular exhibit hours. The Invited Address will be given by Inez Fung, Berkeley In- Summer Program for Women in Mathematics (SPWM) stitute of the Environment, University of California Berkeley, Reunion, Monday, 1:00 p.m.–4:00 p.m. organized by From global predictions to local action: Mathematical chal- Murli M. Gupta, George Washington University. SPWM lenges in global warming at 11:10 a.m. on Monday. participants will describe their experiences from past Minisymposia and their organizers include programs.

1240 Notices of the AMS Volume 54, Number 9 Meetings & Conferences

Social Events University of Illinois at Urbana-Champaign Depart- ment of Mathematics Alumni Reception, Tuesday, 5:30 All events listed are open to all registered participants. p.m.–7:30 p.m. Everyone ever connected with the depart- It is strongly recommended that for any event requiring ment is encouraged to get together for conversation and to a ticket, tickets should be purchased through advance hear about mathematics at the University of Illinois. Please registration. Only a very limited number of tickets, if any, see www.math.uiuc.edu/jmm-reception.html. will be available for sale on site. If you must cancel your University of Iowa Mathematics Department Recep- participation in a ticketed event, you may request a 50% tion, Monday, 5:45 p.m.–7:00 p.m. refund by returning your ticket(s) to the Mathematics Knitting Circle, Monday, 8:15 p.m.–9:45 p.m. Bring a Meetings Service Bureau (MMSB) by December 21. After project (knitting/crochet/tatting/beading/etc.) and chat that date no refunds can be made. Special meals are avail- with other mathematical crafters! able at banquets upon advance request, but this must be Lehigh University Reception, Monday, 5:45 p.m.–7:00 indicated on the Advance Registration/Housing Form. p.m. All friends and graduates of the Lehigh Math Program AMS Banquet: As a fitting culmination to the meetings, are invited to attend. the AMS banquet provides an excellent opportunity to MAA–Project NExT Reception, Tuesday, 8:30 p.m.– socialize with fellow participants in a relaxed atmosphere. 10:30 p.m., organized by T. Christine Stevens, St. Louis The participant who has been a member of the Society for University, Joseph A. Gallian, University of Minnesota, the greatest number of years will be recognized and will Duluth, and Aparna W. Higgins, University of Dayton. All receive a special award. The banquet will be held on Wednes- Project NExT Fellows, consultants, and other friends of day, with a cash bar reception at 6:30 p.m. and dinner at 7:30 Project NExT are invited. p.m. Tickets are US$52, including tax and gratuity. MAA Two-Year College Reception, Monday, 5:45 p.m.– Association of Christians in the Mathematical Sci- 7:00 p.m., is open to all meeting participants, particularly ences (ACMS) Reception and Banquet, Tuesday, 6:00 two-year faculty members. This is a great opportunity to p.m.–10:00 p.m. This annual dinner at 6:30 p.m. is pre- meet old friends and make some new ones. There will be ceded by a reception and will be followed by an after- hot and cold refreshments and a cash bar. Sponsored by dinner talk by Fernando Gouvêa, Colby College. Tickets Addison Wesley. must be ordered by November 30; see www.acmsonline. Mathematical Reviews Reception, Tuesday, 6:00 p.m.– org for details. 7:00 p.m. All friends of Mathematical Reviews (MR) are ACMS Worship Service, Sunday, 7:00 a.m.–7:50 a.m. Begin the joint meetings by attending a nondenomina- invited to join reviewers and MR editors and staff (past tional service provided by members of the Association of and present) for a reception in honor of all the efforts that Christians in the Mathematical Sciences. go into the creation and publication of the Mathematical Association of Lesbian, Gay, Bisexual, and Transgen- Reviews database. Refreshments will be served. dered Mathematicians Reception, Monday, 5:45 p.m.–7:00 Mathematical Institutes Open House, Sunday, 5:30 p.m. Everyone is welcome to attend this open reception. p.m.–8:00 p.m. Participants are warmly invited to attend Meet some new friends or get together with some old this open house cosponsored by several North American friends. Please join us! mathematical institutes. Come find out about the latest AWM Reception: There is an open reception on Sunday activities and programs at each of the Institutes that may at 9:30 p.m. after the AMS Gibbs Lecture. This has been a be suited to your own research interests. popular, well-attended event in the past. MER Banquet: The Mathematicians and Education Re- AWM Luncheon to honor Noether Lecturer, Audrey form (MER) Forum welcomes all mathematicians who are Terras, Monday. Those interested may email awm@awm- interested in precollege, undergraduate, and/or graduate math.org; a sign-up sheet for those interested will also educational reform to attend the MER banquet on Mon- be located at the AWM table in the exhibit area and also at day evening. This is an opportunity to make or renew the AWM panel discussion and Business Meeting. contacts with other mathematicians who are involved in Budapest Semesters in Mathematics Reunion, Tuesday, education projects and to engage in lively conversation 6:00 p.m.–8:00 p.m. All alumni, family, and spouses are about educational issues. The after-dinner discussion is invited. an open forum for participants to voice their impressions, University of Chicago Mathematics Alumni Recep- observations, and analyses of the current education scene. tion, Monday, 6:00 p.m.–7:00 p.m. There will be a cash bar beginning at 6:30 p.m. Dinner will Reception for Graduate Students and First-Time Par- be served at 7:30 p.m. Tickets are US$50 each, including ticipants, Sunday, 5:30 p.m.–6:30 p.m. The AMS and the tax and gratuity. MAA cosponsor this social hour. Graduate students and NAM Banquet, Tuesday, 6:00 p.m.–9:30 p.m. The Na- first-timers are especially encouraged to come and meet tional Association of Mathematicians will host a banquet some old-timers to pick up a few tips on how to survive on Tuesday evening. A cash bar reception will be held at the environment of a large meeting. Refreshments will 6:00 p.m., and dinner will be served at 6:30 p.m. Tickets be served. are US$49 each, including tax and gratuity. Hawkes Learning Systems Courseware Presenta- NSA Women in Mathematics Society Networking Ses- tion, Tuesday, 6:00 p.m.–7:00 p.m. Alll participants are sion, Monday, 6:30 p.m.–8:30 p.m. Everyone is invited to invited. this annual session.

October 2007 Notices of the AMS 1241 Meetings & Conferences

New Mexico State University Department of Math- subject classification will be available for your perusal. ematical Sciences Reception, Monday, 5:45 p.m.–7:15 p.m. This is a great place to relax between sessions and forge All members and friends are invited. new friendships. Student Hospitality Center, Sunday–Tuesday, 9:00 a.m.–5:00 p.m., and Wednesday, 9:00 a.m.–3:00 p.m., Registering in Advance and Obtaining organized by Richard and Araceli Neal, American Society Hotel Accommodations for the Communication of Mathematics. Reception for Undergraduates, Sunday, 4:00 p.m.–5:00 The AMS and MAA make every effort to keep participant p.m. expenses at meetings and registration fees for meetings Wine and Jazz Evening, Tuesday, 7:00 p.m.–10:00 p.m. as low as possible. We work hard to negotiate the best Join your colleagues for an informal evening enjoying fine hotel rates and to make the best use of your registration wines and cool jazz at the San Diego Wine & Culinary Cen- dollars to keep the meetings affordable for you. The AMS ter Cafe, 200 Harbor Drive (across from the Convention and the MAA encourage all participants to register for Center). Relax in the casual atmosphere and enjoy a deli- the meeting. When you pay the registration fee, you are cious menu of reasonably priced appetizers and entrees, helping to support a wide range of activities associated with wines, both locally produced and international, priced with planning, organizing, and running a major meeting by the glass or bottle. of this size. How to Register in Advance: The importance of ad- vance registration cannot be overemphasized. Advance Other Events of Interest registration fees are considerably lower than the fees that AMS Information Booth: All meetings participants are will be charged for registration at the meetings. Participants invited to visit the AMS Information Booth during the registering by November 15 may receive their badges, pro- meetings. A special gift will be available for participants, grams, and tickets (where applicable) in advance by mail compliments of the AMS. AMS staff will be at the booth approximately three weeks before the meetings. Par- to answer questions about AMS programs and member- ticipants who wish to have their registration materials ship. mailed must check the appropriate box on the Advance Book Sales and Exhibits: All participants are encour- Registration/Housing Form, and provide a home address aged to visit the book, education media, and software for mailing. Registration materials will be mailed only to exhibits from 12:15 p.m.–5:30 p.m. on Sunday, 9:30 a.m.– those who checked the box on the form and who provided 5:30 p.m. on Monday and Tuesday, and 9:00 a.m.–1:00 a home address. Because of delays that occur in U.S. mail p.m. on Wednesday. Books published by the AMS and MAA to Canada, advance registrants from Canada must pick will be sold at discounted prices somewhat below the cost up their materials at the meetings. Because of delays that for the same books purchased by mail. These discounts occur in U.S. mail to overseas, materials are never mailed will be available only to registered participants wearing overseas. There will be a special Registration Assistance the official meetings badge. Most major credit cards will Desk at the Joint Meetings to assist individuals who either be accepted for book sale purchases at the meetings. do not receive this mailing or who have a problem with Also, AMS electronic products and the AMS website will their registration. Please note that a US$5 replacement fee be demonstrated. Participants visiting the exhibits are will be charged for programs and badges that are mailed required to display their meetings badge in order to enter but not taken to San Diego. Acknowledgments of registra- the exhibit area. tions will be sent by email to the email addresses given The AMS and the MAA cordially invite all registered on the Advance Registration/Housing Form. If you do participants to enjoy complimentary tea and coffee (avail- not wish your registration acknowledged by email, please able at noon and 2:00 p.m. on Sunday; 9:00 a.m., noon, mark the appropriate box on the form. and 2:00 p.m. on Monday and Tuesday; and 9:00 a.m. on Email Advance Registration: This service is available Wednesday) while perusing the associations’ booths. for advance registration and housing arrangements by Mathematical Sciences Employment Center: Those requesting the forms via email from meetreg-request@ wishing to participate in the Mathematical Sciences ams.org or by visiting http://www.ams.org/amsmtgs/ Employment Center should read carefully the important 2109_reg.html. VISA, MasterCard, Discover, and Ameri- article about the center beginning on page 1213 in this can Express are the only methods of payment which can issue of Notices or at www.ams.org/emp-reg/. be accepted for email advance registration, and charges Networking Opportunities: There are many opportu- to credit cards will be made in U.S. funds. Completed nities to meet new friends and greet old acquaintances email forms should be sent to [email protected]. in addition to the vast array of scientific sessions offered All advance registrants will receive acknowledgment of at these meetings. These opportunities are listed on payment prior to the meetings. the newcomers page at www.ams.org/amsmtgs/2109_ Internet Advance Registration: This service is avail- newcomers.html. Newcomers may want to investigate the able for advance registration and housing arrangements many receptions listed in the “Social Events” section, the at http://www.ams.org/amsmtgs/2109_reg.html. Student Hospitality Center, and the Employment Center. VISA, MasterCard, Discover, and American Express are the On site a Networking Center featuring casual seating and only methods of payment which are accepted for Internet lists of registered participants sorted by school and math advance registration, and charges to credit cards will be

1242 Notices of the AMS Volume 54, Number 9 Meetings & Conferences 2 9 6 3 5 8 10 1 4 7 0.75 1.05 0.70 0.45 0.06 1.06 1.10 0.33 0.12 0.05 Distance from SDCC 500 West Hotel Rodeway Inn and Suites Courtyard San Diego Downtown by Marriott Embassy Suites Hotel San Diego Bay - Downtown Hilton San Diego Gaslamp Quarter Holiday Inn Express San Diego Downtown Holiday Inn San Diego on the Bay Horton Grand Hotel Omni San Diego Hotel San Diego Marriott Hotel & Marina Headquarters Hotel Joint Mathematics Meetings Jan 6, 2008 to 9, 1 2 3 4 5 6 7 8 9 10 Hotel Downtown San Diego

OCTOBER 2007 NOTICES OF THE AMS 1243 Meetings & Conferences for for all Î ts/Cancellation Continued see descriptions below Please note that early departure 72-hour cancellation policy Raffle and Room Lottery qualification: and Lottery Room Raffle MMSB: through Reservations MMSB: through Changes/cancellations One night depositcheck, or by One night Credit cards accepted: VISA, MC, Deadlines: • October 31, 2007 • 15,November 2007 • 7, December 2007 Guarantee Requiremen Policy: • • AMEX, Diners, and Discover (except for does Horton not acceptGrand which Discover) • excepthotels 500 West (24-hour (7-day cancellation policy) and Omni cancellation policy) • penalties will apply ofat the some hotels – with a with at which time rooms rooms time at which to make a reservation to make , cannot be taken by phone. All other hotels will ONLY ONLY other hotels will All Please call the Student Hostel (paper or electronic) atics Meetings Service Bureau Service Meetings atics December 17 December at some hotels are offering free hotelsairport atare some offering these hotels before 18. December . A higher rate will be applied to any rectly for reservations. please submit a completed housing section of the a completed housing please submit Participants register advance orderin must to obtain How to Obtain Hotel Accommodations How Accommodations to Hotel Obtain November 15. November Sorry, reservations reservations must be made through the Mathematics Meetings Meetings Mathematics the be through made reservations must Check-in 3:00 12:00 p.m./checkout Check-in – p.m. all hotels except for Hilton,the see - descriptionsrooms open some below in Windows each in Seehotel. age arebedslimits Children only. free existing in of cribs, availability free of charge Limited all where linens policy regarding hotelsenvironmental a All limited have (CC) hotels is Center to indicated Diego San Convention the in from Distance Go to a specialCloud meeting. discount for 9is this offering Shuttle see Wirelesshotels descriptions- some is in free below. are not and sending some email by send confirmations only hotels will Some hotels have All ADA. hotels are All acceptable in with compliance Participants interestedsuites should contact reserving in MMSBthe for further information. hotel accommodations through Mathem the hotel accommodations at the meeting (MMSB). for this Special been negotiated rates have exclusively hotels. With Hostel exception Student the of the and Hotel following Occidental, Service Bureau (MMSB) to receive rates.these and Hotel Occidental di start accepting after directly reservations Form (ARH) Registration/Housing Advance byguarantee • Diego San Marriott Suites, 4:00 12:00 (check-in p.m./checkout p.m.) Embassy 3:00andExpress11:00 Holiday Inn (check-in p.m./checkout a.m.) • • • • be honored. will of requestslinens for change a limited • each listing. • https://www.hudsonltd2.com/cgi- General Instructions: General Information: bin/cld1/res?LOGON=GO&USERIDENTRY=JMM08 • • see - descriptions below. confirmations any • TTYs/TDDs request. text telephonesby or on the premises can rent them and and receiveNote discount. this also th shuttles. and rates will be basedand rates will on availability reserved rooms directly with any of a reservation,To make For for details. How To Register in Subject to 10.6 % state and orcertified students Only for detailed Form See ARH Room Raffle/Lottery:Room are offering we this meeting, a special for anyone raffle reserves ata room the who Marriott Hotel Marina by & October 31. We are also Lottery Room the offering who again for anyone the of reserves ata room any Octoberhotels by following 31. See Advance Rates: • local tax • mathematicians unemployed rates. for student qualify • ratesof for eachbreakdown hotel.

1244 Notices of the AMS Volume 54, Number 9 Meetings & Conferences . Î $75 Continued Complimentary fully fully Complimentary Downtown Seaport Village) (.9 miles to CC) (1 block from trolley) Confirmations willsent be not Confirmations All changes to departure dates must must dates departure to All changes Confirmations provided by email by email provided Confirmations ; Embassy Suites San Diego Bay-Embassy (.45 mile (.45 to CC / across the street from Courtyard by Marriott - Downtown 530 Broadway Street 530 Broadway San92101 Diego, CA 619-446-3000 Single/Double US $109 Hotel; Historic All Non-Smoking Restaurant; BusinessBar; center; Fitness Parking- per center; day Courtyard market; US $24in w/ and valet out All privileges; have rooms Some full amenities; have rooms doovens; Windows not openmicrowave in high speed internet rooms; Complimentary wireless inand complimentary rooms access in the bar and lobby; Children under 18 free; years 601 Pacific Highway 601 Highway Pacific San92101 Diego, CA 619-239-2400 Single/Double US $149 Student Single/Double US $135 Additional US view $20 bay for AllHotel; Suites and evening cocktail cookeddaily breakfast reception included in rates; Restaurant; FitnessLounge; center; Starbucks; Indoor Parking–pool; elevators; US per day Glass airport shuttle;$26 Complimentary valet; suites are with private bedroom rooms All Fullsleeper with sofa; andarea living room in amenities all includingrooms refrigerator openoven; Windows in all and microwave high speedWireless rooms; internet throughout hotel at costUSa of $9.95 per 24 hours plus tax; Children under 18 years free; only US a avoid to check-in at made be charge penalty All ; Confirmations Confirmations Quarter Confirmations provided provided Confirmations (1.8 miles to CC) (2 blocks from trolley) Holiday Express Inn Hilton San Diego Gaslamp (Across the (Across tostreet - CC .06 mile) changes to departure dates must must dates departure to changes US a avoid to check-in at made be $75 charge penalty 401 K. Street San92101 Diego, CA 619-231-4040 Single/Double US $150 Student Single/Double US $140 Hotel; All Non-Smoking Restaurant; Fitness Lounge; center; Outdoor heated pool; Parking per – US $30 day have valet; rooms All high Complimentary full amenities; speed ininternet and room access WiFi in lobby; complimentary openWindows in Children rooms; under free; 18 years only by email provided 1430 7th Avenue San92101 Diego, CA 619-696-0911 Single/Double US $129 Student Single/Double US $119 Hotel; All Non-Smoking Restaurant; Complimentary continental Outdoor breakfast; pool; Parking- US $12 per day self; airport shuttle; All Complimentary including full amenities have rooms Windows and refrigerators; safes open in all Most have rooms; rooms high balconies; Complimentary speed internet inand wireless all androoms lobby; Children under 18 free; years only by email No roll-in showers roll-in No Confirmations Confirmations (1.10 miles to CC) (2 blocks from trolley) Horton HotelGrand (.33 mile to CC - 3 blocks) Holiday on Inn the Bay 311 Island Avenue San92101 Diego, CA 619-544-1886 Single/Double US $155 Student Single/Double US $145 – All Hotel One-Bedded Historic of number limited (Very Rooms with beds); two queen rooms only); breakfast Restaurant (serving Bar; Parking – USper $14day or US $24day night over valet; All including full amenities have rooms High speed fireplace; internetgas in at a cost room US of wireless OR $9.95 plus per day tax; Windows open Balconies rooms; in some rooms Majority of rooms; some one have bed;king Children under free; 10 years provided Confirmations available; only by email 1355 North Harbor Drive San92101 Diego, CA 619-232-3861 Single/Double US $135 Student Single/Double US $125 Additional US view $30 bay for FitnessRestaurants; Lounge; center; Outdoor heated pool; Parking per - US $24day orvalet US $20 self; airport shuttle; All Complimentary including full amenities have rooms Most have rooms refrigerators; patios; open Windows in all rooms; internet in wireless Complimentary alland rooms lobby; Children under free; 18 years only by email provided Confirmations Confirmations Restaurants; ; (Headquarters) Confirmations provided by provided Confirmations (Next door to CC) Omni San Diego Omni Courses; all other at CC) events (Across the(Across tostreet - CC .10 mile) Care, EC, Miscellaneous Sessions, and Short San Diego Marriott Hotel & Marina (Location of Council, Board of Governors, Child 675 Street L. San92101 Diego, CA 619-231-6664 Single/Double US $140 Student Single/Double US $125 Restaurant; Fitness Lounge; center; Outdoor heated pool; Bar; Parking- US $26 per day full or have valet US $14rooms All self; including bar,amenities mini refreshment center, and wired bathrobes; Complimentary internet andin wireless allhotel rooms, lobby, bar, and pool open Windows deck; in all rooms; Children under free; 12 years only by email provided 333 Harbor W. Drive San92101 Diego, CA 619-230-8316 Single/DoubleCity US $172 Single/DoubleBay US $192 Student Single/Double US $138 Hotel; All Non-Smoking FitnessLounges; center; outdoorHeated pools; Starbucks; Shops; Tennis court; Marina; Parking– US per $20day or US self $26 valet; open Windows full amenities; have rooms All in South Balconies in Tower, North Tower; Children High speed under free; 18 years internet in at costUSa of $9.95rooms per day plus andtax includes phone localfor andusage and Lounge long in distance; DW's Wireless lobby lounge - cost based on Business usage; connectionCenter runs wireless in Starbucks at costUSa of $10 Hard lines per foyer day; available at Business Center at a cost US of $5 per 10 minutes; only email

October 2007 Notices of the AMS 1245 Meetings & Conferences and th is located on the corner 5 of Attention Students phones with free localcontinental phonescalls, and free with is Budget a Hotel located the 11 Convention blocks from Center, ohostels.org Hotel Occidental Hotel Hostelling International-San Diego Downtown International-San Hostelling Market Street in the soul of the city's Gaslamp Quarter. It is located four blocks from Quarter. It is located blocks from Streetfour inMarket Gaslamp the soul the of city's dorm thecomfortable Convention offer Centerthe and trolley. They three blocks from Wi-Fi in full rooms, free and breakfast, rooms up pancake to datefree private rooms, kitchen, and onsite laundry. 521 Street Market San92101 Diego, CA (619) 525-1531 (619) 338-0129 (fax) www.sandieg reservations. and information further for directly call Please 2. the trolley, 7andthe blocks 1busfrom block station. from 20 bus The runs every hour from andon range guest rooms every The the weekend. onminutes weekday a andsingles doubles with shared baths to private baths in single, doubles and queen highceiling with ceilings windows, large kitchenettes, private suites. Each features high central andspeedair DVD with wireless TV's players, heat,fans, complimentary digital internetsafes, access, breakfast. 410 Street Elm San92101 Diego, CA 619-232-1336 Hoteloccidental-sandiego.com reservations. and information further for directly call Please As alternative housinglist the As choices, we following: 1. No air air No Confirmations Confirmations 500 West and trolley) ; Cafe; YMCA on lower on YMCA lower ; Cafe; .75 mile from CC) ( (1 block from train station 500 W. Broadway 500 Broadway W. San92101 Diego, CA 800-276-7415 –only Single US $49,occupancy twin beds only Hotel; All Non-Smoking provided conditioning fullwith kitchen;room floor; Common Parking – Laundry; USper $15day overnightno w/ in and out (located next Shared service; door);maid Daily bathrooms; open Windows in all rooms; internet wireless Complimentary throughout hotel; door pool at ; Complimentary ; Complimentary (1.8 miles to CC) (3 blocks from trolley) Rodeway Inn & Suites 719 Street Ash San92101 Diego, CA 619-232-2525 Single/Double US $91 Restaurant No smoking continental Limited breakfast; to outFree access rooms; Inn Holiday the across Express street; Complimentary parking; Complimentary airport shuttle; the Rooms open from outside;full amenities have rooms All Windows includingand refrigerators; safes high open in all rooms; Complimentary speed internet inand wireless all rooms and lobby; Children under free; 18 years only by email provided Confirmations

1246 Notices of the AMS Volume 54, Number 9 Meetings & Conferences made in U.S. funds. All Internet advance registrants will Librarian: Any librarian who is not a professional receive acknowledgment of payment upon submission of mathematician. this form. Unemployed: Any person currently unemployed, Cancellation Policy: Those who cancel their advance actively seeking employment, and not a student. It is registration for the meetings, MAA Minicourses, or Short not intended to include any person who has voluntarily Courses by December 28 (the deadline for refunds for resigned or retired from his or her latest position. banquet tickets is December 21) will receive a 50% refund Developing Country Participant: Any person employed of fees paid. No refunds will be issued after this date. in developing countries where salary levels are radically noncommensurate with those in the U.S. Joint Mathematics Meetings Registration Fees Temporarily Employed: Any person currently em- by Dec. 14 at meeting ployed but who will become unemployed by June 1, 2008, Member of AMS, ASL, Canadian and who is actively seeking employment. Mathematical Society, MAA, SIAM US$214 US$279 Nonmathematician Guest: Any family member or friend Emeritus Member of AMS, MAA; who is not a mathematician and who is accompanied by a Unemployed; Librarian; participant in the meetings. These official guests will receive High School Teacher; a badge and may attend all sessions and the exhibits. Developing Countries Special Rate 43 53 Participants Who Are Not Members of the AMS and Graduate Student 44 54 register for the meetings as a nonmember will receive Undergraduate Student 23 29 mailings after the meetings are over with a special mem- Temporarily Employed 172 200 bership offer. Nonmember 332 431 Advance registration and on-site registration fees only High School Student 5 10 partially cover the expenses of holding meetings. All One-Day Member mathematicians who wish to attend sessions are expected of AMS, ASL, CMS, MAA, SIAM n/a 153 to register and should be prepared to show their badges One-Day Nonmember n/a 238 if so requested. Badges are required to enter the exhibit Nonmathematician Guest 15 15 area, to obtain discounts at the AMS and MAA Book Sales, MAA Minicourses 60 60* and to cash a check with the Joint Meetings cashier. *if space is available Advance registration forms accompanied by insufficient payment will be returned, thereby delaying the processing of Employment Center (please note that earlier deadlines any housing request, or a US$5 charge will be assessed if an apply for inclusion in the Winter Lists) invoice must be prepared to collect the delinquent amount. 1st Table (computer, self-scheduled, US$245 US$325 Overpayments of less than US$5 will not be refunded. or combination interview) For each invalid check or credit card transaction that 2nd Table (computer, self-scheduled, 95 125 results in an insufficient payment for registration or or combination interview) housing, a US$5 charge will be assessed. Participants Employer Posting Fee 50 N/A should check with their tax preparers for applicable de- Applicants (all services) 44 82 ductions for education expenses as they pertain to these Applicants (Winter List & meetings. message center only) 22 22 If you wish to be included in a list of individuals sorted by mathematical interest, please provide the one math- AMS Short Course ematics subject classification number of your major area Member of AMS or MAA US$94 US$125 of interest on the Advance Registration/Housing Form. Nonmember 125 155 (A list of these numbers is available by sending an empty Student/Unemployed/Emeritus 42 63 email message to [email protected]; include the num- MAA Short Course ber 1035 as the subject of the message.) Copies of this MAA or AMS Member $125 $140 list will be available for your perusal in the Networking Nonmember 175 190 Center. Student/Unemployed/Emeritus 50 60 If you do not wish to be included in any mailing list Full-Time Students: Those currently working toward used for promotional purposes, please indicate this in a degree or diploma. Students are asked to determine the appropriate box on the Advance Registration/Hous- whether their status can be described as graduate (work- ing Form. ing toward a degree beyond the bachelor’s), undergradu- Advance Registration Deadlines ate (working toward a bachelor’s degree), or high school There are four separate advance registration dead- (working toward a high school diploma) and to mark the lines, each with its own advantages and benefits. Advance Registration/Housing Form accordingly. Emeritus: Any person who has been a member of the EMPLOYMENT CENTER advance registration AMS or MAA for twenty years or more and who retired (inclusion in the Winter Lists) October 24 because of age or long-term disability from his or her EARLY meetings advance registration latest position. (room lottery and raffle) October 31

October 2007 Notices of the AMS 1247 Meetings & Conferences

ORDINARY meetings advance registration Participants should also inquire about this at check-in and (hotel reservations, materials make their final plans accordingly. mailed) November 15 Participants should also be aware that it is general hotel FINAL meetings advance registration practice in most cities to hold a nonguaranteed reservation (advance registration, Short Courses, until 6:00 p.m. only. When one guarantees a reservation by paying a deposit or submitting a credit card number as a Employment Center, MAA Minicourses, guarantee in advance, however, the hotel usually will honor banquets) December 14 this reservation up until checkout time the following day. Employment Center Advance Registration: Applicant If the individual holding the reservation has not checked and employer forms must be received by October 24 in in by that time, the room is then released for sale, and the order to appear in the publications distributed to all par- hotel retains the deposit or applies one night’s room charge ticipants. For detailed information on the Employment to the credit card number submitted. Center, see the separate article on page 1213. If you hold a guaranteed reservation at a hotel but are Early Advance Registration: Those who register by the informed upon arrival that there is no room for you, there early deadline of October 31 will be included in a random are certain things you can request the hotel do. First, they drawing to select winners of complimentary hotel rooms should provide for a room at another hotel in town for in San Diego. Multiple occupancy is permissible. The loca- that evening at no charge. (You already paid for the first tion of rooms to be used in this lottery will be based on night when you made your deposit.) They should pay for the number of complimentary rooms available in the vari- taxi fares to the other hotel that evening and back to the ous hotels. Therefore, the free room may not necessarily meetings the following morning. They should also pay for be in the winner’s first-choice hotel. The winners will be one telephone toll call so that you can let people know you notified by mail prior to December 20. So register early! are not at the hotel you expected. They should make every Applicant and employer forms must be received by Oc- effort to find a room for you in their hotel the following tober 24 in order to be reproduced in the Winter Lists for day and, if successful, pay your taxi fares to and from the the Employment Center. second hotel so that you can pick up your baggage and Ordinary Advance Registration: Those who register bring it to the first hotel. Not all hotels in all cities follow after October 31 and by the ordinary deadline of Novem- this practice, so your request for these services may bring ber 15 may use the housing services offered by the MMSB mixed results or none at all. but are not eligible for the room lottery and raffle. You Importance of Staying in the Official Meetings Ho- may also elect to receive your badge and program by mail tels: Your patronage of the official headquarters hotels in advance of the meetings. enables the JMM to secure the meeting space at a greatly Final Advance Registration: Those who register after reduced cost which helps to keep the cost of the meeting November 15 and by the final deadline of December and your registration fees down. Also, networking events 14 must pick up their badges, programs, and any tick- will be held at the Marriott for the convenience of our ets for social events at the meetings. Unfortunately, participants. it is sometimes not possible to provide final advance Headquarters Raffle: Win an Olympus FE-230 digital registrants with housing, so registrants are strongly camera and Fujifilm 1 GB xD picture card valued at over urged to make their hotel reservations by November 15. US$200! Participants who register and reserve a room Please note that the December 14 deadline is firm; any at the Marriott by October 31, 2007, will be eligible to forms received after that date will be returned and full enter this drawing. All participants who are eligible will refunds issued. Please come to the Meetings Registration receive a raffle ticket on their badge sheet. Those who Desk in Hall B1 at the San Diego Convention Center. wish to enter the drawing must turn in their tickets at the Meetings Registration Desk in the San Diego Convention Hotel Reservations Center. You must turn in your ticket to be entered into Participants should be aware that the AMS and MAA the drawing! The winning ticket will be drawn before the contract only with facilities who are working toward being end of the meeting on Wednesday, specific day and time in compliance with the public accommodations require- to be announced. ments of the ADA. Room Lottery: Win FREE room nights at our official Participants requiring hotel reservations should read hotels as listed on the hotel pages. Multiple winners! Par- the instructions on the following hotel pages. Participants ticipants who register and reserve a room at any of the who did not reserve a room during advance registration meetings hotels listed by October 31, 2007, will automati- and would like to obtain a room at one of the hotels listed cally be included in a random drawing to select a winner on the following pages should call the hotels directly after of free room nights in that hotel. The number of drawings December 17. However, after that date the MMSB can no to be made will be based on the number of complimen- longer guarantee availability of rooms or special conven- tary room nights available in the various hotels. Multiple tion rates. Participants should be aware that most hotels occupancy is permissible. The winners will be drawn at are starting to charge a penalty fee to guests for departure random from the hotel reservation lists and notified by changes made before or after guests have checked into email or phone prior to December 20, 2007. their rooms. These hotels are indicated on the hotel page at http://www.ams.org/amsmtgs/2109_hotelpage.html.

1248 Notices of the AMS Volume 54, Number 9 Meetings & Conferences

Miscellaneous Information they will be charged a late fee of US$5 per child for every 15 minutes thereafter. Audio-Visual Equipment: Standard equipment in all ses- Cancellations must be made to KiddieCorp prior to De- sion rooms is one overhead projector and screen. (Invited cember 9, 2007, for a full refund. Cancellations made after 50-minute speakers are automatically provided with two that date will be subject to a 50% cancellation fee. Once the overhead projectors and a laptop projector; AMS Spe- program has begun, no refunds will be issued. cial Sessions and MAA Contributed Paper Sessions on a To register, go to https://www.kiddiecorp.com/ specific topic are provided with the standard equipment jmmkids.htm or call KiddieCorp at (858) 455-1718 to re- and a laptop projector.) Blackboards are not available. quest a form. Organizers of sessions that by their nature demand Email Services: Limited email access for all Joint Meet- additional equipment (e.g., VCR and monitor or laptop ings participants will be available. The hours of operation projection device) and where the majority of speakers will be published in the program. in the session require this equipment should contact the Information Distribution: Tables are set up in the ex- audio-visual coordinator for the meetings at the AMS of- hibit area for dissemination of general information of fice in Providence at 401-455-4140 or by email at wsd@ possible interest to the members and for the dissemination ams.org to obtain the necessary approvals. Individual of information of a mathematical nature not promoting a speakers must consult with the session organizer(s) if product or program for sale. additional equipment or services are needed. If your ses- If a person or group wishes to display information of a sion has no organizer, please contact the audio-visual mathematical nature promoting a product or program for coordinator directly. All requests should be received by sale, they may do so in the exhibit area at the Joint Books, November 1. Journals, and Promotional Materials exhibit for a fee of Equipment requests made at the meetings most likely US$58 (posters are slightly higher) per item. Please contact will not be granted because of budgetary restrictions. the exhibits manager, MMSB, P.O. Box 6887, Providence, Unfortunately no audio-visual equipment can be provided RI 02940, for further details. for committee meetings or other meetings or gatherings The administration of these tables is in the hands of the not on the scientific program. AMS-MAA Joint Meetings Committee, as are all arrange- Childcare: The American Mathematical Society and ments for Joint Mathematics Meetings. the Mathematical Association of America will again offer Local Information: For information about the city see childcare services for the Joint Mathematics Meetings to www.meetmeinsandiego.com/AMS/ and for complete res- registered participants. taurant information, including maps and menus, see www. The child care will be offered through KiddieCorp Chil- sandiego.org/nav/Visitors/DiningAndNightlife. dren’s Program. KiddieCorp is an organization that has been Petition Table: At the request of the AMS Committee providing high quality programs for children of all ages at on Human Rights of Mathematicians, a table will be made meetings throughout the United States and Canada since available in the exhibit area at which petitions on behalf of 1986. Read all about them at http://www.kiddiecorp. named individual mathematicians suffering from human com/. rights violations may be displayed and signed by meet- The childcare services provided at the JMM are for chil- ings participants acting in their individual capacities. For dren ages 6 months through 12 years old. Space per day will details contact the director of meetings in the Providence be limited and is on a space available basis. The dates and office at 401-455-4137 or by email at [email protected]. times for the program are January 6–9, 2008, 8:00 a.m.–5:00 Signs of moderate size may be displayed at the table p.m. each day. It will be located at the San Diego Marriott but must not represent that the case of the individual in Hotel and Marina, 333 W. Harbor Dr., San Diego, CA 92101. question is backed by the Committee on Human Rights Parents are encouraged to bring snacks and beverages for unless it has, in fact, so voted. Volunteers may be present their children but items such as juice boxes, cheerios, and at the table to provide information on individual cases, crackers will be provided. KiddieCorp can arrange meals for but notice must be sent at least seven days in advance of children at cost plus 15% or parents can be responsible for the meetings to the director of meetings in the Providence meals for their children. office. Since space is limited, it may also be necessary to Registration starts in September. The registration fee limit the number of volunteers present at the table at any is US$30 per family (nonrefundable). Additional cost will one time. The Committee on Human Rights may delegate a be US$9 per hour per child or US$7 per hour per child for person to be present at the table at any or all times, graduate students. These reduced child care rates are taking precedence over other volunteers. made possible to the meetings participant by the American Any material that is not a petition (e.g., advertisements, Mathematical Society and the Mathematical Association résumés) will be removed by the staff. At the end of the of America, who subsidize this service thus keeping this exhibits on Monday, any material on the table will be dis- program affordable for families. Parents must be registered carded, so individuals placing petitions on the table should for the JMM to participate. Full payment is due at the time be sure to remove them prior to the close of exhibits. of registration with KiddieCorp. Deadline for registering is Telephone Messages: The most convenient method for December 9, 2007. leaving a message is to do so with the participant’s hotel. If parents do not pick up their children at the time Another method would be to leave a message at the meet- scheduled or by the end of the day (no later than 5:00 pm), ings registration desk from January 5 through 8 during the

October 2007 Notices of the AMS 1249 Meetings & Conferences hours that the desk is open. These messages will be posted ready for pickup, as vehicles are not allowed to wait in on the Math Meetings Message Board; however, staff at the the pickup area. The last airport pickup for the Embassy desk will try to locate a participant in the event of a bona Suites is at 10:30 p.m. Please check with the other hotels fide emergency. The telephone number will be published to see when the last pickup is available. in the program and daily newsletter. Shuttle service is available from the airport to the down- town hotels for approximately US$8–11 per person one Discounted Air Travel way and US$16–22 per person round trip. See www.san. San Diego is on Pacific Standard Time. San Diego Inter- org/airport/ground_transportation/shuttle_services.asp national Airport (SAN) www.san.org/airport/splash. for shuttle information. Shuttles can be picked up from asp is served by all major airlines and is slightly over three the Transportation Plazas across from Terminals 1 and 2, miles from the downtown area and the Convention Center. and curbside at the Commuter Terminal. From Terminal For reference, the floor plan of the San Diego International 1 you must cross the skybridge, and take the escalators Airport can be seen at www.san.org/airport/terminals/ or the elevators to street level. From Terminal 2, cross terminal_maps.asp#t1. Airlines arriving and departing at the Terminal 2 skybridge and take the escalators or the each of the three terminals are listed, and the locations elevators to street level, or use the pedestrian crosswalk of the baggage claim areas and ground transportation conveniently located outside the Terminal 2 Baggage Claim areas are marked. While you are at the airport, you might Area to access the Transportation Plaza. A Transportation need to travel between terminal buildings. The airport Coordinator will assist you with getting a shuttle. provides free transportation between the terminals on Special Deal! Sign up for the Cloud 9 shuttle online the Red Bus. in advance and save at https://www.hudsonltd2.com/cgi- The official airline for the meetings is Delta. The AMS bin/cld1/res?LOGON=GO&USERIDENTRY=JMM08. Shuttle and MAA have made an agreement with Delta that will service from the airport to the hotels if you reserve in enable meetings’ participants to enjoy exclusive discounts! advance using this link is US$6 (per person, one-way), or Discounts vary depending on the cabin and available US$12 (round trip). Regular Cloud 9 price is US$8 one way, airfare level. We cannot guarantee that these will be the and US$16 round trip. The telephone number for Cloud lowest fares when you make your arrangements. However, 9 is 800-9-SHUTTLE (1-800-974-8885). we strongly urge participants to make use of this special Public Transportation from/to the airport: General deal if at all possible, since the AMS and MAA can earn information on San Diego public transportation is at complimentary tickets. These tickets are used to send http://www.sdmts.com/. meetings’ staff (not officers or other staff) to the Joint The Metropolitan Transit System Bus, Flyer Route No. Mathematics Meetings, thereby keeping the costs of the 992, runs every 10 minutes between 5:00 a.m. and 12:50 meetings (and registration fees) down. a.m. to and from the airport and downtown San Diego, To make reservations, visit www.ams.org/ stopping between Terminals 1 and 2 and the Commuter amsmtgs/2109_travel.html#delta and click on the Delta Terminal of the San Diego International Airport. Flyer Air Lines logo. This will bring you to the Delta Air Lines Route No. 992 connects with Trolley, Coaster and Amtrak website where you can make your reservations and have stations and is wheelchair accessible. Information on Flyer your tickets issued. The applicable discount will automati- Route No. 992 is available at www.sdmts.com/RouteFiles/ cally apply and the total airfare noted including all taxes routes/pdf/992.pdf. The price is currently US$2.25, exact and fees—convenient, fast, and no special meeting code is fare is appreciated. Flyer Route No. 992’s final stop is at needed. Reservations must be made through this link to be 5th Avenue and J Street in the Gaslamp District not far recognized as a Joint Mathematics Meetings participant. If from the Convention Center. However depending on your you go to the www.delta.com website directly you will not destination, it may be more convenient to transfer to the get a discount. Your benefits include no airline or agency downtown trolley route when the Flyer stops at Broadway booking fees; Delta SkyMile frequent flyer bonus miles, and Kettner Blvd, (where the Amtrak station is located). 500 round trip, 250 one way; and skip the airport lines! Trolley information is located at: http://www.sdmts. Check in online and print your boarding pass within 24 com/Trolley/Trolley.asp.The trolley has a regular stop hours of your flight time. at the San Diego Convention Center. Traveling from the airport: To depart the San Diego Taxicabs: Taxi fare to the downtown area is approxi- airport, head for the baggage claim area at any of the mately US$10–12 dollars one way. In the airport follow terminals. The shuttles, taxis, car rental companies, and the signs leading to the Ground Transportation Plazas, the bus can be accessed from this location. and a Transportation Coordinator will place you with the Airport Shuttle: Please note that Embassy Suites, Com- first available taxi. fort Inn, Holiday Inn Express, and the Holiday Inn on the Driving Directions from the airport to the Conven- Bay provide complimentary airport shuttles. In the Bag- tion Center: The San Diego Convention Center is located gage Claim area, either locate the nearest courtesy phone at 111 W. Harbor Drive, San Diego, CA 92101. Upon and call the hotel, or call the hotel directly from your cell leaving the airport, drive out of parking lot, and follow phone. Identify yourself as a person who has a reservation signs to Interstate 5/Downtown. The ramp will put you and you will be given a pickup location and an estimated on Harbor Drive going south. Follow signage to the parking time of arrival. Guests are advised to call the hotel only entrance for the San Diego Convention Center. For driving after they have claimed their luggage and are actually directions from other points, see www.visitsandiego.com/

1250 Notices of the AMS Volume 54, Number 9 Meetings & Conferences maps/. The hotels being used by the Joint Mathematics States have experienced unusual delays in obtaining travel Meetings are downtown and locations can be ascertained visas. If you need a letter of invitation from the AMS and by checking the map. have not yet requested it, please send email to meet@ Train: The Union Station (Santa Fe Depot) train station ams.org and an invitation will be forwarded as soon as is conveniently located in downtown San Diego at 1050 possible. In order to compose and send your letter, we Kettner Boulevard. There is a trolley stop at the train will need your document number, email address, and your station. For additional information on Amtrak service to complete mailing address. Also see this very informative or from San Diego, telephone 1-800-USA-RAIL, or visit document from the U.S. Department of State which lists Amtrak www.amtrak.com/servlet/ContentServer?pagen answers to frequently asked questions about the process- ame=Amtrak/HomePage or Amtrak California at www. ing of visas (www.ams.org/amsmtgs/FAQ-Bus-1-Visa. amtrakcalifornia.com/rail/go/amtrak/index.cfm. pdf). You should also be aware that this meeting has been registered with the U.S. Department of State. Discounted Car Rental Machine Readable Passports Required by June 26, Avis Rent A Car is the official car rental company 2005: The Department of Homeland Security reminds for the meetings. All car rentals include unlimited free travelers from the 27 Visa Waiver Program (VWP) countries mileage. Renters must meet Avis’s age, driver, and credit (see the website cited above for a list) that as of June 26, requirements. Avis offers special convention rental rates 2005, they must have a machine-readable passport to effective December 30–January 16, 2008. enter the United States without a visa. Beginning June 26, Car Type Daily Weekly Weekend 2005, transportation carriers will be fined US$3,300, per Daily violation, for transporting any VWP traveler to the United Subcompact US$38 US$151 US$22 States without a machine-readable passport. Similarly, Compact 43 162 24 VWP travelers arriving in the United States on that date Intermediate 48 184 26 without a machine-readable passport should not antici- Full-Size 2-Door 50 194 29 pate being granted one-time entry into the country. As an Full-Size 4-Door 54 206 33 alternative for persons with immediate travel plans who Premium 60 270 41 are unable to obtain a machine-readable passport in time, Luxury, 87 368 66 the individual may apply for a U.S. visa at a U.S. Consulate Minivan 60 302 60 or Embassy abroad. Convertible 60 305 60 Sport Utility 60 302 60 Weather These rates are guaranteed. Return to the same rental The temperature in January ranges from about 50˚F. to location or additional surcharges may apply. Weekend 66˚F. The sun shines during 72% of the daylight hours. Av- daily rates are available from noon Saturday until 11:59 erage precipitation in January is 2.28 inches. For more cur- p.m. Thursday (vehicle must be checked out by 3:00 p.m. rent information use your favorite search engine or try the Sunday). Should a lower qualifying rate become available, sites: http://asp.usatoday.com/weather/basemaps/ Avis is pleased to present a 5% discount off the lower usa/ca/nw722900.htm or www.weather.com/weather/ qualifying rate or the meetings rate, whichever is lowest. local/92101. Rates do not include any state or local surcharges, tax, optional coverages, or gas refueling charges. Reservations can be made by calling 800-331-1600 or online at www. avis.com; cite group ID number J098887. New York, New York All car rental agencies are off-site and do not have Courant Institute of New York University counters inside the terminal facilities. The car rental res- ervation boards are located near the baggage claim areas March 15–16, 2008 of Terminals 1 and 2. Use the courtesy phones provided Saturday – Sunday to request shuttle transport to the car rental company of your choice. Please note that using a reservation board is Meeting #1036 not always necessary. Car rental shuttles regularly oper- Eastern Section ate at the Terminal 1 center traffic aisle and at the traffic Associate secretary: Lesley M. Sibner island at the far west end of Terminal 2. If you follow the Announcement issue of Notices: January 2008 signage to any of these areas, it is likely that a shuttle Program first available on AMS website: January 31, will be waiting. 2008 Program issue of electronic Notices: March 2008 Travel Information for International Participants Issue of Abstracts: Volume 29, Issue 2 International participants should view the impor- tant information about traveling to the United States at Deadlines www7.nationalacademies.org/visas/Traveling_to For organizers: Expired _US.html. For consideration of contributed papers in Special Ses- Because of increased scrutiny of visa applicants, many sions: November 27, 2007 potential attendees of scientific meetings in the United For abstracts: January 22, 2008

October 2007 Notices of the AMS 1251 Meetings & Conferences

The scientific information listed below may be dated. The scientific information listed below may be dated. For the latest information, see www.ams.org/amsmtgs/ For the latest information, see www.ams.org/amsmtgs/ sectional.html. sectional.html.

Invited Addresses Invited Addresses Weinan E, Princeton University, Title to be announced. Maria Chudnovsky, Columbia University, Title to be Ilya Kapovich, University of Illinois at Urbana- announced. Champaign, Title to be announced. Soren Galatius, Stanford University, Title to be an- Ovidiu Savin, Columbia Univeristy, Title to be an- nounced. nounced. Zhongwei Shen, University of Kentucky, Title to be Ravi Vakil, Stanford University, Title to be an- announced. nounced. Mark Shimozono, Virginia Polytechnic Institute & State University, Title to be announced. Special Sessions Algebraic Combinatorial Geometry (Code: SS 3A), Ju- Special Sessions lianna Tymoczko, University of Iowa, and Linda Chen, Geometric and Combinatorial Representation Theory Ohio State University. (Code: SS 7A), Promad N. Achar and Daniel S. Sage, Loui- Buckminster Fuller’s Synergetics and Mathematics siana State University. (Code: SS 5A), Christopher J. Fearnley and Joe Clinton, Harmonic Analysis and Partial Differential Equations Synergetics Collaborative. in Real and Complex Domains (Code: SS 3A), Loredana Isoperimeric Problems and Partial Differential Equations Lanzani, University of Arkansas, and Zhongwei Shen, (Code: SS 6A), Bernd Kawohl, University of Cologne, and University of Kentucky. Marcello Lucia, City University of New York. Knot and 3-Manifold Invariants (Code: SS 6A), Oliver L-Functions and Automorphic Forms (Code: SS 1A), Alina T. Dasbach and Patrick M. Gilmer, Louisiana State Uni- Bucur, Institute for Advanced Study, Ashay Venkatesh, versity. Courant Institute of Mathematical Sciences, Stephen D. Nonlinear Evolution Equations of Mathematical Physics Miller, Rutgers University, and Steven J. Miller, Brown (Code: SS 5A), Jerry L. Bona, University of Illinois at Chi- University. cago, and Michael M. Tom, Louisiana State University. Mathematics of Multiscale Phenomena (Code: SS 4A), Recent Advances in Knot Theory: Quandle Theory and Sam Nelson Peter McCoy and Reza Malek-Madani. Categorified Knot Invariants (Code: SS 4A), , Pomona College, and Alissa S. Crans, Loyola Marymount Nonlinear Elliptic Equations and Geometric Inequalities University. (Code: SS 2A), Fengbo Hang, Princeton University, and Structural Graph Theory (Code: SS 2A), Maria Chud- Xiaodong Wang, Michigan State University. novsky, Columbia University. White Noise Distribution Theory and Orthogonal Polyno- mials (Code: SS 1A), Jeremy J. Becnel, Stephen F. Austin Baton Rouge, State University, and Aurel I. Stan, The Ohio State Univer- Louisiana sity at Marion. Louisiana State University, Baton Rouge Bloomington, Indiana March 28–30, 2008 Indiana University Friday – Sunday April 5–6, 2008 Meeting #1037 Saturday – Sunday Southeastern Section Associate secretary: Matthew Miller Meeting #1038 Announcement issue of Notices: February 2008 Central Section Program first available on AMS website: February 14, Associate secretary: Susan J. Friedlander 2008 Announcement issue of Notices: February 2008 Program issue of electronic Notices: March 2008 Program first available on AMS website: February 21, Issue of Abstracts: Volume 29, Issue 2 2008 Program issue of electronic Notices: April 2008 Deadlines Issue of Abstracts: Volume 29, Issue 3 For organizers: Expired For consideration of contributed papers in Special Ses- Deadlines sions: December 11, 2007 For organizers: Expired For abstracts: February 5, 2008 For consideration of contributed papers in Special Ses- sions: December 18, 2007

1252 Notices of the AMS Volume 54, Number 9 Meetings & Conferences

For abstracts: February 12, 2008 For abstracts: March 11, 2008

The scientific information listed below may be dated. The scientific information listed below may be dated. For the latest information, see www.ams.org/amsmtgs/ For the latest information, see www.ams.org/amsmtgs/ sectional.html. sectional.html.

Invited Addresses Invited Addresses Shi Jin, University of Wisconsin, Title to be an- Michael Bennett, University of British Columbia, Title nounced. to be announced. Michael J. Larsen, Indiana University, Title to be an- Chandrashekhar Khare, University of Utah, Title to be nounced. announced. Mircea Mustata, University of Michigan, Title to be an- Huaxin Lin, University of Oregon, Title to be an- nounced. nounced. Margaret H. Wright, New York University-Courant In- Anne Schilling, University of California Davis, Title to stitute, Title to be announced. be announced.

Special Sessions Special Sessions Algebraic Aspects of Coding Theory (Code: SS 5A), Heide Diophantine Problems and Discrete Geometry (Code: SS Gluesing-Luerssen, University of Kentucky, and Roxana 3A), Matthias Beck, San Francisco State University, and Smarandache, San Diego State University. Lenny Fukshansky, Texas A&M University. Birational Algebraic Geometry (Code: SS 3A), Mircea I. Dynamical Systems and Differential Equations (Code: Mustata, University of Michigan, and Mihnea Popa, Uni- SS 1A), Adolfo Rumbos, Pomona College, Mario Martelli, versity of Illinois at Chicago. Claremont McKenna College, and Alfonso Castro, Harvey Combinatorial and Geometric Aspects of Commutative Mudd College. Algebra (Code: SS 1A), Juan Migliore, University of Notre Operators, Functions and Linear Spaces (Code: SS 2A), Dame, and Uwe Nagel, University of Kentucky. Asuman G. Aksoy, Claremont McKenna College, Stephan Hyperbolic and Kinetic Equations (Code: SS 2A), Shi Jin, R. Garcia, Pomona College, Michael Davlin O’Neill, Cla- University of Wisconsin, and Marshall Slemrod, Univesity remont McKenna College, and Winston C. Ou, Scripps of Wisconsin. College. Some Mathematical Problems in Biology, from Macro- Recent Developments in Riemannian and Kaehlerian molecules to Ecosystems (Code: SS 6A), Santiago David Geometry (Code: SS 4A), Hao Fang, University of Iowa, Schnell, Indiana University, and Roger Temam, Indiana Zhiqin Lu, University of California, Irvine; Dragos-Bogdan University. Suceava, California State University Fullerton; and Mihaela Weak Dependence in Probability and Statistics (Code: B. Vajiac, Chapman University. SS 4A), Richard C. Bradley and Lahn T. Tran, Indiana University. Rio de Janeiro, Brazil Claremont, Instituto Nacional de Matemática Pura e Aplicada (IMPA) California June 4–7, 2008 Claremont McKenna College Wednesday – Saturday May 3–4, 2008 Meeting #1040 Saturday – Sunday First Joint International Meeting between the AMS and the Sociedade Brasileira de Matemática. Meeting #1039 Associate secretary: Lesley M. Sibner Western Section Announcement issue of Notices: February 2008 Associate secretary: Michel L. Lapidus Program first available on AMS website: To be an- Announcement issue of Notices: March 2008 nounced Program first available on AMS website: March 20, 2008 Program issue of electronic Notices: To be announced Program issue of electronic Notices: May 2008 Issue of Abstracts: To be announced Issue of Abstracts: Volume 29, Issue 3 Deadlines Deadlines For organizers: November 1, 2007 For organizers: October 4, 2007 For consideration of contributed papers in Special Ses- For consideration of contributed papers in Special Ses- sions: To be announced sions: January 15, 2008 For abstracts: To be announced

October 2007 Notices of the AMS 1253 Meetings & Conferences

The scientific information listed below may be dated. For the latest information, see www.ams.org/amsmtgs/ Middletown, internmtgs.html. Connecticut AMS Invited Addresses Ruy Exel, University Federal de Santa Catarina, Title to Wesleyan University be announced. October 11–12, 2008 Velimir Jurdjevic, University of Toronto, Title to be announced. Saturday – Sunday Andre Nachbin, Institute for Pure-Applied Mathemat- Meeting #1042 ics, Title to be announced. Eastern Section Richard M. Schoen, Stanford University, Title to be Associate secretary: Lesley M. Sibner announced. Announcement issue of Notices: August 2008 Ivan P. Shestakov, University of Sao Paulo, Title to be Program first available on AMS website: August 28, 2008 announced. Program issue of electronic Notices: October 2008 Amie Wilkinson, Northwestern University, Title to be Issue of Abstracts: Volume 29, Issue 4 announced. Deadlines For organizers: March 11, 2008 Vancouver, Canada For consideration of contributed papers in Special Ses- sions: June 24, 2008 University of British Columbia and the For abstracts: August 19, 2008 Pacific Institute of Mathematical Sciences (PIMS) The scientific information listed below may be dated. For the latest information, see www.ams.org/amsmtgs/ October 4–5, 2008 sectional.html. Saturday – Sunday Special Sessions Meeting #1041 Algebraic Geometry (Code: SS 1A), Eyal Markman and Jenia Tevelev, University of Massachusetts, Amherst. Western Section Associate secretary: Michel L. Lapidus Announcement issue of Notices: August 2008 Kalamazoo, Michigan Program first available on AMS website: August 21, 2008 Program issue of electronic Notices: October 2008 Western Michigan University Issue of Abstracts: Volume 29, Issue 4 October 17–19, 2008 Deadlines Friday – Sunday For organizers: March 9, 2008 For consideration of contributed papers in Special Ses- Meeting #1043 sions: June 17, 2008 Central Section For abstracts: August 12, 2008 Associate secretary: Susan J. Friedlander Announcement issue of Notices: August 2008 Program first available on AMS website: September 4, The scientific information listed below may be dated. 2008 For the latest information, see www.ams.org/amsmtgs/ Program issue of electronic Notices: October 2008 sectional.html. Issue of Abstracts: Volume 29, Issue 4

Invited Addresses Deadlines Richard Kenyon, University of British Columbia, Title For organizers: March 17, 2008 to be announced. For consideration of contributed papers in Special Ses- Alexander S. Kleshchev, University of Oregon, Title to sions: July 1, 2008 be announced. For abstracts: July 26, 2008 Mark Lewis, University of Alberta, Title to be an- nounced. The scientific information listed below may be dated. Audrey A. Terras, University of California San Diego, For the latest information, see www.ams.org/amsmtgs/ Title to be announced. sectional.html.

1254 Notices of the AMS Volume 54, Number 9 Meetings & Conferences

Invited Addresses M. Carme Calderer, University of Minnesota, Title to Shanghai, People’s be announced. Alexandru Ionescu, University of Wisconsin, Title to Republic of China be announced. Fudan University Boris S. Mordukhovich, Wayne State University, Title to be announced. December 17–21, 2008 David Nadler, Northwestern University, Title to be an- Wednesday – Sunday nounced. Meeting #1045 First Joint Interntional Meeting Between the AMS and the Huntsville, Alabama Shanghai Mathematical Society Associate secretary: Susan J. Friedlander University of Alabama, Huntsville Announcement issue of Notices: To be announced Program first available on AMS website: To be an- October 24–26, 2008 nounced Friday – Sunday Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Meeting #1044 Deadlines Southeastern Section For organizers: To be announced Associate secretary: Matthew Miller For consideration of contributed papers in Special Ses- Announcement issue of Notices: August 2008 sions: To be announced Program first available on AMS website: September 11, For abstracts: To be announced 2008 Program issue of electronic Notices: October 2008 The scientific information listed below may be dated. Issue of Abstracts: Volume 29, Issue 4 For the latest information, see www.ams.org/amsmtgs/ internmtgs.html. Deadlines Invited Addresses For organizers: March 24, 2008 L. Craig Evans, University of California Berkeley, Title For consideration of contributed papers in Special Ses- to be announced. sions: July 8, 2008 Zhi-Ming Ma, Chinese Academy of Sciences, Title to be For abstracts: September 2, 2008 announced. Richard Schoen, Stanford University, Title to be an- The scientific information listed below may be dated. nounced. For the latest information, see www.ams.org/amsmtgs/ Richard Taylor, Harvard University, Title to be an- sectional.html. nounced. Xiaoping Yuan, Fudan University, Title to be an- Invited Addresses nounced. Weiping Zhang Mark Behrens, Massachusetts Institute of Technology, , Chern Institute, Title to be an- nounced. Title to be announced. Anthony Michael Bloch, University of Michigan, Ann Arbor, Title to be announced. Roberto Camassa, University of North Carolina, Chapel Washington, District Hill, Title to be announced. Mark V. Sapir, Vanderbilt University, Title to be an- of Columbia nounced. Marriott Wardman Park Hotel and Omni Shoreham Hotel January 7–10, 2009 Wednesday – Saturday Joint Mathematics Meetings, including the 115th Annual Meeting of the AMS, 92nd Annual Meeting of the Math- ematical Association of America (MAA), annual meetings of the Association for Women in Mathematics (AWM) and the National Association of Mathematicians (NAM), and the

October 2007 Notices of the AMS 1255 Meetings & Conferences winter meeting of the Association for Symbolic Logic (ASL), Program first available on AMS website: To be an- with sessions contributed by the Society for Industrial and nounced Applied Mathematics (SIAM). Program issue of electronic Notices: To be announced Associate secretary: Lesley M. Sibner Issue of Abstracts: To be announced Announcement issue of Notices: October 2008 Program first available on AMS website: November 1, Deadlines 2008 For organizers: September 4, 2008 Program issue of electronic Notices: January 2009 For consideration of contributed papers in Special Ses- Issue of Abstracts: Volume 30, Issue 1 sions: To be announced For abstracts: To be announced Deadlines For organizers: April 1, 2008 For consideration of contributed papers in Special Ses- sions: To be announced San Francisco, For abstracts: To be announced California Urbana, Illinois San Francisco State University April 25–26, 2009 University of Illinois at Urbana-Champaign Saturday – Sunday March 27–29, 2009 Western Section Associate secretary: Michel L. Lapidus Friday – Sunday Central Section Announcement issue of Notices: To be announced Associate secretary: Susan J. Friedlander Program first available on AMS website: To be an- Announcement issue of Notices: To be announced nounced Program first available on AMS website: To be an- Program issue of electronic Notices: To be announced nounced Issue of Abstracts: To be announced Program issue of electronic Notices: To be announced Deadlines Issue of Abstracts: To be announced For organizers: September 25, 2008 Deadlines For consideration of contributed papers in Special Ses- For organizers: August 29, 2008 sions: To be announced For consideration of contributed papers in Special Ses- For abstracts: To be announced sions: To be announced For abstracts: To be announced Waco, Texas The scientific information listed below may be dated. For the latest information, see www.ams.org/amsmtgs/ Baylor University sectional.html. Special Sessions October 16–18, 2009 Geometric Group Theory (Code: SS 2A), Sergei V. Iva- Friday – Sunday nov, Ilya Kapovich, Igor Mineyev, and Paul E. Schupp, Central Section University of Illinois at Urbana-Champaign. Associate secretary: Susan J. Friedlander q-Series and Partitions (Code: SS 1A), Bruce Berndt, Announcement issue of Notices: To be announced University of Illinois at Urbana-Champaign. Program first available on AMS website: To be an- nounced Program issue of electronic Notices: To be announced Raleigh, North Issue of Abstracts: To be announced Deadlines Carolina For organizers: March 17, 2009 North Carolina State University For consideration of contributed papers in Special Ses- sions: To be announced April 4–5, 2009 For abstracts: To be announced Saturday – Sunday Southeastern Section Associate secretary: Matthew Miller Announcement issue of Notices: To be announced

1256 Notices of the AMS Volume 54, Number 9 Meetings & Conferences

with sessions contributed by the Society of Industrial and Boca Raton, Florida Applied Mathematics (SIAM). Associate secretary: Matthew Miller Florida Atlantic University Announcement issue of Notices: October 2009 Program first available on AMS website: November 1, October 30 – November 1, 2009 2009 Friday – Sunday Program issue of electronic Notices: January 2010 Southeastern Section Issue of Abstracts: Volume 31, Issue 1 Associate secretary: Matthew Miller Announcement issue of Notices: To be announced Deadlines Program first available on AMS website: To be an- For organizers: April 1, 2009 nounced For consideration of contributed papers in Special Ses- Program issue of electronic Notices: To be announced sions: To be announced Issue of Abstracts: To be announced For abstracts: To be announced

Deadlines For organizers: March 30, 2009 Lexington, Kentucky For consideration of contributed papers in Special Ses- sions: To be announced University of Kentucky For abstracts: To be announced March 27–28, 2010 Saturday – Sunday Southeastern Section Riverside, California Associate secretary: Matthew Miller University of California Announcement issue of Notices: To be announced Program first available on AMS website: To be an- November 7–8, 2009 nounced Saturday – Sunday Program issue of electronic Notices: To be announced Western Section Issue of Abstracts: To be announced Associate secretary: Michel L. Lapidus Deadlines Announcement issue of Notices: To be announced For organizers: August 28, 2009 Program first available on AMS website: To be an- For consideration of contributed papers in Special Ses- nounced sions: To be announced Program issue of electronic Notices: To be announced For abstracts: To be announced Issue of Abstracts: To be announced

Deadlines For organizers: Expired New Orleans, For consideration of contributed papers in Special Ses- sions: To be announced Louisiana For abstracts: To be announced New Orleans Marriott and Sheraton New Orleans Hotel San Francisco, January 5–8, 2011 Wednesday – Saturday California Joint Mathematics Meetings, including the 117th Annual Moscone Center West and the San Fran- Meeting of the AMS, 94th Annual Meeting of the Math- ematical Association of America, annual meetings of the cisco Marriott Association for Women in Mathematics (AWM) and the National Association of Mathematicians (NAM), and the January 6–9, 2010 winter meeting of the Association for Symbolic Logic (ASL), Wednesday – Saturday with sessions contributed by the Society for Industrial and Joint Mathematics Meetings, including the 116th Annual Applied Mathematics (SIAM). Meeting of the AMS, 93rd Annual Meeting of the Math- Associate secretary: Susan J. Friedlander ematical Association of America (MAA), annual meetings Announcement issue of Notices: October 2010 of the Association for Women in Mathematics (AWM) and Program first available on AMS website: November 1, the National Association of Mathematicians (NAM), and the 2010 winter meeting of the Association for Symbolic Logic (ASL), Program issue of electronic Notices: January 2011

October 2007 Notices of the AMS 1257 Meetings & Conferences

Issue of Abstracts: Volume 32, Issue 1 Program first available on AMS website: To be an- nounced Deadlines Program issue of electronic Notices: To be announced For organizers: April 1, 2010 Issue of Abstracts: To be announced For consideration of contributed papers in Special Ses- sions: To be announced Deadlines For abstracts: To be announced For organizers: April 1, 2012 For consideration of contributed papers in Special Ses- sions: To be announced Boston, For abstracts: To be announced Massachusetts Baltimore, Maryland John B. Hynes Veterans Memorial Conven- Baltimore Convention Center tion Center, Boston Marriott Hotel, and Boston Sheraton Hotel January 15–18, 2014, Wednesday – Saturday Joint Mathematics Meetings, including the 120th Anual January 4–7, 2012 Meeting of the AMS, 97th Annual Meeting of the Math- Wednesday – Saturday ematical Association of America, annual meetings of the Joint Mathematics Meetings, including the 118th Annual Association for Women in Mathematics (AWM) and the Meeting of the AMS, 95th Annual Meeting of the Math- National Association of Mathematicians (NAM), and the ematical Association of America, annual meetings of the winter meeting of the Association for Symbolic Logic, with Association for Women in Mathematics (AWM) and the sessions contributed by the Society for Industrial and Ap- National Association of Mathematicians (NAM), and the plied Mathematics (SIAM). winter meeting of the Association for Symbolic Logic (ASL), Associate secretary: Matthew Miller with sessions contributed by the Society for Industrial and Announcement issue of Notices: To be announced Applied Mathematics (SIAM). Program first available on AMS website: To be an- Associate secretary: Michel L. Lapidus nounced Announcement issue of Notices: October 2011 Program issue of electronic Notices: To be announced Program first available on AMS website: November 1, Issue of Abstracts: To be announced 2011 Program issue of electronic Notices: January 2012 Deadlines Issue of Abstracts: Volume 33, Issue 1 For organizers: April 1, 2013 For consideration of contributed papers in Special Ses- Deadlines sions: To be announced For organizers: April 1, 2011 For abstracts: To be announced For consideration of contributed papers in Special Ses- sions: To be announced For abstracts: To be announced San Diego, California San Diego Convention Center and San Diego Marriott Hotel and Marina January 9–12, 2013 Wednesday – Saturday Joint Mathematics Meetings, including the 119th Annual Meeting of the AMS, 96th Annual Meeting of the Math- ematical Association of America, annual meetings of the Association for Women in Mathematics (AWM) and the National Association of Mathematicians (NAM), and the winter meeting of the Association for Symbolic Logic (ASL), with sessions contributed by the Society for Industrial and Applied Mathematics (SIAM). Associate secretary: Lesley M. Sibner Announcement issue of Notices: To be announced

1258

Program at a Glance

This document provides a thumbnail sketch of all scientific and social events so you can easily see which events may overlap and better plan your time.

Friday, January 4

8:00 a.m.– 5:00 p.m. AMS Short Course on Applications of Knot Theory (Part I) 8:00 a.m.– 5:00 p.m. MAA Short Course on Combinatorics: Past, Present, and Future (Part I)

Saturday, January 5

8:00 a.m.– 6:00 p.m. MAA Board of Governors 9:00 a.m.– 5:00 p.m. AMS Short Course on Applications of Knot Theory (Part II) 9:00 a.m.– 5:00 p.m. MAA Short Course on Combinatorics: Past, Present, and Future (Part II) 1:30 p.m.– 10:00 p.m. AMS Council 3:00 p.m.– 7:00 p.m. Joint Meetings Registration, Exhibit Hall B, San Diego Convention Center

Sunday, January 6

7:30 a.m.– 4:00 p.m. Joint Meetings Registration, Exhibit Hall B, San Diego Convention Center 7:00 a.m.– 7:50 a.m. Association for Christians in the Mathematical Sciences Nondenominational Worship Service 8:00 a.m.– 10:50 a.m. AMS-MAA SPECIAL SESSION ON THE SCHOLARSHIP OF TEACHING AND LEARNING IN MATHEMATICS, I

AMS-SIAM SPECIAL SESSIONS 8:00 a.m.– 10:50 a.m. Asymptotic Methods in Analysis with Applications, I 8:00 a.m.– 10:50 a.m. Environmental Mathematics: Some Mathematical Problems on Climate Change and Geophysical Fluid Dynamics, I 8:00 a.m.– 10:50 a.m. AMS-ASL Special Session on Set Theory and Banach Spaces, I 8:00 a.m.– 10:50 a.m. AMS-AWM Special Session on Zeta Functions of Graphs, Ramanujan Graphs, and Related Topics, I

AMS SPECIAL SESSIONS 8:00 a.m.– 10:50 a.m. Automorphic Forms and Related Topics, I 8:00 a.m.– 10:50 a.m. Recent Advances in Mathematical Biology, Ecology, and Epidemiology, I 8:00 a.m.– 10:50 a.m. Progress in Commutative Algebra, I 8:00 a.m.– 10:50 a.m. The Mathematics of Information and Knowledge, I 8:00 a.m.– 10:50 a.m. Hyperbolic Dynamical Systems, I 8:00 a.m.– 10:50 a.m. Interactions Between Noncommutative Algebra and Algebraic Geometry, I 8:00 a.m.– 10:50 a.m. Algebraic Topology, I 8:00 a.m.– 10:50 a.m. Groups, Representations, and Character Theory, I

1260 Notices of the AMS Volume 54, Number 9 Joint Meetings Advance Registration/Housing Form Note: Write your name as you would like it to appear on your badge (no titles, please). Badges and programs can only be mailed to home addresses. If you would like your registration materials mailed to you on December 13, please register by November 15, provide your home address, and check this box: I want my materials mailed to the following address on 12/13/07. I do not want my materials mailed. I will pick them up onsite.

Name

Mailing Address

Membership Telephone: Fax: ¢ all that apply. First column is eligible for In case of emergency (for you) at the meeting, call: Day #: Evening #: member registration fee ❏ AMS ❏ ASA Email Address ❏ MAA ❏ AWM Affiliation for name badge ❏ ASL ❏ NAM ❏ ❏ Nonmathematician guest badge name (please note charge below) CMS YMN ❏ SIAM Acknowledgment of this registration will be sent to the email address listed, unless you check this box: Send by U.S. Mail Registration Fees Payment

Joint Meetings by Dec 14 at mtg Subtotal Registration & Event Total (total from column on left) $ ❏ Member AMS, ASL, CMS, MAA, SIAM US $214 US $279 ❏ Nonmember US $332 US $431 Hotel Deposit (only if paying by check) $ ❏ Graduate Student US $ 44 US $ 54 ❏ Undergraduate Student US $ 23 US $ 29 Total Amount To Be Paid $ ❏ High School Student US $ 5 US $ 10 (Note: A US $5 processing fee will be charged for each returned check or ❏ Unemployed US $ 43 US $ 53 invalid credit card. Debit cards are not accepted.) ❏ Temporarily Employed US $172 US $200 Method of Payment ❏ Developing Countries Special Rate US $ 43 US $ 53 ❏ Check. Make checks payable to the AMS. Checks drawn on foreign banks ❏ Emeritus Member of AMS or MAA US $ 43 US $ 53 must be in equivalent foreign currency at current exchange rates. ❏ High School Teacher US $ 43 US $ 53 ❏ Credit Card. VISA, MasterCard, AMEX, Discover (no others accepted) ❏ Librarian US $ 43 US $ 53 ❏ Nonmathematician Guest US $ 15 US $ 15 Card number: $ Exp. date: Zipcode of credit card billing address: AMS Short Course: Applications of Knot Theory (1/4–1/5) ❏ Member of AMS or MAA US $ 94 US $125 Signature: ❏ Nonmember US $125 US $155 ❏ Student, Unemployed, Emeritus US $ 42 US $ 63 Name on card: $ ❏ MAA Short Course: Combinatorics: Past, Present, Future. (1/4–1/5) Purchase order # (please enclose copy) ❏ Member of MAA or AMS US $125 US $140 ❏ Nonmember US $175 US $190 Other Information ❏ Student, Unemployed, Emeritus US $ 50 US $ 60 Mathematical Reviews field of interest # $ MAA Minicourses (see listing in text) How did you hear about this meeting? Check one:❏ Colleague(s) ❏ Notices I would like to attend: ❏ One Minicourse ❏ Two Minicourses ❏ Focus ❏ Internet Please enroll me in MAA Minicourse(s) #______and/or #______❏ This is my first Joint Mathematics Meeting. In order of preference, my alternatives are: #______and/or #______❏ I am a mathematics department chair. Price: US $60 for each minicourse. ❏ For planning purposes for the MAA Two-year College Reception, please (For more than 2 minicourses, call or email the MMSB.) $ check if you are a faculty member at a two-year college. Employment Center ❏ I would like to receive promotions for future JMM meetings. Applicant résumé forms and employer job listing forms will be ❏ Please ¢Ÿthis box if you have a disability requiring special services. on the AMS website at www.ams.org/emp-reg/. ❏ Please do not include my name on any promotional mailing list. Employer—First Table US $245 US $325 ❏ Computer-scheduled ❏ Self-scheduled ❏ Combination Interview Mail to: Employer— Each Additional Table US $ 95 US $125 ❏ Computer-scheduled ❏ Self-scheduled ❏ Combination Interview Mathematics Meetings Service Bureau (MMSB) ❏ Employer—Posting Job Description Only US $ 50 N/A P. O. Box 6887 ❏ Applicant (all services) US $ 44 US $ 82 Providence, RI 02940-6887 Fax: 401-455-4004 ❏ Applicant (Winter List & Message Ctr only) US $ 22 US $ 22 Questions/changes call: 401-455-4143 or 1-800-321-4267 x4143; [email protected] $ Events with Tickets Deadlines Please register by the following dates for: MER Banquet (1/7) US $50.00 #____Regular #____Veg #____Kosher Résumés/job descriptions printed in the Winter Lists Oct. 24, 2007 NAM Banquet (1/8) US $49.00 #____Regular #____Veg #____Kosher To be eligible for the room lottery and the raffle: Oct. 31, 2007 AMS Banquet (1/9) US $52.00 #____Regular #____Veg #____Kosher For housing reservations, badges/programs mailed: Nov. 15, 2007 $ For housing changes/cancellations through MMSB: Dec. 7, 2007 Other Events For advance registration for the Joint Meetings, Employment ❏ AMS Workshop on Grant Writing (1/6) (no charge) Center, Short Courses, MAA Minicourses, & Tickets: Dec. 14, 2007 ❏ Graduate Student/First Time Attendee Reception (1/6) (no charge) For 50% refund on banquets, cancel by: Dec. 21, 2007*

For 50% refund on advance registration, Minicourses & Total for Registrations and Events $ Short Courses, cancel by: Dec. 28, 2007* Registration for the Joint Meetings is not required for the Short Courses, *no refunds after this date but it is required for the Minicourses and the Employment Center San Diego Joint Meetings Hotel Reservations

To ensure accurate assignments, please rank hotels in order of preference by writing 1, 2, 3, etc., in the column on the left and by circling the requested room type and rate. If the rate or the hotel requested is no longer available, you will be assigned a room at a ranked or unranked hotel at a comparable rate. Participants are urged to call the hotels directly for details on suite configurations, sizes, and availability; however, suite reservations can be made only through the MMSB to receive the convention rates listed. Reservations at the following hotels must be made through the MMSB to receive the convention rates listed. Reservations made directly with the hotels may be changed to a higher rate. All rates are subject to a 10.6% sales tax. Guarantee requirements: First night deposit by check (add to payment on reverse of form) or a credit card guarantee. ❏ Deposit enclosed (see front of form) ❏ Hold with my credit card Card Number Exp. Date Signature

Date and Time of Arrival Date and Time of Departure

Name of Other Room Occupant Arrival Date Departure Date Child (give age(s)

Order Hotel Single Double Double Triple Triple Triple - king Quad Quad Suites of choice 1 bed 2 beds 2 beds 2 beds w/cot or queen w/cot 2 beds 2 beds w/cot Starting rates San Diego Marriott Hotel & Marina (hqtrs)

Cityview US $172 US $172 US $172 US $192 US $192 US $192 US $212 US $212 N/A Bayview US $192 US $192 US $192 US $212 US $212 US $212 US $232 US $232 US $685 Student US $138 US $138 US $138 US $158 US $158 US $158 US $178 US $178 N/A Horton Grand Hotel US $155 US $175 US $195 US $155 US $155 (very limited) (very limited) N/A N/A (very limited) N/A US $215 Student US $145 US $145 N/A N/A N/A N/A N/A N/A N/A Hilton San Diego Gaslamp Quarter US $150 US $150 US $150 US $170 N/A US $190 US $190 N/A US $489 Student US $140 US $140 US $140 US $160 N/A US $180 US $180 N/A N/A Embassy Suites-Cityview Suites No rollaways; have No rollaways; have US $149 US $149 US $149 US $169 sleeper sofa sleeper sofa US $189 N/A all suites Bayview Suites No rollaways; have No rollaways; have US $169 US $169 US $169 US $189 sleeper sofa sleeper sofa US $209 N/A all suites Student Suites No rollaways; have No rollaways; have US $135 US $135 US $135 US $145 sleeper sofa sleeper sofa US $155 N/A all suites Omni San Diego Jr. Suite: US $399; US $140 US $140 US $140 US $160 N/A US $185 US $180 N/A 1BR US $499 Student US $125 US $125 US $125 US $145 N/A US $170 US $165 N/A N/A Holiday Inn on the Bay-Cityview US $135 US $135 US $135 US $150 N/A US $160 US $165 N/A N/A Bayview US $165 US $165 US $165 US $180 N/A US $190 US $195 N/A US $338 Student US $125 US $125 US $125 US $140 N/A US $150 US $155 N/A N/A Holiday Inn Express US $129 US $129 US $129 US $144 N/A N/A US $159 N/A US $239 Student US $119 US $119 US $119 US $134 N/A N/A US $149 N/A N/A Courtyard Marriott Downtown US $109 US $109 US $109 US $119 N/A King only-US $119 US $129 N/A US $169 Rodeway Inn and Suites US $91 US $91 US $91 US $101 $121 US $121 US $111 US $131 N/A 500 West Hotel US $49 N/A N/A N/A N/A N/A N/A N/A N/A

Special Housing Requests:. Email confirmations (no paper) will be sent by the Hilton, Embassy Suites, Holiday Inns, Horton, Marriott (hqtrs), ❏ I have disabilities as defined by the ADA that require a sleeping room that is accessible to the Omni & Rodeway Inn. Please provide your email address: physically challenged. My needs are: If you are not making a reservation, please check off one of the following: ❏ Other requests: ❏ I plan to make a reservation at a later date. ❏ ❏ I am a member of a hotel frequent-travel club and would like to receive appropriate credit. I will be making my own reservations at a hotel not listed. Name of hotel: ❏ The hotel chain and card number are: I live in the area or will be staying privately with family or friends. ❏ I plan to share a room with , who is making the reservations. Meetings and Conferences of the AMS

Associate Secretaries of the AMS 249), Chicago, IL 60607-7045; e-mail: [email protected]; Western Section: Michel L. Lapidus, Department of Math- telephone: 312-996-3041. ematics, University of California, Surge Bldg., Riverside, CA Eastern Section: Lesley M. Sibner, Department of Math- 92521-0135; e-mail: [email protected]; telephone: ematics, Polytechnic University, Brooklyn, NY 11201-2990; 951-827-5910. e-mail: [email protected]; telephone: 718-260-3505. Central Section: Susan J. Friedlander, Department of Math- Southeastern Section: Matthew Miller, Department of Math- ematics, University of Illinois at Chicago, 851 S. Morgan (M/C ematics, University of South Carolina, Columbia, SC 29208-0001, e-mail: [email protected]; telephone: 803-777-3690.

The Meetings and Conferences section of the Notices April 25–26 San Francisco, California p. 1256 gives information on all AMS meetings and conferences Oct. 16–18 Waco, Texas p. 1256 approved by press time for this issue. Please refer to the page Oct. 30–Nov. 1 Boca Raton, Florida p. 1257 numbers cited in the table of contents on this page for more Nov. 7–8 Riverside, California p. 1257 detailed information on each event. Invited Speakers and Special Sessions are listed as soon as they are approved by the cognizant program committee; the codes listed are needed 2010 for electronic abstract submission. For some meetings the January 6–9 San Francisco, California p. 1257 list may be incomplete. Information in this issue may be Annual Meeting dated. Up-to-date meeting and conference information can March 27–29 Lexington, Kentucky p. 1257 be found at www.ams.org/meetings/. 2011 January 5–8 New Orleans, Louisiana p. 1257 Meetings: Annual Meeting 2007 2012 October 5–6 Chicago, Illinois p. 1221 January 4–7 Boston, Massachusetts p. 1258 October 6–7 New Brunswick, New Jersey p. 1222 Annual Meeting October 13–14 Albuquerque, New Mexico p. 1223 2013 November 3–4 Murfreesboro, Tennessee p. 1223 January 9–12 San Diego, California p. 1258 December 12–15 Wellington, New Zealand p. 1224 Annual Meeting 2008 2014 January 6–9 San Diego, California p. 1225 January 15–18 Baltimore, Maryland p. 1258 Annual Meeting Annual Meeting March 22–23 New York, New York p. 1251 March 28–30 Baton Rouge, Louisiana p. 1252 Important Information Regarding AMS Meetings April 4–6 Bloomington, Indiana p. 1252 Potential organizers, speakers, and hosts should refer to May 3–4 Claremont, California p.1253 page 78 in the the January 2007 issue of the Notices for gen- June 4–7 Rio de Janeiro, Brazil p. 1253 eral information regarding participation in AMS meetings and October 4–5 Vancouver, Canada p. 1254 conferences. October 11–12 Middletown, Connecticut p. 1254 October 17–19 Kalamazoo, Michigan p. 1254 Abstracts October 24–26 Huntsville, Alabama p. 1255 Speakers should submit abstracts on the easy-to-use interac- December 17–21 Shanghai, People’s tive Web form. No knowledge of is necessary to submit Republic of China p. 1255 an electronic form, although those who use may submit abstracts with such coding, and all math displays and simi- larily coded material (such as accent marks in text) must 2009 be typeset in . Visit http://www.ams.org/cgi-bin/ January 7–10 Washington, DC p. 1255 abstracts/abstract.pl. Questions about abstracts may be Annual Meeting sent to [email protected]. Close attention should be paid to March 27–29 Urbana, Illinois p. 1256 specified deadlines in this issue. Unfortunately, late abstracts April 4–5 Raleigh, North Carolina p. 1256 cannot be accommodated.

October 2007 Notices of the AMS 1271 Essential New and Forthcoming MATH Titles!

Now in Paperback! Elements of the Heights in Representation Theory Diophantine Geometry of Associative Algebras Enrico Bombieri and Daniel Simson and Walter Gubler Andrzej Skowro´nski New Mathematical Monographs London Mathematical Society $70.00: Pb: 978-0-521-71229-3: 655 pp. Student Texts

Volume 2: Tubes and Concealed Algebras of Euclidean type $125.00: Hb: 978-0-521-83610-4: 320 pp $55.00: Pb: 978-0-521-54420-0 Rigid Volume 3: Representation-infinite Cohomology Tilted Algebras Bernard Le Stum $130.00: Hb: 978-0-521-88218-7: 464 pp. Cambridge Tracts in Mathematics $58.00: Pb: 978-0-521-70876-0 $95.00: Hb: 978-0-521-87524-0: 334 pp.

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The Classical Field Outer Circles Structural Features of the Real and An Introduction to Rational Numbers Hyperbolic 3-Manifolds H. Salzmann, T. Grundhöfer, H. Hähl, A. Marden and R. Löwen Encyclopedia of Mathematics and its $75.00: Hb: 978-0-521-83974-7: 446 pp. Applications $115.00: Hb: 978-0-521-86516-6: 416 pp.

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New and Noteworthy of the American Mathematical Society Piecewise-smooth Dynamical Lie Sphere Geometry An Introduction to Bayesian Volume 54, Number 9 2ND October 2007 Systems With Applications to EDITION Scientifi c Computing Theory and Applications Submanifolds Ten Lectures on Subjective Computing M. di Bernardo , University of Bristol, UK; University T. E. Cecil , College of the E. Somersalo , Helsinki University of Technology, of Naples Federico II, Italy; C. Budd , University of Holy Cross, Worcester, MA, USA Helsinki, Finland; D. Calvetti , Case Western Reserve Bath, UK; A. Champneys , University of Bristol, UK; This book provides a modern treatment of Lie’s University, Cleveland, OH, USA P. Kowalczyk , University of Bristol, UK; University of geometry of spheres, its applications and the study This book has been written for undergraduate and Exeter, UK of Euclidean space. It begins with Lie’s construction graduate students in various areas of mathematics This book presents a coherent framework for of the space of spheres, including the fundamental and its applications. It is for students who are understanding the dynamics of piecewise-smooth notions of oriented contact, parabolic pencils of willing to get acquainted with Bayesian approach to

and hybrid systems. An informal introduction spheres and Lie sphere transformation. The link with computational science but not necessarily to go expounds the ubiquity of such models via Euclidean submanifold theory is established via the through the full immersion into the statistical numerous. The results are presented in an informal Legendre map. This provides a powerful framework analysis. It has also been written for researchers style, and illustrated with many examples. The book for the study of submanifolds, especially those working in areas where mathematical and statistical The Character is aimed at a wide audience of applied mathemati- characterized by restrictions on their curvature modeling are of central importance, such as biology cians, engineers and scientists at the beginning spheres. and engineering. Table for E postgraduate level. Almost no mathematical This new edition contains revised sections on taut 8 background is assumed other than basic calculus submanifolds, compact proper Dupin submanifolds, 2007. Approx. 215 p. (Surveys and Tutorials in the and algebra. reducible Dupin submanifolds, Lie frames and frame Applied Mathematical Sciences, Volume 2) page 1122 reductions. Completely new material on isopara- Softcover 2007. Approx. 510 p. 234 illus. (Applied Mathemat- metric hyperspaces in spheres, Dupin hyperspaces ISBN 978-0-387-73393-7  $39.95 ical Sciences, Volume 163) Hardcover with three and four principle curvatures is also ISBN 978-1-84628-039-9  $99.00 included. An Introduction to Manifolds Paul Halmos: L. W. Tu , Tufts University, Medford, MA, USA The Riemann Hypothesis 2nd ed. 2008. Approx. 305 p. 14 illus. (Universitext) In His Own Words Softcover This book introduces the fundamental theory of A Resource for the Affi cionado and Virtuoso ISBN 978-0-387-74655-5  approx. $49.95 manifolds in a readable but rigorous manner. In Part page 1136 Alike I the theory of diff erential forms on Rn is presented P. Borwein , S. Choi , B. Rooney , Simon Fraser Semiparallel as a natural bridge between calculus and the theory University, Burnaby, BC, Canada; A. Weirathmueller , Submanifolds in of manifolds. Once this intuitive foundation is laid, University of Western Ontario, London, ON, Canada manifolds are defi ned in Part II, and several San Diego Meeting Space Forms examples considered. In Parts III and IV tangent This book presents the Riemann Hypothesis, spaces are introduced, along with Lie groups and connected problems, and a taste of the body of Ü. Lumiste , University of page 1225 Lie algebras. Throughout, the author emphasizes theory developed towards its solution. It is targeted Tartu, Estonia the connection between tangent spaces and the at the educated non-expert. Almost all the material This book off ers a familiar methods of linear approximation from is accessible to any senior mathematics student, comprehensive survey to calculus. With this background in place, calculus on and much is accessible to anyone with some date of the theory of manifolds is studied, and important topological university mathematics. The appendices include a semiparallel submani- invariants, such as the de Rham cohomology, are selection of original papers that encompass the folds. Introduced in 1985, semiparallel submani- computed. most important milestones in the evolution of folds have emerged as an important area of Assuming only a year of real analysis and a semester research within diff erential geometry and topology.

theory connected to the Riemann Hypothesis. The Volume 54, Number 9, Pages 1113–1272, October 2007 of abstract algebra at the undergraduate level, and appendices also include some authoritative Lumiste begins with the necessary background on: with all necessary point-set topology summarized expository papers. These are the “expert witnesses” symmetric and semisymmetric Riemannian in an appendix, this book introduces manifolds at a whose insight into this fi eld is both invaluable and manifolds, smooth manifolds in space forms, and level suitable for advanced undergraduates and irreplaceable. parallel submanifolds. Semiparallel submanifolds beginning graduate students. are introduced in Chapter 4, where characteriza- 2007. Approx. 590 p. 25 illus. (CMS Books in tions of their class and several subclasses are given. 2007. Approx. 390 p. 104 illus. (Universitext) Mathematics) Hardcover In later chapters Lumiste introduces the concept of Softcover ISBN 978-0-387-72125-5  approx. $79.95 main symmetric orbit and presents all known ISBN 978-0-387-48098-5  approx. $49.95 results concerning umbilic-like main symmetric orbits. Semiparallel Submanifolds in Space Forms will appeal to both researchers and graduate students.

2008. Approx. 325 p. Hardcover ISBN 978-0-387-49911-6  approx. $79.95

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