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Weitzner, H.-T. Yau, P. Zhang. John Toth Forthcoming Articles Takeshi Tsuji • On the Discrete Group Analysis for Solving Some Classe_s David Vogan of Emden-Fowler Equations, M. Hadizadeh, A . R. Zokayi, and P. Darania Dan Voiculescu Using G1 Ball-Spline Curves, • Space Curves Approximation Andrei Zelevinsky Germain E. Randriambelosoa Madej Zworski Hindawi Publishing Corporation, 410 Park Avenue, 15th Floor, #287 pmb, New York, NY 10022, USA; HINDAWI Fax: 1-866-446-3294 (USA, toll-free); URL: http://hindawi.com; E-mail: [email protected] NEW f6 FORTHCOMING from Birkhiiuser Variational Methods D·Modules, Perverse Geometric Problems on in Shape Optimization Sheaves, and Maxima and Minima Problems Representation Theory TITU ANDREESCU,American Mathematics Competitions, Lincoln, NE; OLEG MUSKAROV, Institute for Mathematics, DORIN BUCUR, Universite de Metz, France and RYOSHI HOTTA, Okayama University of Science, Japan; Bulgarian Academy of Sciences, Sofia, Bulgaria; and GIUSEPPE BUTTAZZO, Universita di Pisa, Italy KIYOSHI TAKEUCHI, University ofTsukuba, Japan; and LUCHEZAR STOYANOV, University of Western Australia, TOSHIYUKI TANISAKI, Osaka City University, Japan Crawley, WA The study of shape optimization problems involves a wide (Translated by K Takeuchi) area of academic research and applications to the real This carefully developed problem book takes a unique, world. 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Reflecting the authors' experience as teachers and ISBN 0-8176-4359-l/$1 09.00 Significant topics that have emerged as studies in their Olympiad coaches, this volume is ideal for use at the own right include a treatment of the theory of holonom junior and senior undergraduate level, as well as for Cornerstones of Geometric ic D-modules, perverse sheaves, the Riemann-Hilbert enrichment programs and Olympiad training for correspondence, Hodge modules, and Kazhdan-Lusztig advanced high school students. The book will also Function Theory polynomials. To further aid the reader, appendices are appeal to graduate students, professional mathemati Explorations in Complex Analysis provided as reviews for the theory of derived categories cians, and puzzle enthusiasts alike. and algebraic varieties. STEVEN G. 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The book's New to the second edition: Material on Diophantine MICHAEL DEMUTH, Technische Universittit Clausthal, careful development of the topic and its emphasis on approximation of complex dimensions of nonlattice Germany and MAD DALY KRISHNA, Institute of Mathematical mathematics and physics make it useful for graduate strings • Periodic orbits of self-similar flows • Sciences, Chennat; India students and researchers in both disciplines. Discussion of connections between fractality and self The spectral theory of Schriidinger operators, in 2005/304 PP./HARDCOVER similarity in the non-lattice case. particular those with random potentials, continues to be ISBN 0-8176-3339-1/$79.95 2005/APPROX. 320 PP,30 ILLUS./HARDCOVER a very active field of research. This work focuses on ISBN 0-8176-3209-3/$64.95 various known criteria in the spectral theory of selfad joint operators in order to identify the spectrum and its Frobenius Splitting components a Ia Lebesgue decomposition. It provides a Methods in Geometry and Homogenization of Partial well-developed exposition of criteria that are especially Representation Theory Differential Equations useful in determining the spectra of deterministic and VLADIMIR MARCHENKO and EVGUENI KHRUSLOV, both, MICHEL BRION, Universite Grenoble 1- CNRS, St.-Martin random Schrodinger operators occurring in quantum B. Verkin Institute for Low Temperature Physics and Engineering, d'Heres, France and SHRAWAN KUMAR, University of North theory. Coverage also examines a series of applications Kharkov, Ukraine to show point spectrum and continuous spectrum in Carolina, Chapel Hill, NC This work, treating homogenization problems describing some models of random operators. The theory of Frobenius splittings has made a significant impact in the study of the geometry of flag varieties and various physical processes in micro-inhomogeneous 2005/2BB PP./HARDCOVER media, will benefit applied mathematicians, advanced ISBN O-B176-4366-4/$115.00 representation theory. This work systematically develops the theory and covers all its major developments. level graduate students, physicists, engineers, and specialists in mechanics. 2005/254 PP./HARDCOVER/ISBN 0-8176-4191-2/$69.95 2005/APPROX. 450 PP./HARDCOVER ISBN 0-8176-4351-6/$189.00 CALL: 1-800-777-4643 • FAX: (201) 348-4505 E-MAIL: [email protected] • www.birkhauser.com Please mention promotion #Y968l to guarantee listed prices, valid until 10/31 /05. Birkhiiuser $ Prices are valid in the Americas only. For price and ordering information outside the Americas, Boston · Basel · Berlin please contact Birkhauser Verlag AG by E-mail: [email protected] 12/04 Promotion #Y9683 Notices December 2004 of the American Mathematical Society Feature Articles 1320 Olga Alexandrovna Ladyzhenskaya (1922-2004) Susan Friedlander, Peter Lax, Cathleen Morawetz, Louis Nirenberg, Gregory Seregin, Nina Ural'tseva, and Mark Vishik The authors recall the life and mathematical legacy of the inf1uential Russian mathematician. 0.8 0.4 1 336 Levy Processes-From Probability to Finance - OA and Quantum Groups 0.8 David Applebaum 1.2 Stochastic processes are families of random variables; Levy processes are families indexed by the positive reals which are independent with stationary increments and are stochastically continuous. The author reviews the basic proper ties of Levy processes and considers some of their applications. Communications Commentary 1332 Double Cusp Group 1 31 7 Opinion David]. Wright 1 318 Letters to the Editor 1350 WHAT IS ... aFlip? 1 3 52 Strange Curves, Counting Rabbits, Alessio Corti and Other Mathematical 1355 Mathematicians' Group to Provide Explorations- A Bobk Review Advice on Math Standards Reviewed by Harold R. Parks Allyn jackson 1357 Deligne Receives 2004 BalzanPrize Notices Departments of the American Mathematical Society Mathematics People ...... 1359 Bjorken and Callan Awarded 2004 Dirac Medals, PECASE EDITOR: Andy Magid Awards Announced, Prizes of the Academie des Sciences, ASSOCIATE EDITORS: NDSEG Fellowships Awarded, AWM Essay Contest Winners Susanne C. Brenner, Bill Casselman (Graphics Editor), Announced, National High School Calculus Student Award, Pi Robert j. Daverman, Nathaniel Dean, Rick Durrett, Mu Epsilon Student Paper Presentation Awards. Susan Friedlander, Robion Kirby, Steven G. Krantz, Elliott H. Lieb, Mark Saul, Karen E. Smith, Audrey Terras, Lisa Traynor Mathematics Opportunities ...... 1361 SENIOR WRITER and DEPUTY EDITOR: NDSEG Fellowships, EDGE Summer Program, CMI Liftoff Allyn Jackson Program for Summer 2005, Call for Nominations for Waterman MANAGING EDITOR: Sandra Frost Award, News from the Mittag-Leffler Institute, News from the CONTRIBUTING WRITER: Elaine Kehoe Fields Institute, News from the IMA , AMS Mentoring Workshop, PRODUCTION ASSISTANT: Muriel Toupin Newton Fellowship Program. PRODUCTION: Marcia Almeida, Kyle Antonevich, Stephen Moye, Lori Nero, Karen Ouellette, Donna Inside the AMS ...... 1365 Salter, Deborah Smith, Peter Sykes AMS Email Support for Frequently Asked Questions, Deaths of ADVERTISING SALES: Anne Newcomb AMS Members. SUBSCRIPTION INFORMATION: Subscription prices Reference and Book List 1367 for Volume 51 (2004) are $40llist; $32 1 institutional member; $241 individual member. 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[Notices of the American Mathematical Society is published From the monthly except bimonthly in june/july by the American Mathematical Society at 201 Charles Street, Providence, RJ AMS Secretary 02904-2294 USA, CST No . 12189 2046 RT****. Periodicals postage paid at Providence, RJ, and additional mailing offices. POSTMASTER: Send address change notices to Notices of the American Mathematical Society, P.O. Box 6248, Providence, Statistics on Women Mathematicians Compiled RI 02940-6248 USA. ] Publication here of the Society's street by the AMS ...... 1 3 72 address and the other information in brackets above is a tech nical requirement of the U.S. Postal Service. Tel: 401-455-4000, email: noti ces@ams. org. © Copyright 2004 by the American Mathematical Society. All rights reserved. Printed in the United States of America.The paper used in this jourm,tl is acid-free and falls within the guidelines established to ensure permanence and durability. Opinions expressed in signed No tices articles are those of the authors and do not necessarily reflect opinions of the editors or po li cies of the Ame rican Mathematical Society. Opinion Changing Teaching of Future Teachers K-12 students need at every grade level to be successful. One Algebra I spend more time dis Some years ago, one of us taught mathematics courses for fu noted, "even in Beginning of a fraction .. .it helps my stu ture elementary teachers much as he did other college math cussing the various meanings ematics courses-lecture, drill, and test. Connections to school dents gain a deeper understanding of something they felt they mathematics were not part of the course because they were had already 'learned."' Finally, participants told us they thought not part of his education and experience. After reading The students learned better after these changes. One said that for Mathematical Education of Teachers (MET), edited by Cathy the first time her students "were able to make the connection Kessel (lead editor), Judith Epstein, and Michael Keynes (CBMS between fractions, decimals, and percents without my mak Issues in Mathematics Education, vol. 11, AMS and MAA, 2001) ing it for them." Others cited differences in how students han and Liping Ma's Knowing and Teaching Elementary Mathe dled problems-both with respect to the explanations they pro matics: Teachers' Understanding of Fundamental Mathemat vided of their own reasoning and the representations they used ics in China and the United States (Lawrence Erlbaum Associ to construct their answers. On the latter, one noted, "units no ates, 1999) and while working with mathematics educators on longer disappear at the beginning of the work only to mys the Mathematical Association of America's Preparing Mathe teriously reappear as part of the solution." maticians to Educate Teachers (PMET) project, he is again Changing teaching of future teachers canimprove K- 12 teaching these courses- but in a very different way. mathematics, and early evidence suggests the PMET workshops This conversion illustrates the goal of PMET and like are effectively inducing mathematics faculty to make appro minded efforts to help mathematics faculty improve the math priate changes. But few mathematicians from research uni ematical preparation of future teachers. Workshops, mini versities have so far participated in these workshops. In ad courses, and conferences for college and university faculty are dition to the fact that their presence would enrich the PMET's main vehicles for accomplishing this goal. During the experience, we believe there are several reasons why more past three years, thirteen PMET workshops have been held with should do so. over 300 participants. Nine new PMET workshops are sched • Research institutions prepare future teachers, and research uled for summer 2005, including two at historically black in faculty should be involved in the development and teach stitutions, one at the Southwest Indian Polytechnic Institute, ing of courses for future teachers. In the words of the MET and one at Park City Mathematics Institute. One initiative Report, "All mathematicians should be concerned about similar to PMET workshops is the Michigan-Georgia NSF Cen teacher education, and all have a role to play in the edu ter for Proficiency in Teaching Mathematics summer institutes. cation of teachers." Are these efforts improving the mathematical education • The mathematics required for teaching, in the words of MET, of teachers? Preliminary evidence suggests they are. Aimed is "quite different from that required by students pursu at changing college faculty understanding and behavior, PMET ing other mathematics-related professions." Most of us learning than are pro is farther removed from improving K-12 know some bits and pieces of the mathematics of K-12 at K-12 teachers. So an ultimate evaluation of jects directed teaching, but this mathematics needs more structure if we impact will require considerable time. But as an intermediate are to incorporate it coherently into college courses. step, we contacted participants in the 2003 workshops to see • Research mathematicians wield tremendous influence on if they have changed how they teach future teachers. future college and university faculty members, and the Certainly, they overwhelmingly say they have. Ninety-five of research faculty influence all col percent of those contacted report more emphasis on group priorities and attitudes work and collaborative approaches. Eighty-eight percent re lege and university faculty. port requiring students to explain reasoning when solving • Mathematics education is a major public policy issue, and problems- for example, through writing in and out of class, mathematicians should be positioned to steer policy toward asking for oral explanations in class, and group discussion. improving education. Research mathematicians can help And the changes were apparent to students as well. As one add unity and credibility to this case for improvement. participant reported, "after a couple of days .. .I had one stu In the September 2004 Notices, Lynn Arthur Steen wrote dent ask me if we were only going to do 'word problems' ... an that to contribute to K- 12 education "mathematicians should other asked if we were ever going to do 'a page full of calcu focus first on the mathematical education of teachers." Were lations' ... this seems to be unlike any math course they have inforce his call with some encouraging reports of changes being ever had before, given their previous beliefs of what it was made through PMET, noting, as he did, that everybody in the like to 'do math."' mathematics community needs to be involved. Workshop participants also told us they had changed how - Peter Ewell, National Center for Higher Education they teach particular mathematical concepts. These covered Management Systems (NCHEMS), PMET evaluator, a wide array of topics- from greater emphasis on the concept [email protected] of "the whole" in interpreting fractions, through materials for - Bernard Madison, University of Arkansas, teaching algebraic reasoning, to particular approaches to T co-director, bmadi son@uark. edu teaching topics in measurement and geometry. Others re PME ported they are much more aware of the need to instill in their students an understanding of the mathematical knowledge that DECEMBER 2004 NOTICES OF THE AMS 1317 letters to the Editor lim{l/n} exists and is 0. But the latter Underrepresentation conclusion requires independent ex In his article on doctoral degrees istence hypotheses about the pres earned by ethnic minorities, Herbert More on the Prisoner's Dilemma ence of 0 and the nature of its neigh Medina points out that "Blacks, His In his letter (August 2004, page 735) borhood system. Choosing defection panics/Latinos, Native Americans are commenting on Steven E. Landsburg's in the game contradicts none of Hof underrepresented in earning doctoral remark about the Prisoner's Dilemma stadter's hypotheses. The reasoning degrees in the mathematical sciences. ("Quantum game theory", April2004), is inconclusive, and rational choices That is, these ethnic groups do not Dr. Marcus perpetuates the fallacious are not based on inconclusive rea earn doctorates comparable to the inference of Douglas R. Hofstadter in soning. percentage of the population they his justly admired 1985 book Meta What the symmetry argument does comprise." Most of the article is con magical The mas. The general issue is accomplish is to demonstrate that ad cerned with various atterppts to try to what hypotheses assure socially de ditional hypotheses can consistently reduce if not eliminate this under sirable choices when individual be added to entail mutual coopera representation. The final section of choices are relatively penalized unless tion. What could such hypotheses be? the article begins, "Supposing that we all players choose to act for the social A pre-arranged agreement? That is aim to solve the underrepresentation good. Clear thinking about this is im safe, but more than is necessary. The by the year 2025." From the discus portant, since many crucial situations minimum is to assume, along with sion that follows it is clear that the resemble the Prisoner's Dilemma, no knowledge of the symmetry, a dispo problem will be "solved" when each of these groups is earning degrees at a tably the need to limit births as we sition to choose cooperation in a sit rate roughly proportional to its per near the carrying capacity of our uation where all know that mutual planet. centage of the population. cooperation will have a payoff in ex Before getting to the crux of the fal I agree strongly that it is desirable cess of any other. This, of course, is lacy, let me repair one obvious defi to try to provide conditions that might ciency of the argument. The hy just a restatement of the conclusion. increase the doctoral percentages of potheses that the players are rational Explicitly adopting such a hypothesis the study's underrepresented groups, and selfish are what we know about renders the whole question trivial. but I seriously question the way the them, but to impel a player to act, he Further, it is clearly a moral hypoth eventual goal is formulated. Do we must know this about the other, and esis, in the same category as selfish really want to make our objective "to then know that the other knows that ness, and not at all akin to rational each according to his/her population he knows, and so ad infinitum. This ity. percentage"? If this criterion is to be may be a little awkward to describe, Since the behavior of the players is applied uniformly, then we will have but there is no difficulty in annexing not determined by the hypotheses, it to worry about overrepresentation as this iterated hypothesis of mutual is clear that any claim that "Rational well as underrepresentation. I notice, complete knowledge (and Hofstadter selfish players always choose to de using the data provided with the ar essentially did so). These hypotheses fect" is also incorrect-rational self ticle, that the group Asian/Pac. Isl. is remain insufficient. ish players need not choose the Nash currently earning more than four Hofstadter weaves a magical spell equilibrium in every case. Such claims times as many doctorates as its pop about the theme that with symmetry as Landsburg's are epimathematical ulation would warrant. Should we selfish players will each cooperate as imprecise heuristics that provide a then hope that by 2025 the percent a rational choice. Ironically, it is the perspective to ease the assimilation of age of doctorates earned by this group symmetry that makes it easy to refute the mathematics and to suggest ap will be reduced by a factor of four? I this. A selfish player can rationally plications of it. In this role they do lit doubt that Professor Medina would be decide on cooperation only on the tle harm. It is when they are sepa in favor of such a resolution, but it's basis of an inference that the other rated from this role and exalted into an unfortunate theorem that if we are player will choose cooperation-the to eliminate underrepresentation we exaggerated claims that they are ob inference must precede the decision. will have to suppress overrepresen jectionable. Mathematicians cherish The symmetry guarantees that nei tation. (Unfortunately we can't be like ther gets the necessary precedence. rationality and elegant arguments, the students in the schools of Lake The argument never gets beyond the and imputing to rationality more than Woebegone who are all above aver magic to a valid conclusion. It is the it can deliver is sure to damage these age). finitary nature of logic that prevents values. I have seen the criterion of popu such a leap. lation proportionality applied in other A simple analogy may allay any re -H. E. Stone cases, notably that of gender, and I ob maining doubts. The valid part of the University of Texas at Dallas ject to it there for the same reasons. symmetry argument is like proving [email protected] The fact is, some groups in our soci that the tails of the sequence {1/n} be ety-whether cultural, ethnic, or even come arbitrarily small. Hofstadter's (Received August 18, 2004) religious-have put more emphasis conclusion is like the assertion that on mathematical achievement than 1318 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Letters to the Editor others. It seems to me that to try to Postings that are not removed then Review of A Handbook of level everyone by imposing the arbi provide solutions to students else Mathematical Discourse trary criterion of population per where before the fact. Steven G. Krantz's review of my book, centage would be a serious mistake. The first student also told me that A Handbook of Mathematical Dis he was also able to find many posted course, in the August 2004, issue of -David Gale solutions for our current discrete Notices of the American Mathematical UC Berkeley mathematics text at one site by Society shows that he misunderstood Googling a combination of the au the purpose of the book. Its focus is (Received August 26, 2004) thor's name and some other sugges on mathematical discourse, that is, tive words. the way math is communicated in Not everyone will agree that post speech and writing. It is not primar Homework and Google ing solutions on the Web nets out neg ily about math itself. For decades calculus texts included atively. We're supposed to be in the Students may deal dysfunctionally answers to their odd-numbered exer business of disseminating mathe with quantifiers, definitions, the use cises in an appendix; answers to the matical knowledge! All along, many of of English words such as if with mean even-numbered exercises were avail us have accepted solutions from stu ings different from those of ordinary able only in limited circulation in dents industrious enough to comb li discourse, and other aspects of math structor's answer manuals. This ped brary books. However, the excessive ematical discourse. Much of the book agogical arrangement was undercut convenience of the Web (copy and is devoted to discussing these diffi here in Chapel Hill a decade ago when paste!) could soon remove many culties, which inhibit understanding a teaching assistant put the answer nice/ classic problems from being el of many mathematical ideas. No at manual on reserve in the library: Not igible for graded homework assign tempt was made to cover all the im only did his 3 5 students receive access ments. If you are concerned about the portant specific mathematical con to solutions for all of their assigned potential effects of your actions on the cepts. even-numbered problems, but so did pedagogical approaches of fellow in The Handbook has entries about some of the 700-odd students in the structors (even if this does not affect certain ideas from linguistics, rhetoric, other 20-odd sections of that course your own teaching techniques), you cognition theory, and research in that semester (namely, those students may wish to consider posting your mathematical education and argues who happened upon the manual or solutions in a secure area requiring a that, if teachers and students are who learned about it from a friend). password for access. If this approach aware of these ideas from outside After I turned in my undergradu is not readily available, some low-tech mathematics, they will improve their ate group theory grades in May, one strategies could be considered: Avoid chances of communicating success student told me that he had been able including the name of the text's au fully. These ideas may not belong in to find solutions for some standard thor in your website. Do not include a book about math, but they do belong problems via Web searches when he the statement of the problem. Delib in a book about mathematical dis got completely stuck. Later I tried typ erately misspell the key words. (This course. ing the following into Google: could be fun: "Let f and g be infective As the introduction states, the Solution Prove that the composition functions ..."!) Remove your posting as book is incomplete in meeting its own of two injective functions is injective soon as possible. goals, never mind the goals Professor Some of the top ten hits gave so Some solutions will always be avail Krantz expected it to have. Much more lutions for related problems, but none able on the Web. Proofs/solutions of work in this field is necessary. included a solution for this problem. all standard statements/problems will Recently I reported this failed effort eventually appear on the Web, per -Charles Wells to the student while a friend of his haps in a central eBourbaki reposi Oberlin, OH was present. She opined that her peers tory. But in the meantime: If most in were far more adept at Googling than structors post their solutions below (Received September 1, 2004) faculty and suggested artfully placing the search engines' radars, this could quotes while using her favorite search lower the Googling success ratio suf engine. So I then typed ficiently so that the less industrious Solution "Prove that" "the compo students won't bother. sition of" "injective functions is" "in -Bob Proctor jective" University of North Carolina, into http: I jwww. dog pile. com. One Chapel Hill of the top five hits (which was not in North America) provided a solution to (Received September 1, 2004) this problem (in English). My brief so journs indicated that the instructors who posted solutions were providing them to their students after the fact (following a quiz or an assignment). DECEMBER 2004 NOTICES OF THE AMS 1319 Olga Alexandrovna Ladyzhenskaya (1922-2004) Susan Friedlander, Peter Lax, Cathleen Morawetz, Louis Nirenberg, Gregory Seregin, Nina Ural'tseva, and Mark Vishik Olga Alexandrovna La from uniqueness of solutions of PDE to convergence dyzhenskaya died in her of Fourier series and finite difference approxima sleep on January 12th, 2004, tion of solutions. She used functional analytic tech in St. Petersburg, Russia, at niques to treat nonlinear problems using Leray the age of eighty-one. She left Schauder degree theory and pioneered the theory a wonderful legacy for math of attractors for dissipative equations. Develop ematics in terms of her fun ing ideas of De Giorgi and Nash, Ladyzhenskaya and damental results connected her coauthors gave the complete answer to Hilbert's with partial differential equa nineteenth problem concerning the dependence tions and her "school" of stu of the regularity of the solution on the regularity dents, collaborators, and col of the data for a large class of second-order ellip leagues in Russia. In a life tic and parabolic PDE. She published more than 2 50 dedicated to mathematics articles and authored or coauthored seven mono she overcame personal graphs and textbooks. Her very influential book The tragedy arising from the cat Mathematical Theory of Viscous Incompressibl aclysmic events of twentieth e Flow, which was published in 1961, has become a century Russia to become one classic in the field. Her main mathematical of that country's leading "love" was the PDE of fluid dynamics, particularly mathematicians. Denied a the place as an undergraduate at Navier-Stokes equation. This equation has a long university, she was an exceptionally gifted young and glorious history but remains extremely chal girl, but one whose father disappeared in Stalin's lenging: for example, the issue of existence of phys gulag. She eventually became a leading member of ically reasonable solutions to the Navier-Stokes the Steklov Institute (POMI) and was elected to the equations in three dimensions was chosen as one Russian Academy of Science. Her mathematical of the seven millenium "million dollar" prize prob achievements were honored in many countries. lems of the Clay Mathematical Institute. (The CMI She was a foreign member of numerous acade website gives a description by Fefferman of the mies, including the Leopoldina, the oldest German prize problem.) The three-dimensional problem academy. Among other offices, she was president remains open to this day, although it was in the of the Mathematical Society of St. Petersburg and, 1950s that Ladyzhenskaya obtained the key result as such, a successor of Euler. of global unique solvability of the initial boundary problem for the two-dimensional Navier-Stokes Ladyzhenskaya made deep and important con equation. She continued to obtain influential results tributions to the whole spectrum of partial differ and to raise stimulating issues ential equations and worked on topics that ranged in fluid dynamics, even up to the days before her death. 1320 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Selected Honors of Olga Ladyzhenskaya This memorial article contains brief surveys of 1969 The State Prize of the USSR some of Ladyzhenskaya's significant mathematical 1985 Elected a foreign member of the Deutsche Akademie achievements by two of her collaborators in St. Pe Leopoldina tersburg, Gregory Seregin and Nina Ural'tseva. 1989 Elected a member of the Accademia Nazionale dei Lincei These are followed by "memories" of Olga Alexan 1990 Elected a full member of the Russian Academy of Science drovna by other distinguished mathematicians who 2002 Awarded the Great Gold Lomonosov M~dal of the Russian have known her and her work for many years, Academy namely Peter Lax, Cathleen Morawetz, Louis Niren 2002 Doctoris Honoris Causa, University of Bonn berg, and Mark Vishik. Olga Alexandrovna was a woman of great charm and beauty. We are very grateful to Tamara Rozhkovskaya for presenting some of the lovely photographs of Olga that appear in the two volumes in honor of the eightieth birthday of Ladyzhenskaya edited by Rozhkovskaya, who is a "mathematical grandchild" of Olga and editor and publisher of the International Mathematical Series in which these volumes appear. At the conclusion of her appreci ation article in the second of these two volumes, Nina Ural'tseva ( a "mathematical child" and close friend and collaborator of Olga) writes "In the Sci ence Museum in Boston there is an exhibition de voted to mathematics. The names of the most in fluential mathematicians of the 20th century are carved on a large marble desk ... and Olga La H. H. YpaJibQeBa dyzhenskaya is among them". -Susan Friedlander Left to right, Nina Ural'tseva, Olga Ladyzhenskaya, V. Smirnov. for them. The eminent mathematician V. Smirnov; the great pianist and professor of the Academy of Gregory Seregin and Nina Ural'tseva Music, N. Golubovskaja; the distinguished world Olga Alexandrovna Ladyzhenskaya passed away famous poets A. Akhmatova and ]. Brodsky; and quite unexpectedly on January 12 this year. She was the famous writer A. Solzhenitsyn are found among in good spirits two days before that. She had just them. sketched a paper on some computational aspects Her influence on twentieth century mathemat in hydrodynamics and planned to finish it in ics is highly valued by the world scientific com Florida. Olga was fond of sunlight; therefore, every munity. It was not only Olga's scientific results, winter, the darkest period in our St. Petersburg, she though truly deep and fundamental, but also her longed for the South .... In her last years she had personal integrity and energy that played an es serious problems with her eyes, and she suffered pecial role in her contribution to mathematics. enormously because of the winter darkness. She re Olga's focus in life was not limited to mathe sisted such problems by all means, for example, matics and science. She was deeply interested in using special pencils when writing. She was to leave arts and intellectual life in general. She loved ani for Florida on January 12. On the eve of January mals, was a passionate mushroom lover, and en 11 she went to rest before her long trip and did not joyed flowers. She was an enthusiastic traveler and wake up. God gave her an easy death. had the wonderful skill of a storyteller when shar Olga Ladyzhenskaya was a brilliant mathemati ing her impressions with friends. cian and an outstanding person who was admired There were few things that did not touch her; by distinguished scientists, writers, artists, and she reacted keenly to any injustice, to the misfor musicians, often becoming a source of inspiration tunes of others; and she helped lone and feeble peo ple. She took this very personally. Susan Friedlander, is professor of mathematics at the Uni versity of Illinois-Chicago. Her email address is She expressed openly her views on social mat [email protected]. ters, even in the years of the totalitarian political Gregory Seregin is professor of mathematics at the St. Pe regime, often neglecting her own safety. tersburg Department of the Steklov Institute. His email ad Olga grew up during very hard times in Russia. dress is seregi n@pdmi. ras. ru. She was born on March 7, 1922, in the tiny town Nina Ural'tseva is professor of mathematics at St. Peters of Kologriv in the north part of Russia. Her father, burg University, Russia. Her email address is ural tsev@ Alexander Ivanovich, taught mathematics in a high euclid.pdmi .ras.ru. school. Her mother, Anna Mikhailovna, kept house DECEMBER 2004 NOTICES OF THE AMS 1321 and looked after her husband fall of 1941 she worked as a teacher in the town and three daughters. Olga's of Gorodets, and in the spring of 1942 she re "grandfather"1 , Gennady La turned to Kologriv, where she took her father's dyzhensky, was a famous position as a high school mathematics teacher. In painter. There were many October 1943 she finally became a student at books, including books on Moscow State University and graduated in 1947. history and fine arts, in their During these years, I. G. Petrovskii was her adviser. house. Books were almost the At that time she was strongly influenced by only source of cultural edu Gelfand's seminar. cation, because Kologriv was In 194 7 Olga married A. A. Kiselev, a Leningrad too far from cultural centers. resident, so she moved there, with a recommen The town was situated dation from Moscow State University to the grad among wild forests, near the uate school of Leningrad State University (LGU). At picturesque river Unzha. All LGU S. L. Sobolev was appointed to be her scien her life Olga carefully kept tific adviser. From the time she came to LGU, a very beautiful landscape paintings close friendship developed between Olga and V. I. Olga as a baby, with her father, by her grandfather, some of Smirnov and his family. In the fall of 194 7 Smirnov, mother, and two sisters. them depicting fine views of at Ladyzhenskaya's request, became head of a sem the Unzha. inar on mathematical physics, which has been ac It was in the summer of 1930 that Alexander tive ever since. The seminar brought together many Ivanovich decided to teach mathematics to his own mathematicians of the city working in the area of daughters. After he made partial differential equations and their applica some explanation of the tions. Until her last days Ladyzhenskaya was one basic notions of geome of the leading participants. try, he formulated a theo rem and suggested that Finite-Difference Method and Hyperbolic his daughters prove it Equations themselves. It turned out Even the first results that Ladyzhenskaya obtained that the youngest one, in the late 1940s and in the early 1950s were a Olga, was the best of his breakthrough in the theory of PDEs. In her Ph.D. , students. She loved to dis thesis, defended at LGU in 1949, she proposed a cuss mathematics with difference analog of Fourier expansions for peri her father, and soon they odic functions on grids and investigated their con studied calculus together. vergence as the grid step goes to zero in the dif In October 193 7 Alexander Ivanovich was arrested ference analogues of the space W~. Using these and soon killed by NKVD, the forerunner of the KGB. expansions, she investi It was a great shock for the family. Later, in 1956, gated various difference he was officially exonerated "due to the absence of schemes for model equa a corpus delicti". His death put the family in a very tions, distinguished those distressed situation. The mother and older daugh that are stable for certain ters had to go to work. Olga's mother had grown ratios of grid steps in the up in a small village in Estonia and could do craft space and time variables, work. She made dresses, shoes, soap, and many and then proved the sta other things. That was the way the family survived bility of these schemes for in those days. equations with variable In 1939 Olga graduated with honors from Kolo coefficients. In particular, griv High School and went to Leningrad to continue she gave a simpler proof her education. However, it was forbidden for a per of unique local solvability son whose father was considered an "enemy of his of the Cauchy problem for Nation" to enter Leningrad State University.2 She hyperbolic quasilinear sys was accepted at Pokrovskii Pedagogical Institute, tems than the proof that Petrovskii had given. and finished two years of studies there in June After defending her Ph.D. thesis, Ladyzhenskaya 1941. The war forced her to leave Leningrad. In the decided to study initial boundary-value problems 1 Olga's actual grandfather was Ivan whose brother was for linear hyperbolic equations of second order. She the painter Gennady Ladyzhensky. Gennady lived with Ivan started with justification of the Fourier method. In and his family. Olga and her sisters always called Gennady her publications of 1950-1952, Ladyzhenskaya "Dedushka" which means grandfather. gave exhaustive answers concerning series expan 2She had passed the entrance exams to this university which sions of functions in W~(Q) in the eigenfunctions at the time was considered the best in the Soviet Union. of arbitrary symmetric second-order elliptic 1322 NOTICES OF THE AMS VOLUME 51, NUMBER 11 operators in a bounded domain Q E JR. n, under any Dirichlet problem was reduced to obtaining a pri of the classical boundary conditions on oO. More ori bounds for its solutions in c1+ lX norm. Up to over, in [1] she found a solution to the problem of the mid-1950s the program had been realized for describing the domain of the closure in L2(0) of the Dirichlet problem for two-dimensional elliptic an elliptic operator L with the Dirichlet boundary equations, but even in those cases some unnatural condition. The solution is based on the inequality conditions were supposed. The conception of a generalized solution first (1) llullw:f DECEMBER 2004 NOTICES OF THE AMS 1323 parabolic types (the latter writtenjointlywith Solon [3] 0. A. LADYZHENSKAYA and N. N. URAL'TSEVA, A variational nikov). The books presented a rather complete the problem and quasi-linear elliptic equations in many ory for quasilinear equations of divergence form independent variables, Dokl. Akad. Nauk SSSR 135 and, in particular, global solvability of the classi (1960), 1330-1333; English transl., Soviet Math. Dokl. 1 (1960), cal boundary-value problems 1390-1394. under natural growth [4] __ , Quasi-linear elliptic equations and variational restrictions. Moreover, the methods developed by problems in several independent variables, Uspekhi the authors in [9] enabled them to analyze the de Mat. Nauk 16:1 (1961), 19-90; English transl., Russian pendence of smoothness of generalized solutions Math. Surveys 16:1 (1961), 17-91. on the smoothness of data for equations of diver [5] __ ,A boundary value problem for linear and quasi gence form. It was proved that under natural growth linear parabolic equations, Dokl. Akad. Nauk SSSR restrictions, the regularity of weak extremals for 139 (1961), 544-547; English transl., Soviet Math. Dokl. the higher-dimensional variational is completely de 2 (1961), 969-972. termined by the smoothness of the integrand. In a [6] __ , On the smoothness of weak solutions of quasi linear equations in several variables and of variational sense this concluded the investigation of Hilbert's problems, Comm. PureAppl. Math. 14 (1961), 481-495. nineteenth and twentieth problems for second [7] __ , Boundary value problems for linear and quasi order equations. Also, classes of quasilinear sys linear parabolic equations. I, Izv. Akad. Nauk SSSR tems with diagonal principal part and a special Ser. Mat. 26 (1962), 5-52; English transl., Amer. Math. structure of the terms quadratic in gradients were Soc. Trans/. (2) 47 (1966), 217-267. singled out there, and it was shown that they share [8] __ , Boundary value problems for linear and quasi properties that are characteristic of scalar diver linear parabolic equations. Il, Izv. Akad. Nauk SSSR Ser. gence equations. Such systems later became the ob Mat. 26 (1962), 753-780; English transl., Amer. Math. ject of detailed studies in research on harmonic Soc. Trans/. (2) 47 (1966), 268-299. [9] __ , Linear and Quasi-Linear Elliptic Equations, maps of manifolds. Nauka, Moscow, 1964; English transl., Academic Press, The books [9]-[11] also presented a number of New York, 1968. deep results in the theory of quasilinear equations [10] __ , Linear and Quasi-Linear Elliptic Equations, of general nondivergence form. However, for such 2nd rev. ed., Nauka, Moscow, 1973. (Russian) equations it was only later, at the beginning of the [11] 0. A. LADYZHENSKAYA, V. A. SOLONNIKOV, and N. N. 1980s, that unnatural restrictions were completely URAL'TSEVA, Linear and Quasi-Linear Equations of Par removed and the results brought to the same level abolic Type, Nauka, Moscow, 1967; English transl., of generality as in the divergence form case. This Amer. Math. Soc., Providence, Rl, 1968. required techniques developed by N. V. Krylov and [12] 0. A. LADYZHENSKAYA and N. N. URAL'TSEVA, Solvability of the first boundary value problem for quasi-linear V. M. Safonov for investigating linear equations of elliptic and parabolic equations in the presence of nondivergence form with bounded measurable co singularities, Dokl. Akad. Nauk SSSR 281 (1985), efficients. In [12]-[14], the conditions on the data 275-279; English transl., Soviet Math. Dokl. 31 (1985), were made even weaker, the presence of integrable 296-300. singularities with respect to the independent vari [13] __ , A survey of results on the solvability of bound ables was allowed, and the solvability of the Dirich ary value problems for uniformly elliptic and parabolic let problem was studied in Sobolev spaces. second-order quasi-linear equations having unbounded The methods developed in the monographs singularities, Uspekhi Mat. Nauk 41:5 (1986), 59-84; [9]-[11] turned out to be effective also in the English transl., Russian Math. Surveys 41:5 (1986), study 1-31. of broader classes of equations that contain non [14] __ , Estimates on the boundary of the domain for uniformly elliptic operators like mean curvature op the first derivatives of functions satisfying an elliptic erator [15]. The joint work of Ladyzhenskaya with or a parabolic inequality, Trudy Math. Inst. Stek/ov. 179 N. M. Ivochkina was devoted to geometric topics as (1988), 102-125; English transl., Proc. Stek/ov Inst. well. In 1994-1997, they published a series of pa Math. 1989,no. 2,109-135. pers investigating the global classical solvability of [15] __ , Local estimates for gradients of solutions of the first initial boundary-value problem for non non-uniformly elliptic and parabolic equations, Comm. linear equations of parabolic type that describe Pure Appl. Math. 23 (1970), 677-703. the flows generated by the symmetric functions of Hydrodynamics the Hessian of the unknown surface or by its prin cipal curvatures. The mathematical theory of viscous incompress ible fluids was the favorite topic of Olga La References dyzhenskaya. She was involved with this activity [1] 0. A. LADYZHENSKAYA, The first boundary value problem from the middle of the 1950s till the very end of for quasi-linear parabolic equations, Dokl. Akad. Nauk her life. Her personal contributions to mathemat SSSR 107 (1956), 636-638. (Russian) ical hydrodynamics were deep and very impor [2] __ , Solution of the first boundary value problem tant. But what was perhaps even more important in the large for quasi-linear equations, Trudy Moskov. is that she was a great source of new problems for Mat. Obshch. 7 (1958), 219-220. (Russian) others. 1324 NOTICES OF THE AMS VOLUME 51, NUMBER 11 In the middle of the 1950s, Ladyzhenskaya began with the simplest case, the stationary Stokes sys tem: /.ltl.U - "\lp = -f} . (0.1) . 0 ill Q, ulan= 0 dIV U = Here, Q is a domain in JRn(n = 2, 3), f E Lz(Q;JRn) is a given force, 11 is constant viscosity, u and p are unknown velocity field and pressure. If we define by H(Q) and HI(Q) the closures of the set 0 C0(Q;JRn) = {v E CQ'(O;JRn) II div v = 0} in Lz(Q;JRn) and W}(Q;JRn), respectively, the ve locity can be determined from the variational iden Ladyzhenskaya near the River Dnieper in the tity Ukraine, while on a break from a math conference. (0.2) 11 I "Vu : \lvdx =I f·vdx, 'dv E HI(Q). n n saying that the class of weak solutions introduced by E. Hopf is too wide to prove uniqueness. At that time, Ladyzhenskaya had already been able One of the most remarkable results, proved by to prove that the solution u to (0.2) has the second Ladyzhenskaya at the end of the 1950s and pub derivatives which are locally square summable in lished in [4], was the global unique solvability of Q. In order to recover the pressure, she proved the the initial boundary problem for the 2D Navier following fundamental fact: Stokes equations. For the Cauchy problem, it was Theoremo0.1. Let w E Lz(Q; JRn) be orthogonal to established by ]. Leray. The proof was based on ideas developed in [2] and on new types of in all v E CQ'(O;JRn), then w = "Vp for some equalities, which nowadays are called multiplica P E L2,1odQ) with \lp E Lz(Q; JRn). tive inequalities. In particular, Ladyzhenskaya The theorem was proved in the celebrated mono proved that, for any v E CQ'(O), it holds: graph [1], which contains the main results obtained by Ladyzhenskaya in the 1950s on Stokes and (0.4) llviiL D ECEMBER 2004 NOTICES OF THE AMS 1325 As we mentioned above, Ladyzhenskaya be lieved that in the 3D case the Navier-Stokes equa tions, even with very smooth initial data, do not pro vide uniqueness of their solutions on an arbitrary time interval. Hopf and later other mathematicians, Ladyzhenskaya among them, tried unsuccessfully to state a reasonable principle of choice for deter minacy. Giving up these attempts, Ladyzhenskaya introduced the so-called modified Navier-Stokes equations, which are now known as Ladyzhen skaya's model. These equations differ from the classical ones only for large-velocity gradients. For them, she proved global unique solvability under reasonably wide assumptions on the data of the problem. These results were the main content of her report to the International Congress of Math ematicians in 1966. For a long time, problems of this type were not very popular due to their diffi Ladyzhenskaya, age 79, in her St. Petersburg apartment. culties, and it is only in the last decade that they have attracted the attention of many mathemati Theorem 0.2. Assume that v is a weak Leray-Hopf cians trying to improve on Ladyzhenskaya' s old re solution and sults. (0.5) At the end of this section, we would like to men tion the remarkable results Ladyzhenskaya ob for positive numbers s and l satisfying the condi tained on the solvability of stationary problems for tion the Navier-Stokes equations. The first attempts in this direction were made by Odqvist and Leray. 3 2 (0.6) -+-<1 However, the question of global solvability (for all s l - ' s > 3. values of Reynolds numbers) had remained open Then any other weak Leray-Hopf solution to the same till the end of the 1950s. Ladyzhenskaya's ap initial boundary-value problem coincides with v. proach was based on her conception of weak so lution and a good choice of the energy space. This Ladyzhenskaya later included results of this type t;;urned out to be the space H 1(D.), the closure of in the second Russian edition [9] of her mono C0(Q) in the Dirichlet integral norm. Using known graph. a priori estimates for the velocity gradient in L2(0), In 1967, Ladyzhenskaya proved in [10] that in she proved in [13] and [14] the existence of at least fact weak Leray-Hopf solutions satisfying condF one solution in the energy space H 1(Q). Later, in tions (0.5) and (0.6) are smooth. the 1970s, Ladyzhenskaya, together with Solon nikov, successfully studied stationary problems in Theorem 0.3. Assume that all conditions of Theo domains with noncompact boundaries. rem 0. 2 are fulfilled. Let, in addition, f E L2(Qy), a E H 1 (D.), and Q is the bounded domain in JR. 3 of References class C2. Then OtV, "V 2v, and "V p are inL2(Qy). [1] 0. LADYZHENSKAYA, The Mathematical Theory ofViscous Incompressible Flow, Fizmatgiz, 1961; English transl., As it was indicated in one of the last papers by La Gordon and Breach, New York, 1969. dyzhenskaya [11], this theorem might be a good [2] 0. A. LADYZHENSKAYA and A. A. K:!SELEV, On the existence guideline for those who would like to solve the main and uniqueness of the solution of the non-stationary problem of mathematical hydrodynamics. By the problem for a viscous incompressible fluid, Izv. Akad. way, t adyzhenskaya formulated it as follows: One Nauk SSSR Ser. Mat. 21 (1957), 665- 680; English transl., Amer. Math. Soc. Trans/. (2) 24 (1 963), 79- 106. should look for the right functional class in which [3]]. LERAY, Sur le mouvement d'un liquide visqueux em global unique solvability for initial boundary value plissant l'espace, Acta Math. 63 (1934), pp. 193-248. problems for the Navier-Stokes takes place. [4] 0. A. LADYZHENSKAYA, Solution "in the large" of bound Up to now, very few qualitatively new results on ary value problems for the Navier-Stokes equations in global unique solvability results for the three two space variables, Dokl. Akad. Nauk SSSR 123 (1958), dimensional nonstationary problem are known. 427-429; English transl., Soviet Phys. Dokl. 3 (1959), 1128- 1131 and Comm. Pure App. Math. 12 (1 959), The most impressive among them is Ladyzhen 427-433. skaya's result for the Cauchy problem in the class [5] E. HorF, Ober die Anfangswertaufgabe fUr die hydro of radially asynllletric flows with zero angular ve dynamischen Grundgleichungen, Math. Nachrichten 4 locity. This was proved in [12]. (1950- 51), 213- 231. 1326 NOTICES OF THE AMS VOLUME 51, N UMBER 11 [6] J.-L. LioNs and G. PRom, Un theoreme d'existence et unic ties of J'vl. It is invariant, each trajectory on J'vl can ite dans les equations de Navier-Stokes en dimension be extended to negative times, and in a sense it is 2, C. R. Acad. Sci. Paris 248 (1959), 3519-3521. finite-dimensional. The latter means that there is [7] G. PRom, Un teorema di unicita per el equazioni di a number N with the following property: If for two Navier-Stokes, Ann. Mat. Pura Appl. 48 (1 959), pp. full trajectories lying in J'vl the 173- 182. projections on the finite dimen [8]]. SERRIN, The initial value problem for the Navier Stokes equations, Nonlinear Problems (R. Langer, ed.), sional space spanned by the first pp. 69-98, The University of Wisconsin Press, Madi N eigenfunctions of the Stokes op son, 1963. erator coincide, then the trajecto [9] 0. A.l.ADYZHENSKAYA, Mathematical Problems of the Dy ries themselves coincide. In the namics of Viscous Incompressible Fluids (2nd edition) conclusion of this remarkable Nauka, Moscow, 1970. paper, it was claimed that the pro [10] __ , Uniqueness and smoothness of generalized posed approach is applicable to solutions of the Navier-Stokes equations, Zap. Nauchn. many other dissipation problems, Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 5 in particular, to problems of par (1967), 169-185; English transl., Sem. Math. V. A. abolic types. So, [1] opened a chap Steklov Math. Inst. Leningrad 5 (1969), 60-66. ter in the theory of PDE, namely sixth problem of the millenium: The [11] __ , The the theory of stability "in the Navier-Stokes equations, existence and smoothness, Uspekhi Mat. Nauk.58:2(2003), 181-206; English transl., large". This program was realized Russian Math. Surveys 58:2(2003), 395-425. in her last monograph [3]. [12] __ , Unique global solvability of the three-dimen In her survey article [2], she sional Cauchy problem for the Navier-Stokes equations proposed to call the set :M a "global minimal 'B in the presence of axial symmetry, Zap. Nauchn. Sem. attractor". Her explanation of that was as follows. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 7 (1968), The word "minimal" indicates that no proper sub 15 5-177; English transl., Sem. Math. V. A. Steklov Math. set of :M attracts the whole of H(D.), and the let Inst. Leningrad 7 (1970), 70- 79. ter 'B emphasizes that any bounded set in H(D.) is [1 3] _ _ , A stationary boundary value problem for vis uniformly attracted to :M. Certainly, this makes cous incompressible fluid, Uspekhi Mat. Nauk, 13 sense. (19 58), 219-220 (Russian). [14] __ ,Stationary motion of viscous incompressible References fluids in pipes, Dokl. Akad. Nauk SSSR 124 (1959), [1] 0. A.l.ADYZHENSKAYA, A dynamical system generated by 551-553; English transl., Soviet Physics Dokl. 124(4) the Navier-Stokes equations, Zap. Nauchn. Sem. (1959), 68-70. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 27 (1972), English transl.,]. Soviet. Math. 3 (1975), Attractors for PDEs 91-115; 458-479. In [1], Ladyzhenskaya considered a semigroup gen [2] __ , Finding minimal global attractors for the Navier erated by the two-dimensional initial boundary Stokes equations and other partial differential equa value problem for the Navier-Stokes equations. tions, Uspekhi Mat. Nauk 42:6, 1987, 25-60; English Solution operators were defined as Vr(a) = v(t), and transl., Russian Math. Surveys 42:6, 1987, 27-73. the phase space was H(D.). It was assumed that [3] _ _ , Attractors for semigroups and evolution equa the force fin (0.3) is independent of time and be tions, Lezioni Lincei, 1988, Cambridge Univ. Press, Cambridge, 1991. longs to L z(Q). It was known that solution opera tors are continuous in (a, t) on H(D.) x JRl and each bounded set 'B c H(D.) is pulled into the ball 'B(Ro) ={u II llullr 2 (0J < Ro} c H(D.) ofradiusRo > M. I. Vishik (i\p)- 1 llfllr2 (0J in a finite time, where i\ is the first eigenvalue of the Stokes operator for the domain I first met Olga Alexandrovna Ladyzhenskaya in D., and 'B stays there for all large t. She showed that 1945, and we became friends at once. She was then solution operators are compact on H(D.) for each a third-year student at Moscow State University. We fixed positive t. For finite-dimensional phase spaces often met at the seminars, and we discussed math this result is immediate, but in the case of infinite ematical problems while walking along the wide dimensional phase spaces that was a very impor corridors of the Department of Mechanics and tant step. Then Ladyzhenskaya took the intersec Mathematics of the university. tion Her scientific adviser at Moscow State University was Ivan Georgi~vich Petrovskii. In 1946 Israel (0.1) :M = n Vr('B(Ro)) t >O Mark Vishik is professor of mathematics at the Moscow and proved that the set J'vl is nonempty and com State University and at the Institute ofInformation Trans pact and attracts any bounded subsets of the phase mission Problems of the Russian Academy of Science. His space. She found many other interesting proper- email address is vi shi k@i i tp. ru. DECEMBER 2004 NOTICES OF THE AMS 1327 Moiseevich Gelfand organized a seminar for three In 19 53, at Moscow State University, Olga Alexan young mathematicians: 0. A. Ladyzhenskaya, 0. A. drovna defended her "habilitation" dissertation Oleinik, and myself. As a result each participant of devoted to the problem of regularity of solutions the seminar got an interesting mathematical prob of a mixed boundary-value problem for a general lem to seriously work on. 0. A. Ladyzhenskaya got hyperbolic equation of the second order. She found the problem of describing the domain of an ellip rather sharp conditions guaranteeing that the so tic operator of the second order with Dirichlet lutions of these equations are the solutions in the boundary conditions and with right-hand side be classical sense. Olga Alexandrovna justified the longing to L2(Q). She proved that if this boundary Fourier method for the solution of hyperbolic value problem has a unique solution, then the el boundary-value problems. Furthermore, she also liptic operator is an isomorphism between the studied the application Sobolev space H 2(D.) n H6(D.) and L2(D.). She also of the method of the found an estimate for the norm for the corre Laplace transform to sponding inverse operator. these equations. All In the late forties Olga Alexandrovna moved to these problems were ex Leningrad, where she became a postgraduate stu pounded in her book [2]. dent of Vladimir Ivanovich Smirnov. Vladimir In the fifties and six Ivanovich admired her talent, and she took an ac ties Olga Alexandrovna tive part in his seminar. Later Olga Alexandrovna often gave talks at the became the head of the seminar. From time to time seminars of Ivan Olga Alexandrovna organized conferences on dif Georgievich Petrovskii ferential equations and their applications. These at Moscow State Uni conferences were very popular. Many mathemati- versity. I recall how cians from other universi greatly the listeners ties and institutes in the So were impressed by her viet Union used to take part proof of the uniqueness theorem for the initial in them. boundary-value problem for the two-dimensional In Leningrad Olga Navier-Stokes system. Since the existence theorem Alexandrovna married An for these equations was proved earlier, the well drey Alekseevich Kiselev, posedness of the main boundary-value problem who looked very much like for the Navier-Stokes system in two dimensions was Pierre Bezukhov, the hero established thanks to the remarkable result of Olga of the novel War and Peace Alexandrovna. The uniqueness theorem for the by Leo Tolstoy. My wife and three-dimensional Navier-Stokes system is still not I often visited them when proved. Olga Alexandrovna devoted her book on we were in Leningrad. We fluid dynamics to three people she most respected, witnessed how tender and namely, her father, Vladimir Ivanovich Srnirnov, loving Andrey Alexeevich and Jean Leray. In this book she studied in great was. She literally meant the detail many problems related to the stationary and world to him. However, they nonstationary Navier-Stokes system. Olga Ladyzhenskaya with her separated later. Andrey In collaboration with Nina Nikolaevna Ural'tseva, husband, Andrey Kiselev. Alexeevich wanted to have Olga Alexandrovna wrote a book [4] on linear and children, but Olga Alexan quasilinear elliptic equations. Many fundamental drovna did not. She justified her decision by her results were obtained in this book, which remains wish to devote her life to mathematics only, to a real encyclopedia on the subject. In the sixties, which children might be an obstacle. Thus, Olga Olga Alexandrovna, Nina Nikolaevna Uralt'seva, Alexandrovna stayed single for the rest of her life. and Vsevolod Alekseevich Solonnikov wrote a book For many years starting in the late forties, Olga [5] on linear and quasilinear parabolic equations. Alexandrovna visited us many times, and some In section 2 of this memorial article, Nina Niko times even stayed with us. She was usually inter laevna writes more about this wonderful mono ested in what new mathematical ideas I had worked graph. Olga Alexandrovna is also the author of the out over the summer, and she told me, in turn, of book [6] on the attractors of semigroups and evo her own new achievements. We also used to discuss lution equations. This book is based on a lecture with her new compelling and timely mathematical course that Olga Alexandrovna gave in different uni problems; the connections between functional versities in Italy, the so-called Lezioni Lincei. analysis and the theory of differential equations and Olga Alexandrovna was a very educated and many other things. Ladyzhenskaya and I published highly cultured person. The famous Russian poet, a paper on these problems in Uspekhi Matem Anna Akhmatova, who knew Ladyzhenskaya very aticheskih Nauk (see [1]). well, devoted a poem to her. 1328 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Olga Alexandrovna was once a member of the figures were-Gelfand, Kolmogorov, Petrovsky, city council of people's deputies. She helped many Pontryagin, Sobolev, Vinogradov-and knew the mathematicians in Leningrad to obtain apartments names of some of the up-and-coming new postwar (free of charge) for their families. generation-Faddeev, Arnold, Ladyzhenskaya, Once in the Steklov Mathematical Institute in Oleinik. We were aware of Gelfand's spectacular Leningrad, removing my coat in the cloakroom, I work on normed rings and were influenced by said jokingly to the cloakroom attendant that I Petrovsky's survey article on partial differential was going to take away Olga Alexandrovna to equations. But in general we were woefully igno Moscow with me, and I got a serious answer: "We rant-few of us knew Russian, or even the Cyrillic will never give up our Olga Alexandrovna!" alphabet; personal encounters were highly re Olga Alexandrovna was a deeply religious stricted. woman. The thaw started only Olga Alexandrovna devoted her life to mathe after Stalin died; a key matics, sacrificing her own happiness for it. Now, event was Khrushchev's de we can surely say that she has become a "classic nunciation of Stalin's figure" of mathematical science. crimes in 1956, the year the Soviet Government reha References bilitated Ladyzhenskaya's [1] M. l. VISHIK and 0. A. LADYZHENSKAYA, Boundary-value father, shot as a traitor in problems for partial differential equations and certain 1937. Khrushchev's speech classes of operator equations, Uspekhi Matern. Nauk, was m eant only for the 6 (72) (1956), 41-97; English transl., Amer. Math. Soc. party faithful, but it was Trans/. (2) 10, 1958, 223-281. soon disseminated gener [2] 0. A. LADYZHENSKAYA, Mixed Boundary-Value Problem for ally thanks to the CIA Hyperbolic Equation, Gostekhizdat, Moscow, 1953. credit where credit is due. (Russian) [3] _ _ , The Mathematical Theory of Viscous Incom A few visitors were allowed pressible Flow, Gostehizdat, Moscow, 1961; English to enter the Soviet Union transl., Gordon and Breach, New York-London, 1963. and have relatively free ac (4] 0. A. LADYZHENSKAYA and N. N. URAL'TSEVA, Linear and cess to Soviet scientists; the Quasilinear Equations ofElliptic Type, Nauka, Moscow, impressions of these visi 1964 (2nd. ed.), 1973; English transl., Academic Press, tors were eagerly sought. New York-London, 1968. Leray reported that in [5] 0. A. LADYZ HENSKAYA, V. A. SOLONNIKOV, and N. N. Leningrad he saw the Her URAL'TSEVA, Linear and Quasilinear Equations of Para mitage, Peterhof, and La bolic Type, Nauka, Moscow, 1967; En glish transl., dyzhenskaya. Translations of Mathematical Monographs, 23, Amer. The Iron Curtain worked in both directions; Math. Soc., Providence, Rl, 1968. when Ladyzhenskaya first started to work on the [6] 0. A. LADYZHENSKAYA, Attractors for Semigroups and Evo the lution Equations, Lezioni Lincei, 1988, Cambridge Univ. Navier-Stokes equation, she was unaware of Press., Cambridge, 1991. work of Leray and Hopf. A major sign of a thaw was the large Soviet del egation, Olga among them, at the Edinburgh In ternational Congress of Mathematicians in 1958. For Peter Lax, Cathleen Morawetz, and many of us this was the beginning of a mathe Louis Nirenberg matical and personal friendship with Olga. After the close of the Congress, by chance I (PDL) ran into Young mathematicians today would have a hard a group of Soviet mathematicians at the National time imagining how thoroughly the Iron Curtain iso Gallery in London. Olga and I started talking and lated the Soviet Union from the rest of the world got separated from the group. Unfortunately Olga in the 1940s and 1950s. Mathematics was no ex did not remember the name of the hotel where the ception. We were generally aware who the leading delegation was staying, so we were forced to go to the Soviet Consulate; with their help the lost sheep Peter Lax is professor emeritus at the Courant Institute of was reunited with her flock. the Mathematical Sciences, New York University. His email address is l ax@ci ms. nyu. edu. The trickle of Western visitors turned to a tide in the 1960s. An outstanding event was the Open Cathleen Morawetz is professor emeritus at the Courant Institute of the Mathematical Sciences, New York Univer ing Conference of the University and Science City sity. Her email address is morawetz@ci ms. nyu. edu. at Novosibirsk in 1963, under the direction of Lavrentiev. Here friendships started at Edinburgh Louis Nirenberg is professor emeritus at the Courant In much more relaxed condi stitute of the Mathematical Sciences, New York University. were renewed under His email address is ni ren l @ci ms. nyu. edu. tions. LN recalls that Olga had arranged a sailing DECEMBER 2004 NOTICES OF THE AMS 1329 party on the Ob Sea on a vessel with a red sail, made attractors of solutions of the Navier-Stokes equa available by Sobolev, director of the Mathematics tions. Flow-invariant measures on manifolds of Institute at Novosibirsk. such attractors might be a building block of tur The International Congress of Mathematicians bulence. in Moscow in 1966 was another outstanding occa On her last visit abroad, at a conference held in sion for Western and Soviet mathematicians to get Madeira in June 2003, she gave a spirited personal together. account of her work on the Navier-Stokes equation. Western publishers started putting out English For decades, Olga ran a seminar on partial dif translations of important books that originally ap ferential equations that kept up with the develop peared in Russian, including Olga's Mathematical ment of the subject worldwide; it had a great in Theory of Viscous Incompressible Flow and her book fluence in the Soviet Union. with Ural'tseva, Linear and Quasilinear Elliptic Equa Olga's career shows that even in the darkest tions. The AMS performed an immensely useful days of Soviet totalitarianism there were coura service with its vast translation program of articles geous academics, Petrovsky and Smirnov in Olga's and books, including Olga's book with Ural'tseva case, who were willing to defy official proscription and Solonnikov on parabolic equations. of the daughter of a man shot as a traitor, perceive Olga's first work was to use the method of fi her ability, and ease her path so her talent could nite differences to solve the Cauchy problem for bloom and gain recognition. hyperbolic equations, giving a new proof of Petro It is to the great credit of the international math vsky's result-Petrovsky's method is incompre ematical community that at the height of the Cold hensible.This work of Olga's is little known in the War, when both sides were piling thousands of nu West; Olga herself did not return to it, very likely clear weapons on top of each other, Soviet and because she decided (as did Friedrichs) that a pri Western mathematicians formed an intimate fam ori estimates and the methods of functional analy ily, where scientific and personal achievements sis are more effective tools. She did, however, de were admired independently of national origin. vise numerical schemes for solving the Olga was among the most admired, for her courage, Navier-Stokes equation. for overcoming enormous obstacles, for support Olga consistently used the concept of weak so ing those under attack, for her mathematical lutions, a point of view championed by Friedrichs, achievements, and for her overwhelming beauty. whom Olga admired. She was in the forefront of the upsurge of interest in elliptic equations. In a Acknowledgement very early work she showed that second-order el Photographs and the mathematical family tree liptic boundary-value problems have square inte are reproduced from the first two volumes, Non grable solutions up to the boundary under very gen linear Problems in Mathematical Physics and Related eral boundary conditions. Her books with Ural'tseva Topics. In Honor of Professor 0. A. Ladyzhenskaya and Solonnikov contain many deep results con I, II, M. Sh. Birman, S. Hildebrandt, V. A. Solon cerning estimates for solutions of elliptic and par nikov, N. N. Ural'tseva, eds., of the International abolic equations. They have greatly extended ideas Mathematical Series published by Kluwer/Plenum of Serge Bernstein and techniques of DiGiorgi, Publishers (English) and by Tamara Rozhkovskaya Moser, and Nash. These books are basic sources for (publisher, Russian). These photos are reproduced these subjects. here with permission of the publishers of the In The work for which Olga will be remembered ternational Mathematical Series. longest is on the Navier-Stokes equation. This is a technically very difficult field in which every ad vance, even modest, requires great effort. One of the goals is to decide if the initial value problem in three dimensions has a smooth solution for all time, and if not, whether a generalized solution is uniquely determined by the initial data. But even if at some future time these questions are decided, and the Clay Foundation rewards its solver with one of its million-dollar prizes, the main task of hy drodynamics remains to deduce the laws govern ing turbulent flow. In additional to a large body of technical re sults, Olga boldly proposed a modification of the Navier-Stokes equations in regions where the ve locity fluctuates rapidly. She also made important contributions to the theory of finite-dimensional 1330 NOTICES OF THE AMS VOLUME 51, NUMBER 11 IMS, Vol. 1 I.J.Von Littrov The Mathematics Genealogy ProjeO ~'- http://mathgenealogy.mnsu.edu . DECEMBER 2004 NOTICES OF THE AMS 1331 Double Cusp Group David]. Wright People have long been fascinated with repeated patterns that display a rich collection of symmetries. The discovery of hyperbolic geometries in the nine teenth century revealed a far greater wealth of pat terns, some popularized by Dutch artist M. C. Escher in his Circle Limit series of works. The cover illustration on this issue of the Notices portrays a pattern which is symmetric under a group gener ated by two Mobius transformations a(z) and b(z) of the form~~:~ where oc, {3, :y, and o and z are all complex numbers . These are not distance preserving, but they do preserve angles between curves and they map circles to circles. This black lace work (Figure 1) is the set of 'limit points' of the group, meaning Figure 2. any point that may tangency. The trace of the matrix corresponding to be approached by b must be ± 2, giving a polynomial condition on the an infinite se generators a and b. On the other hand, the a trans quence of distinct formation moves points in infinite double spirals transformations ap from its 'repelling' fixed point to its 'attractive' plied to some other point. Euclidean fixed point. wallpaper patterns The complement of the circle web consists of have only one limit four white regions or 'blobs' labelled a, A, b and point at infinity. Es B. We stipulate that the a transformation map the cher's Circle Limit works have a circle of limit points. The limit set here is Figure 1. composed of infi nitely many circles and the accumulation points of these circles. Figure 2 is a finite web of tangent disks from the cover picture that defines how the transfor mations a and b operate. The violet disks are moved from one to the next by the transformation a, indicated by red arrows. The two light blue disks are invariant by the transformation b, shown by the blue arrows. Any Mobius transformation that leaves invariant two tangent disks is called 'parabolic', and has a unique fixed point at the point of David]. Wright is professor of mathematics at Oklahoma S tate University. His email address is [email protected]. Figure 3. 1332 NOTICES OF THE AMS VOLUME 51, NUMBER 11 ring of circles around the A blob into the ring of a terms equal to 0. Thus, the color of the image of circles around the a blob in reverse order, and this disk under any word in a and b is determined similarly for the b transformation and blobs. Also, just by the sum of the exponents of the a terms. disks must be mapped to disks of the same color. Similarly, the disk Dz has stabilizer generated Figure 3 shows some closed loops of arrows by a o b- 1 o a - 1 o b and b- 1 o a 15. Any word in between the disks. Following the arrows corre this subgroup has the exponents of the a's sum sponding to the composition a o b- 1 o a - 1 o b, ming to a multiple of 15. Hence, our coloring will namely, a forward blue arrow, then a backward be consistent if we use 15 colors. red arrow, then a backward blue arrow, then a for Choosing the same color for the D1 and Dz, we ward red arrow, we see that this transformation see the following rule throughout the pattern: two fixes the large outer 'disk' containing oo (which tangent disks belong to different classes if and we'll denote D 1) as well as the largest purple disk only if they have the same color. at the left (which we'll denote D z). That implies that a o b- 1 o a - 1 o b is also parabolic, another poly '.: •.. .· ·...- _;.~ : ··~...... ·· ·;• •.. .. nomial condition on a and b. ,, ...... Furthermore, if we start at D z and proceed by ' ,· .. • :···· · -=-·.: • .. exactly 15 applications of a (red arrows), we arrive -: ::;: . =:.'. :';. ·· ·. ::.-. •.::. • :.:· •.. :. {:- at the symmetrical large purple disk at the right, . · ·. .: ...... •••"' "'• and then we can jump back to D z by b- 1 (back :.: .. ::.' ..·,.. .· ·=:::······, :· .... ·:··. ·.·:·.··=·..~- ~ :.·.. ·. ·::.•...... -,,,...... • ...... :,- · ,.. ...· ... " . .•.... wards blue arrow). This same composition also . . . .. •;•);.·:· . . ,...... ' . • • . • . .. • • 0 .-...... 1 ·····.==·..··•··· • .·.··• . •..• . •·····•···.. .. fixes the disk a - (Dz) just one red arrow prior to ..· ....· - ~'~-;~·.- ~·.. . : . .. : D , that b- 1 o a 15 is parabolic. These par .... . implying .. .. 2 abolic conditions uniquely determine the pattern ...... ·.· ·•·"'····.·.. ··.·· ...... :.":. :.·:...... ···. •,.. ...·. • .-:,i. :..: ., ...... :".:*:'::: :.·.· ... '· . :'•. (up to conjugacy). :.:: .. ...~. · · : ~.:. .: .· .~· . : · The coloring of disks works as follows. Apply .. ~.. · ·'·~• ~ - = . •. :·. :~...... • ing b doesn't change the color; applying a changes ·'·!It- ~ ~- · · · · ·~ .._. ~: · " .:. ·." : ·. the color of the disk to the next one in a cycle of fifteen colors. That this is consistent depends on Figure 5. some properties of this group. Figure 5 is a zoom into the center of the pic ture, where the fixed points of the a transfor mation appear like hypnotic eyes. The title "dou ble cusp group" refers to this group's origin as an extreme 'deformation' of two-generator 'quasi fuchsian' groups. Some discussion of this may be found in Chapter 9 of [2]. About similar kinds of groups and their limit sets, Klein wrote in 1894 [1]: "The question is, what will be the configuration formed by the totality of all the circles, and in par ticular what will be the position of the limiting points. There is no difficulty in answering these questions by purely logical reasoning; but the imag ination seems to fail utterly when we try to form a mental image of the result." All the pictures were rendered using a program "kleinian" written by the author in collaboration with David Mumford. This note was prepared while the author was on sabbatical at the University of Figure 4. Oklahoma in Norman, and the author wishes to thank the department there for indulging his ac Figure 4 simply shows the two equivalence tivities. classes of disks under the action of the group. It extends the coloring of the disks in the original cir References cle web. Each disk is fixed by a sizeable subgroup [l] FELIX KLEIN, Lectures on Mathematics, American Math. of transformations. For example, we have seen the Soc., 2000. outer disk D1 containing oo is invariant under b and [2] DAVID MUMFORD , CAR OLINE SERIES, and DAVID WRIGHT, a o b- 1 o a - 1 o b; these two 'words' generate the Indra's Pearls: The Vision of Felix Klein, Cambridge Uni stabiliz'er subgroup of this disk. All the words in ver sity Press, 2002. this subgroup have the sum of the exponents of the DECEMBER 2004 N OTICES OF THE AMS 1333 Support the future of tnathetnatics Give to the American M athematical Society 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 ma th <;matic~ 1.800.321.4267 • Inspiration of young scholars (U.S. and Canada) or (Epsilon Fund) 1.401.455.4000 www.ams.org (worldwide) • International outreach 06/04 email: [email protected] I( NOW tft/H.AI TH£: b2 1S ALL .ABOOI~ If you know, apply for a Newton Fellowship. You'll expand the minds of New York City high school kids, while discovering a rewarding, exciting future for yourself. Newton Fellowships are designed to train mathematically talented individuals to be outstanding high school math teachers and support them in the early years of their careers. Fellows receive $90,000 in MfA stipends over 5 years. > Year 1 : Full tuition scholarship toward a Master's Degree in Education and living stipend > Years 2-5: Position as New York City high school math teacher plus MfA stipend > Mentoring, coaching, and professional development > Camaraderie with a group of talented math teachers To learn more visit www.mathforamerica.org Levy Processes From Probability to Finance and Quantum Groups David Applebaum he theory of stochastic processes was be embedded into a suitable noncommutative struc one of the most important mathematical ture. T developments of the twentieth century. Stochastic processes are not only mathematically Intuitively, it aims to model the interac rich objects. They also have an extensive range of tion of "chance" with "time". The tools applications in, e.g., physics, engineering, ecology, with which this is made precise were provided by and economics-indeed, it is difficult to conceive the great Russian mathematician A. N. Kolmogorov of a quantitative discipline in which they do not fea in the 1930s. He realized that probability can be ture. There is a limited amount that can be said rigorously founded on measure theory, and then about the general concept, and much of both the a stochastic process is a family of random variables ory and applications focusses on the properties of (X(t), t 2: 0) defined on a probability space (Q, :J, P) specific classes of process that possess additional and taking values in a measurable space (E, T). structure. Many of these, such as random walks and Here Q is a set (the sample space of possible out Markov chains, will be well known to readers. Oth comes), :J is a cr-algebra of subsets of Q (the events), ers, such as semimartingales and measure-valued and Pis a positive measure of total mass 1 on (Q, :J) (the probability). E is sometimes called the state diffusions, are more esoteric. In this article, I will space. Each X(t) is a (:J, T) measurable mapping give an introduction to a class of stochastic from Q toE and should be thought of as a random processes called Levy processes, in honor of the observation made onE at timet. For many devel great French probabilist Paul Levy, who first stud opments, both theoretical and applied, E is Eu ied them in the 1930s. Their basic structure was clidean space [R!.d (often with d = 1); however, there understood during the "heroic age" of probability is also considerable interest in the case where E is in the 1930s and 1940s and much of this was due an infinite dimensional Hilbert or Banach space, or to Paul Levy himself, the Russian mathematician a finite-dimensional Lie group or manifold. In all A. N. Khintchine, and to K.lt6 in Japan. During the of these cases T can be taken to be the Borel cr past ten years, there has been a great revival of in algebra generated by the open sets. To model prob- terest in these processes, due to new theoretical de , abilities arising within quantum theory, the scheme velopments and also a wealth of novel applica described above is insufficiently general and must tions-particularly to option pricing in mathematical finance. As well as a vast number of David Applebaum is professor of probability and statistics at the University of Sheffield. His email address is research papers, a number ofbooks on the subject D. App l ebaum@sheffi e l d. ac. uk. He is the author of have been published ([3], [11], [1], [2], [12]) and Levy Processes and Stochastic Calculus, Cambridge Uni there have been annual international conferences versity Press, 2004, on which part of this article is based. devoted to these processes since 1998. Before we Work carried out at The Nottingham Trent University. begin the main part of the article, it is worth 1336 NOTICES OF THE AMS VOLUME 51, NUMBER 11 listing some of the reasons why Levy processes are characteristic function of X(t) is the mapping so important: ¢r : IJil.d - ( defined by • There are many important examples, such as ¢r(U) = [(eiu·X(t)) = ~ eiu·ypr(dy), Brownian motion, the Poisson process, stable J ~d processes, and subordinators. where Pr is the law (or distribution) of X(t), i.e., • They are generalizations of random walks to 1 continuous time. Pr = P o X(t)- , and [ denotes expectation. ¢r is • They are the simplest class of processes whose continuous and positive definite; indeed, a famous paths consist of continuous motion interspersed theorem of Bochner asserts that all continuous with jump discontinuities of random size ap positive definite mappings from IJil.d to ( are Fourier pearing at random times. transforms of finite measures on !Pl. d. • Their structure contains many features, within It follows from the axiom (Ll) that each X(t) is infinitely divisible, i.e., for each E ~, a relatively simple context, that generalize nat n there exists a probability measure Pr,n on IJil.d with characteris urally to much wider classes of processes, such as semimartingales, Feller-Markov processes, tic function 4>r.n such that ¢r(u) = (¢r,n(u))", for each u E IJil.d. The characteristic functions of infi processes associated to Dirichlet forms, and nitely divisible probability measures were com (generalizing the strictly stable Levy processes) pletely characterized by Levy and Khintchine in the self-similar processes. 1930s. Their result, which we now state, is funda • They are a natural model of noise that can be mental for all that follows: used to build stochastic integrals and to drive stochastic differential equations. Theorem 0.1 [The Levy-Khintchine Formula]. If • Their structure is mathematically robust and X= (X(t), t ;::: 0) is a Levy process, then generalizes from Euclidean space to Banach and ¢r(u) = etry(u), for each t ;::: 0, u E IJil.d, where Hilbert spaces, Lie groups, and symmetric spaces, and algebraically to quantum groups. (0.1) ry(u) = ib · u _1:.u ·au+ 2 The Structure of levy Processes I [eiu·y- 1- iu · y1 11YII DECEMBER 2004 NOTICES OF THE AMS 1337 1.2 0.8 Brownian m otion with drift is the Levy process Ca ,b = (Ca,b(t), t :::0: 0), with characteristics (b, a, 0). 0.4 Each Ca,b(t ) is a Gaussian random variable having mean vector tb and covariance matrix t a . In fact 0 each Ca,b(t) = bt + Ba(t). A Levy process has con tinuous sample paths (w.p.l), or is Gaussian if and -0.4 only if it is a Brownian motion with drift. 2. The Poisson Process -0.8 A Poisson process N?t = (N?t(t), t :::o: 0) with in -1.2 tensity.\ > 0 is a Levy process with characteristics (0, 0, .\b1), where D1 is a Dirac mass concentrated - 1.6 at 1. N?t takes non-negative integer values, and we have the Poisson distribution: -2.0 0 2 3 4 5 P(N?t(t) = n) = e-M(At)n n! Figure 1. Simulation of standard Brownian motion. The path is The paths of N?t are piecewise constant on each continuous but nowhere differentiable. If you were to zoom finite interval, with jumps of size 1 at the random in, the fractal nature of the path would become apparent and times T n = inf{t :::0: 0, N?t(t) = n} . this reflects the self-similarity of the process. 3. The Compound Poisson Process It has mean zero and covariance [ (Bb(s) Let (Yn. n E N) be a sequence of independent B~(t)) = aiJ(s At) (where Bb(s) is the ith compo identically distributed random variables with com nent of the vector Ba(s)). If a is positive definite, mon law q and let N?t be an independent Poisson then each Ba(t) has a normal distribution with den process. The compound Poisson process is the sity fa.t where Levy process Z?t(t) = I~~ itl YJ . It has characteristic exponent T](u) = JIJ!.d (eiu·y - 1).\q(dy) . The com 1 ( 1 - 1 ) f.a,r(x) = d exp - - (x · a x) . pound Poisson process (with d = 1) can be used to (2 rrt)z ...jdet(a) 2 t model the takings at a till in a supermarket, where N?t(t) is the number of customers in the queue at When d = 1, we write B1 = B and call it a stan dard Brownian motion. Brownian motion has a fas time t and YJ is the amount paid by the jth cus cinating history. It is named after the botanist tomer. Robert Brown, who first observed, in the 1820s, the 4. Interlacing Processes irregular motion of pollen grains immersed in We can define a Levy process by the prescrip water. By the end of the nineteenth century, the phe tion X(t) = Ca,b(t) + Z?t(t), provided the two sum nomenon was understood by means of kinetic the mands are assumed to be independent. We call ory as a result of molecular bombardment. Indeed, this an interlacing process since its paths have the in 1905, Einstein, although ignorant of the dis form of continuous motion interlaced with ran covery of the phenomenon and of previous work dom jumps of size IIYn II occurring at the random on it, predicted its existence from purely theoret times T n (where the Yns are as in Example 3 above). ical considerations. Five years earlier L. Bachelier X has characteristic exponent had employed it to model the stock market, where the analogue of molecular bombardment is the in 1 r . (0.2) TJ(U) = ib · u- u · au+ Jll!.}ew·y - 1).\q(dy), terplay of the myriad of individual market decisions 2 that determine the market price. Standard Brownian motion was rigorously con which is quite close to the general form (0.1). In structed by N. Wiener in the 1920s as a family of deed (0.2) was proposed as the form of the most functionals on the space C = C0([0, oo ), rnt) of real general TJ by the Italian mathematician B. de Finetti valued continuous functions on [0, oo) that vanish in the 1920s. His error was in failing to appreciate at zero. In so doing, he equipped the infinite that the finite measure .\q can be replaced by a O" dimensional space C with a Gaussian measure that finite Levy measure v . But if we do this, (eiu·y - 1) is now called Wiener measure in his honour. It fol may not be v-integrable and hence we must adjust lows that the paths t - Ba(t)(w), where w E C, are the integrand. Probabilistically, this corresponds to continuous. In the 1930s Wiener, together with a lack of convergence of a countable number of R. Paley and A. Zygmund, showed that the paths "small jumps", as we will see in the next section. are nowhere differentiable (w.p.l). Although (0.2) is incorrect, the most general TJ can Figure 1 presents a simulation of the paths of be obtained as a pointwise limit of terms of simi standard Brownian motion. lar type, i.e., T](U) = limn- oo TJn(u), where each 1338 NoTicEs oF THE AMS VOLUME 51, NUMBER 11 80 40 l]n(U) = i (b - I yv(dy)) · u !, D ECEMBER 2004 NOTICES OF THE AMS 1339 the structure of the sample paths of Levy processes. Given a characteristic exponent, we can always as sociate to it a Levy process whose paths are right continuous with left limits (w.p.1). It follows that this process X can only have jump discontinuities, and there are, at most, a countable number of these on each closed interval. We formally write X(t) = Xc(t) + L o,;s,;t t.X(s), where Xc has continu ous paths (w.p.1) and t.X(s) = X(s)- X(s-) is the "jump" at times where X(s- ) = limu 1sX(u) is the left limit. We can describe Xc quite easily. It is a Brownian motion with drift, Xc(t) = bt + Ba(t) (although this is by no means easy to prove). The second term is more problematic-in particular, the sum may not converge. It turns out to be helpful to count the 0 1 2 3 4 5 jumps up to time t that are in a given Borel set A and to introduce Figure 3. Simulation of the gamma subordinator. In contrast to the cases shown by the previous two figures, the sample N(t,A) = #{0 5 s 5 t ;t.X(s) E A}. paths of subordinators are considerably more regular. The N is a very interesting object- it is in fact a func path is a non-decreasing step function with jump tion of three variables-time t, the set A, and the discontinuities again shown as vertical lines. sample point w. If we fix t and w, we get a Examples of subordinators include the e<-stable CT-finite measure on the Borel sets of IRI.d. On the ones (0 < C< < 1) that have Laplace exponent other hand, if we fix the set A and ensure that it !Jl(u) = ua. For the case C< = ~. each T(t) is the first is bounded away from zero, we get a Poisson hitting time of a standard Brownian motion to a process with intensity A = v(A). For these reasons level, i.e., T(t) = inf {s > 0; B(s) = Jz}. Furthermore, N is called a Poisson random measure. each T(t) has a Levy distribution with density In any finite time, X can have only a finite num ber of jumps of size greater than 1 (or indeed fr(s) = ( ~) s -~ e -~ .Anotherwell-knownexample 2 greater than any E > 0). We can write this finite sum of a subordinator, where each T(t) has a gamma distribution, is depicted in Figure 3. of jumps as J11xll>l xN(t, dx). Similarly, the sum of An important application of subordinators is all the jumps of size greater than l but less than to the time change of Levy processes. If X is a Levy 1 is h 1340 NOTICES OF THE AMS VOLUME 51, NUMBER 11 "martingale part" of X(t), i.e., the process the point of view of the Levy-Ito decomposition M(t) + Ba(t), has moments to all orders, so if X(t) (0.3), where the small jumps term f lxl< l xN(t, dx) de itself fails to have an nth moment this is entirely scribes the day-to-day jitter that causes minor fluc due to the influence of "large jumps". tuations in stock prices, while the big jumps term f1xld xN(t, dx) describes large stock price move Applications to Finance ments caused by major market upsets arising from, A sociologist investigating the behavior of the prob e.g., earthquakes or terrorist atrocities. ability community during the early 1990s would If we set aside Brownian motion, there are a surely report an interesting phenomenon. Many of plethora of Levy processes to choose from, and our the best minds of this (or any other) generation choice must enable us to derive a pricing formula began concentrating their research in the area of that market analysts can compute with. One in mathematical finance. The main reason for this teresting group of candidates is the (symmetric) hy can be summed up in two words-option pricing. perbolic Levy processes, whose financial applications Essentially, an option is a contract that confers have been extensively developed by E. Eberlein and upon the holder the right, but not the obligation, his group in Freiburg, Germany. These are processes to purchase (or sell) a unit of a certain stock for a with no Brownian motion part in (0.3), and the fixed price k on (or perhaps before) a fixed expiry characteristic function is given by date T, after which the option becomes worthless. For the option to make sense, k should be consid erably less than the current price of the stock. If the stock price rises above k, the holder of the op tion may make a considerable profit; on the other where K1 is a Bessel function of the third kind, and hand, if the stock price falls dramatically, losses ( and 15 are non-negative parameters. will be considerably less through buying options Hyperbolic Levy processes were discovered by than by purchasing the stock itself. 0. Barndorff-Nielsen the 1970s and used as mod The key question is-does the market deter els for the distribution of particle size in wind mine a unique price for a given option, and if so, blown sand deposits. N. H. Bingham and R. Keisel can this price be explicitly computed? Much of the make an interesting analogy between the dynam current interest in the subject derives from Nobel ics of sand production and stock prices in that prize winning work of F. Black, M. Scholes and R. just as large rocks are broken down to smaller and Merton in the 1970s who gave apositive answer to smaller particles "this 'energy cascade effect' might this question. Underlying their analysis was a model be paralleled in the 'information cascade effect', of stock prices that improved upon that of Bache whereby price-sensitive information originates in, her by using geometric Brownian motion; i.e., the say, a global newsflash and trickles down through price S(t) of a given stock at time t is national and local level to smaller and smaller units of the economic and social environment." S(t) = S(O) exp { (Jl - ~ 0'2 ) t + CT B(t)} . A problem with non-Gaussian option pricing is that the market is "incomplete", i.e., there may be The constant J1 E ~ is the (logarithmic) expected more than one possible pricing formula. This is rate of return, while CT > 0, called the volatility, is clearly undesirable, and a number of selection prin a measure of the excitability of the market. We will ciples, such as entropy minilnization, have been em have more to say about volatility below. Black and ployed to overcome this problem. For hyperbolic Scholes obtained an exact formula for the unique processes, a pricing formula has been developed price of a European option (i.e., one that can only that has minimum entropy and that is claimed to be exercised at time n using the normal distribu be an improvement on the Black-Scholes formula. tion. The derivation of this formula involves the use Another problem with the Black-Scholes of tools such as martingales and Girsanov trans Merton formula is the constancy of the volatility. forms, and it is this link with stochastic analysis Empirical studies suggest that this should vary to that so excited the probabilistic community. give a curve called the "volatility smile". This has Although very elegant, the Black-Scholes-Merton prompted some authors to propose "stochastic model has limitations and possible defects that volatility models" wherein CT is replaced in the have led many probabilists to query it. Indeed, em standard Black-Scholes model by a random process pirical studies of stock prices have found evidence that solves a stochastic differential equation. There of heavy tails, which is incompatible with a Gauss are a number of different approaches to this; e.g., ian model, and this suggests that it might be fruit 0. Barndorff-Nielsen and N. Shephard have recently ful to replace Brownian motion with a more gen proposed that (CT(t)2, t :e:: 0) should be an Ornstein eral U~vy process. Indeed, H. Geman, D. Madan and Uhlenbeck process driven by a subordinator M. Yor have argued that this is quite natural from (T(t), t :e:: 0), i.e., DECEMBER 2004 NOTICES OF THE AMS 1341 so that T1 is a pseudodifferential operator with a-(t)z = e- M u(O)z + e- A(t - s)dT(i\s), J: symbol e11J. Formal differentiation can be justified, and we find that where i\ > 0. As T has finite variation (w.p.l), the integral is well defined in the random Lebesgue (Af)(x) = (2rr) -~ I eiCu ,xl i'J(u)f(u)du, Stieltjes sense. J IJ!. d Readers who want to learn more about "Levy fi so A is also a pseudodifferential operator, with sym nance" should consult [12], [4] , chapter 5 of [1], boll']. Using the Levy-Khintchine formula (0.1) and and references therein. elementary properties of the Fourier transform, we obtain the following explicit form for the action Markov Processes, Semigroups, and of the generator on S(IR\d) Pseudodifferential Operators Levy processes are, in particular, Markov processes, (0.4) i.e., their past and future are independent, given d l d the present. This is formulated precisely using (Af)(x) = I b;o;f(x) + z I a;jD;oJf(x) i= l i,j= l the conditional expectation: [(f(X(t + u))l.'fr) = [(f(X(t + u))IX(t)), for all t, u ~ 0 and all + f [f(x + y)- f(x)- I y;o;f(x)liiYII< l(Y)] v(dy). Jmtd -{0} i ~l f E Bb(IR\d)-the Banach space, under the supre mum norm, of all bounded Borel measurable Using more sophisticated methods the domain in functions on IR\d. Here "the past" .'fr is the smallest (0.4) can be extended to a larger space of twice dif sub-a--algebra of .'f with respect to which all ferentiable functions in C0 (1R\d). Here are some spe X(s)(O :s; s :s; t) are measurable. We define a two cific examples of interesting generators: parameter family of linear contractions 1. Brownian motion (with a = I) is generated by (Ts t; 0 :s; s :s; t < oo) on Bb(IR\d) by the prescription (one-half times) the Laplacian, i.e., (Ts: tf)(x) = [(f(X(t))IX(s) = x) = JIJ!.d f(x + y)pr(dy). A= ~ If=l of = ~~- Then the Markov property implies that these form an evolution, i.e., Tr,sTs,t = Tr,t . for all r :s; s :s; t. 2. Rotationally invariant ex-stable processes (with Note that these operators all commute with the nat a- = 1) are generated by fractional powers of ural action ofthe translation group of IR\d onBb(IR\d). the Laplacian: A=-(-~) ~ . Levy processes form a nice subclass of Markov 3. For the relativistic process, we have processes. First, they are time-homogeneous, A= -(.Jm2 c4 - c 2 ~- mc2 ). i.e., Ts,t = To,t-s foralls :s; t.IfwenowwriteTr = To,t. In the last example, -A is called a relativistic the evolution property becomes the semigroup Schrodinger operator in quantum theory. Note that law Ts Tr = Ts +t· Second, Levy processes are Feller A is obtained from its symbol through the corre processes, i.e., each Tr preserves the Banach space spondence p - -i\1, which is precisely the usual C0(1R\d) of continuous functions on IR\d that vanish rule for quantization, although this is more natu at infinity and limr!OIITrf-fii=O, for all rally carried out in a Hilbert space setting (see f E C0 (1R\d). Hence (T1 , t ~ 0) is a strongly continu below). ous, one-parameter contraction semigroup on If A z is the generator of the Levy C0 (1R\d), and by the general theory of such process Z(t) = X(T(t)) obtained from a Levy semigroups, we can assert the existence of the process X with characteristic exponent I'Jx, associ . T(t)f - f ated semigroup (Tf, t ~ 0), and generator Ax using generator Af = hmr 1o , for all f E D A. The t an independent subordinator T with Laplace ex domain D A is a linear space that is dense in C0(1R\d) ponent f./J, then the identity I'Jz = -fjJ o -l']x, quan and A is a closed linear operator. We can explicitly tizes nicely to yield A z = -fjJ( -Ax). In particular, compute the semigroup and its generator as pseu we can use the ex-stable subordinators to define dodifferential operators. For convenience, we work fractional powers of -Ax using the following beau in Schwartz space S(IR\d)-the space of all smooth tiful formula functions on IR\d that are such that they and all their "' (X r xf ds derivatives decay to zero at infinity faster than any -(-Ax) f = f(l- ex) Jco, co) (Ts -f) sl+ e<. negative power of lxl. S(IR\d) is dense in C0(1R\d) and is a natural domain for the Fourier transform A deep generalization due to R. S. Phillips allows the replacement of Ax and Tx with the generator f(u) = (2rr)- ~ JIJ!.d e- i(u ,xlf(x)dx. Fourier inversion 1 of a general contraction semigroup on a Banach then yields f(x) = (2rr) - ~ JIJ!.d f(u)ei(u,xldu. Applying space. theorem 0.1, we compute The semigroup associated with each Levy (Trf)(x) = (2rrt~ ~ ei(u,x)etlJ(u)f(u)du, process also operates in each LP(IR\d)(l :s; p < oo) JIJ!.d and is again strongly continuous and contractive. 1342 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Since S(l~d) is dense in each LP(!RI.d), the pseudo dodifferential operators should be aware that the differential operator representations discussed map x - ry(x, u) does not, in general, have nice above still hold here. From now on, we take p = 2. smoothness properties. The generator corresponding to the symbol 17 Recurrence, Transience, and Bound States has maximal domain J{IJ(!RI.d)-the nonisotropic From an intuitive point of view a stochastic process Sobolev space of all f E L 2(!RI.d) for which is recurrent at a point x if it visits any arbitrarily I~ d lry(u)i2 lf(u)i2du < oo. small neighborhood of that point an infinite num Standard semigroup theory tells us that a nec ber of times (w.p.1), and it is transient if each such essary and sufficient condition for each T1 to be self neighborhood is only visited finitely many times adjoint is that -A is positive, self-adjoint. A nec (w.p.1). More precisely, a Levy process is recurrent essary and sufficient condition for this is that the (at the origin) if liminfr-oo IX(t)l = 0 (w.p.1) and associated Levy process is symmetric, i.e., transient (atthe origin) iflimr-oo IX(t)l = oo (w.p.1). P(X(t) E A)= P(X(t) E -A), and this holds if and The recurrence/transience dichotomy holds in only if that every Levy process is either recurrent or transient. In the 1960s, S. C. Port and C. ]. Stone ry(u) = - -21 u. au+ r (cos(u. y)- 1)v(dy). proved that a Levy process is recurrent if and only J ~d-{ Q } if f11ull 0. It follows This yields a probabilistic proof of self-adjoint that Brownian motion is recurrent ford = 1, 2 and ness (on J{IJ(!RI.d)) of each of the three operators dis that for d = 1 every £X-stable process is recurrent cussed above. if 1 .:-; lX < 2 and transient if 0 < lX < 1. For d ~ 3, Let A be the self-adjoint generator of a sym every Levy process is transient. metric Levy process and for each f,g E C;'(!RI.d), In the 1990s, R. Carmona, W. C. Masters, and define 'E(f,g) =- < f,Ag >, then 'E extends to a B. Simon studied the spectral properties of Hamil 2 symmetric Dirichlet form in L 2(!RI.d), i.e., a closed tonian operators acting in L (!RI.d) of the form symmetric form in H with domain D, such that H = H 0 + V, where H 0 is (minus) the generator of f E D ~ (f V 0) 1\ 1 E D and 'E((f V 0) 1\ 1) .:-; 'E(f) a symmetric Levy process X and Vis a suitable po for all f E D, where we have written 'E(f) = 'E(f, f). tential. In particular, they were able to show that A straightforward calculation yields H has at least one bound state (i.e., a negative eigenvalue) if and only if X is recurrent. In partic ular, in the physically interesting case in which H 0 'E(f, g) -1 Id aiJ i (o;{)(x)(oJg)(x)dx is a relativistic Schrodinger operator, bound states 2 i,j= l ~d are obtained only in dimension 1 and 2. + -21 r (f(x) - f(x + y)) . J( ~dx~d)- D levy Processes in Groups So far we have dealt exclusively with Levy processes (g(x) - g(x + y))v(dy)dx, taking values in a Euclidean space. Now we will re place !RI. d with a topological group G. First some gen where Dis the diagonal, D = {(x, x), x E !RI.d}. This eral remarks. The interaction between probability is the prototype for the Beurling-Deny formula for theory and groups has been an active area of re symmetric Dirichlet forms. search since the 1960s-indeed, this is the natural Now we return to the space C0(!RI.d). The ideas we setting for studying the interaction of "chance" explored there have a far-reaching generalization, with "symmetry". One area of research that is cur originally due toW. von Waldenfels and P. Cour rently attracting enormous interest is random ma rege in the early 1960s and recently systematically trix theory [5], partly because of intriguing links be explored by N. Jacob and his school in Erlangen and tween the asymptotics of uniformly distributed Swansea [7]. The main starting point of this is that matrices in the unitary group U(n) and the zeros if X is a general Feller process defined on !RI.d that of the Riemann zeta function. A survey on random has the property that the smooth functions of com walks and invariant diffusions in groups can be pact support are contained in the domain of its gen found in [10), with particular emphasis on there erator A, then we can always represent A as a lationship between the asymptotic behavior of the pseudodifferential operator process and the volume growth of the group. A Levy process on a topological group G is de (Af)(x) = (2rr) -~ f ei(u,xlry(x, u){(u)du. fined exactly as in the Euclidean case, but within J ~ d the axioms (Ll) and (L3), the increment X(t) - X(s) Note that the symbolry now has an additional x is replaced by X(st1 X(t) (with the group operation dependence; however, each ry(x, ·) is still a char written multiplicatively), whereas in (L2), the role acteristic exponent, so that we get an appealing in of 0 is played by the neutral element that we de tuitive understanding of X as a "field of Levy note by e. If Pr is the law of X(t), then (Pr. t ~ 0) is processes" indexed by space. Aficionados ofpseu- a weakly continuous convolution semigroup of DECEMBER 2004 NOTICES OF THE AMS · 1343 probability measures on G, so that in particular where b = (bl, ... , bn) E ~n, a = (aij), is a non Ps+t(A) = fc Pt(T-1 A)ps(dT). negative definite, symmetric n x n real-valued ma There are three cases of interest-locally com trix and v is a Levy measure on G - {e} . pact abelian groups (LCA groups), Lie groups, and general locally compact groups. The LCA case was Conversely, any linear operator with a representa extensively studied during the 1960s. The fact that tion as in (0.5) is the restriction to C2(G) of the in the dual group G of characters is itself an LCA finitesimal generator of some Levy process. group allows a natural generalization of the Fourier The characteristics (b, a, v) of a Levy process de transform from ~d toG, and a Levy-Khintchine for termine its law, just as in the Euclidean case. mula that characterizes Levy processes can hence In the 1990s, H. Kunita and the_author were be developed similarly to the Euclidean case. We able to generalize the Levy-Ito decomposition to the will not dwell further on this topic here; interested extent that for each f E C2(G), the real-valued readers are directed to section 5.6 in [6]. process f(X) = (f(X(t), t ;::: 0) can be described The case in which G is a Lie group has been ex (using stochastic integrals in the sense ofK. Ito) in tensively studied. For non-abelian G, there is nodi terms of a Brownian motion on ~d and a Poisson rect analogue of the Fourier transform available, random measure on~ + x (G- {e}). We now give and one of the joys of the subject is the challenge some examples of Levy processes on a Lie group of surmounting this obstacle using tools from G: semigroup theory, stochastic analysis, group rep 1. Brownian motion in G. resentations, and noncommutative harmonic analy sis. The first important step in this direction was This is a Levy process that has characteristics (0, I, 0). It has continuous sample paths (w.p.l ), taken by G. A. Hunt in 1956. He effectively char and its generator is (up to the usual factor of one acterized Levy processes in Lie groups by gener half) a left-invariant Laplacian on G, ~G = :Z::f= 1 Yj. alizing the formula (0.4) for the generator in ~d. To The basis dependence is a nuisance here. It can be be precise, let X = (X(t), t ;::: 0) be a Levy process on dispensed with by equipping G with a left-invari ad-dimensional Lie group G and let Pt be the law ant Riemannian metric m, with respect to which of each X(t). We obtain a one-parameter, strongly { Y1, ... , Yd} is orthonormal. ~c is then the Laplace continuous, contraction semigroup (Tr, t ;::: 0) with Beltrami operator associated to (G, m) and the cor generator A on C0(G) by the prescription responding Brownian motion is a geometrically in trinsic object-indeed, it has played a central role (Trf)(T) = IE({(T X(t))) = Lf(TO")Pr(do-). in recent years within the development of analy sis in path and loop spaces. Note that Tr commutes with left translations. Now let {Y 1, ... , Yd} be a fixed basis for the Lie algebra 2. The Compound Poisson Process g of left-invariant vector fields on G. Define a Let CYn. n E N) be a sequence of i.i.d. random linear manifold C2(G) that is dense in C0(G) by the variables taking values in G with common law f1 prescription C2(G) = {f E Co(G); Y;{ E C0(G) and and let (N(t), t ;::: 0) be an independent Poisson Y;Yjf E C0 (G) for all 1 :s: i,j :s: n}. Hunt showed process with intensity i\. > 0. We define the com that there exist functions X; E C2(G), 1 :s: i :s: n pound Poisson processinG by Y(t) = J'1 J'2 ... J'N(tl· so that (x1, ... , Xn) is a system of canonical In this case the generator is bounded and is given coordinates for G at e. A Levy measure v is by (.Jlf)(T) = fc(f(To-)- f(T))v(do-), for each a Borel measure on G- {e} for which f E Co( G) where the Levy measure v( ·) = i\.p( ·) is finite. fc-[eJ [ ( :Z::f=l X;(o-)2) 1\ 1] v(do-) < oo . Hunt was then able to obtain the following key result: 3. Stable Processes Theorem 0.2 [Hunt's Theorem]. If X is a Levy The theory of stable processes in Lie groups processinG with infinitesimal generator .Jl, then was developed by H. Kunita in the 1990s. His ap proach was to generalize the self-similarity prop 1. C2(G) <;: Dom(.Jl). erty, and for this he needed a notion of scaling. This 2. For each T E G, f E C2(G), is provided by a dilation, i.e., a family of automor (0.5) phisms 8 = (8(r), r > 0) for which 8(r)8(s) = 8(rs) for all r, s > 0, which also possess suitable conti d 1 d (5\.f)(T)= L b; Y;{(T) + 2 L aij Y; Yj{(T) nuity properties. A Levy process X in G is stable i=l i,j=l with respect to the dilation 8 if 8(r)X(s) has the same law as X(rs) for each r, s > 0. Dilations (and + r . [f(TU) - f(T)- ±X;(U)Y;{(T)] v(du), hence stable Levy processes) can exist only on sim J c-[e} i=l ply connected nilpotent groups. Stable processes 1344 NOTICES OF THE AMS VOLUME 51, NUMBER 11 in such groups have some surprising properties, gated by A. Bendikov and L. Saloff-Coste at Cornell. e.g., Kunita has shown that there is no dilation It will be interesting to see if the new techniques with respect to which Brownian motion in the they've developed can be applied to moregeneral Heisenberg group is stable. It is however possible classes of Levy processes. to construct a stable process on this group whose first two components are Brownian motion whereas Levy Processes in Quantum Groups the third is a Cauchy process. Through the work of physicists such as N. Bohr, M. Born, and W. Heisenberg and its mathematical 4. Subordinated Processes formulation by J von Neumann, we came to a dual Let Y = (Y(t), t 2. 0) be a Levy process on G and understanding of quantum mechanics. On the one T = (T(t), t ;:::. 0) be a subordinator that is inde hand, physical observables such as position, mo pendent of Y. Just as in the Euclidean case, we can mentum, energy, and spin should be described as construct a new Levy process Z = (Z(t), t ;:::. 0) by (not necessarily bounded) self-adjoint linear oper the prescription Z(t) = Y(T(t)), for each t;:::. 0. ators acting in a complex Hilbert space. On the Levy processes in Lie groups is a subject that is other hand, these observables are also random currently undergoing intense development-see quantities whose statistical properties are deter the author's survey article in [2) and the recent book mined by a unit vector in Hilbert space (for pure by M. Liao [8). The latter contains a lot of interest states) or a more general density matrix (for mixed ing material on the asymptotics of Levy processes states). However, the celebrated Heisenberg un on noncompact semisimple Lie groups, as t ~ oo. certainty principle tells us that certain pairs of Liao has also found some classes of Levy these operators, such as those representing posi processes on compact Lie groups that have L 2- tion and momentum, fail to commute. Conse densities. The density then has a "noncommutative quently they cannot both be described together as Fourier series" expansion via the Peter-Weyl theo measurable functions on the same probability space rem. In the special case of Brownian motion on using Kolmogorov's prescription, and hence they SU(2), Liao obtains the following beautiful formula cannot have a joint probability distribution. for its density Pt at time t: To describe the probabilistic features of quan tum theoretic phenomena systematically, we need ~ ( (n2 - 1)t) sin(2rrne) to take an algebraic viewpoint. We define a quan Pr(e) = ~ n exp - 64rr2 sin(2rr8) ' tum probability space to be a pair (B, w) where B is a complex *-algebra (with identity I) and w is a where 8 E (0, 1) parameterizes the maximal torus state on B, i.e., a positive, linear map for which {diag ( e2rriO, e- 2rri8) , 8 E (0, 1)} . w(I) = 1. If B is a C*-algebra, we can recover a Another important theme, originally due to R. Hilbert space viewpoint by taking the Gelfand Gangolli in the 1960s, is to study spherically sym Naimark-Segal representation. metric Levy processes on semisimple Lie groups G Quantum stochastic processes were introduced (i.e., those whose laws are hi-invariant under the by L. Accardi, A. Frigerio, and J T. Lewis in the action of a fixed compact subgroup K). Using Har 1980s. Every "classical" stochastic process ish-Chandra's theory of spherical functions, one can (X(t), t ;:::. 0) with state space E gives rise to a fam carry out "Fourier analysis" and obtain a Levy ily of * -homomorphisms Ur. t ;:::. 0) from the Khintchine-type formula. One of the reasons why *-algebra Bb(E) of bounded m easurable functions this is interesting is that G I K is a Riemannian on E into the * -algebra L "" (Q, _r, P) by the pre (globally) symmetric space and all such spaces can scription Jr(f) = f o X(t). Given a quantum proba be obtained in this way. The Levy processinG pro bility space (B, w) and a *-algebra A, a quantum jects to a Levy process in G 1K, and this is the pro stochastic process is a family Ur. t 2. 0) of totype for constructions of Levy processes in more *-homomorphisms from A into B. Many concrete general Riemannian manifolds. examples of these have been constructed using Before leaving the subject of Levy processes in the quantum stochastic calculus of R. L. Hudson groups, we briefly mention the general locally com and K. R. Parthasarathy as solutions of operator pact case. Work on Hilbert's fifth problem during valued stochastic differential equations driven b y the 1950s established that every such group has "quantum noise", i.e., the creation, conservation, an open subgroup of the identity that is a projec and annihilation processes acting in a suitable Fock tive limit of Lie groups. This enables the use of Lie space. group methods within the more general case, and In order to clarify the last remark, we make a there has been intensive work on this subject since brief diversion. Fock space [(h) over a complex the 1970s by the German school of H. Heyer, W. Hilbert space h is f(h) := EB ~= o h D ECEMBER 2004 NOTICES OF THE AMS 1345 space, which are the closed sub spaces obtained by Ll : A ~ A ® A and a co-unit E : A ~ 1346 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Conclusion One way of assessing the health of an area of math About the Cover ematics is to explore the extent to which it per Kleinian Pearls meates other aspects of the subject. Another way This month's cover was created by David is to examine its use in applications. Regarding Wright, who explains it in a brief article in this both of these criteria, Levy processes appears to issue (pages 1332-1333). He entered it in the in be flourishing. Indeed, limitations of space this 2003 NSF Visualization Challenge, in which it article have prevented me from discussing a host was a semifinalist. Limit sets of Kleinian of other topics, including new theoretical advances groups and how to draw them are major in the fluctuation theory of real-valued Levy themes of the well-illustrated book Indra's processes due to ]. Bertoin and R. A. Doney and ap Pearls (Cambridge University Press, 2002), plications to turbulence, time series, and the cod written by Wright with coauthors David Mum ification of branching processes. Readers are invited ford and Caroline Series. to join the author in speculating that the interplay of Gaussian continuous motion with Poisson jumps, -Bill Casselman or alternatively its quantum theoretic manifesta Graphics Editor tion within the dance of creation, conservation, ([email protected]) and annihilation operators, is a universal feature of a class of random motions (both classical and quantum) that is sufficiently wide to keep mathe maticians busy for many years to come. Acknowledgement: Thanks are due to Chris Rogers for invaluable advice about simulation. References [1] D. APPLEBAUM, Levy Processes and Stochastic Calculus, Cambridge University Press, 2004. [2] 0. E. BARNDORFF-NIELSEN, T. MIKOSCH, and S. RESNICK (Eds.), Levy Processes: Theory and Applications, Birkhauser, Basel (2001). [3]]. BERTOIN, Levy Processes, Cambridge University Press, Cambridge, 1996. [4] R. CoNT and P. TANKOV, Financial Modelling with jump Processes, Chapman and Hall/CRC (2004). [5] P. DIACONIS, Patterns in eigenvalues, the 70th Josiah Willard Gibbs lecture, Bull. Amer. Math. Soc. 40, 155- 79 (2003). [6] H. HEYER, Probability Measures on Locally Compact Groups, Springer-Verlag, Berlin-Heidelberg, 1977. [7] N. ]ACOB, Pseudo-differential Operators and Markov Processes: 1. Fourier Analysis and Semigroups, World Scientific (2001). 2. Generators and their Potential The ory, World Scientific (2002). [8] M. LIAo, Levy Processes in Lie Groups, Cambridge Uni versity Press, Cambridge, 2004. [9] P.-A. MEYER, Quantum Probability for Probabilists, (sec ond edition), Lecture Notes in Mathematics Vol. 1538, Springer-Verlag, Berlin, Heidelberg, 1995. [10] L. SALOFF-CosTE, Probability on groups: random walks and invariant diffusions, Notices Amer. Math. Soc., 48, 968-77 (2001). [11] K.-l. SATO, Levy Processes and Infinite Divisibility, Cambridge University Press, Cambridge, 1999. [12] W. ScHOUTENS, Levy Processes in Finance: Pricing Fi- nancial Derivatives, Wiley, 2003. · [13] M. ScHDRMANN, White Noise on Bialgebras, Lecture Notes in Mathematics 1544, Springer-Verlag, Berlin, Heidelberg, New York, 1991. DECEMBER 2004 NOTICES OF THE AMS 1347 Global Calculus Global Calculus S. Ramanan, Chennai Mathematics Institute, India Complex differential geometry is a beautiful subject. Its elegant theo rems are drawn from many areas of mathematics and provide deep insight into the geometry of complex manifolds. Here, the story of complex geometry is presented by one of the masters of the subject. Graduate Studies in Mathematics, Volume 65 ; 2005; approximately 360 pages; Hardcover; ISBN 0-8218-3702-8; List $55; All AMS members $44; Order code GSM/65N C!l5~~sroom I The AdvJnture of Numbers For ctJ Classroom Gilles Godefroy, Institut de Six Themes on Use Mathematiques de Jussieu, Paris, Variation 3-Manifolds France, and Directeur de Recherches at John Hempel, Rice University. the C.N.R.S. , Paris, France Robert Hardt, Rice University, Houston, TX, Editor Houston, TX Mathematical World, Volume 21 ; AMS Chelsea Publishing; 2004; 194 pages; Softcover; Student Mathematical 2004; 195 pages; Hardcover; ISBN 0-8218-3304-9; List $29; Library,Volume 26; 2004; ISBN 0-8218-3695- 1; List $29; All AMS members $23; Order approximately 176 pages; code MAWRLD/21 N Softcover; ISBN 0-8218-3720-6; List $29;AII AMS members $23; Order code STMU26N 1-800-321-4AMS (4267) in the U.S. and Canada or 1-401 -455-4000 (worldwide); fax: 1-40 1-455-4046; email: [email protected]. American Mathemati<.:al Society, , 20 I Charles Street, Providence, Rl 02~04-2294 , USA For many more publications of interest, visit the AMS Bookstore , www.ams.org/booksto' re • View papers online prior to their publication in print. • Notices of the AMS and Bulletin of the AM S are free to members. • The AMS also distributes mathematics journals from other publishers. Home 1 Ad, ~-.:.J.rch 1 EmwriAierts 1 For Au t hors 1 Contact 1 Srterv1ap 1 Help 1 Your Subscnptrons @2001 2004 by th~ Am~reo::an Mathematical Sr~cretJ www.ams.org/journals Contact us for additional information or for a complete list of AMS-distributed journals, visit www.ams.org/distribution. *A 30-day free. trial is available to corporations and academic institutions. A downloadable Free Trial Form is available at: www.ams.org/customers/msntrial.pdf or www.ams.org/customers/ejournaltrial.pdf. For more information, contactAMS Membership and Customer Services, 20 I Charles Street, Providence, Rl 02904-2294 USA; phone 1-800-321-4267 or 1-401-455-4000 worldwide; fax 1-40 1-455-4046; email: [email protected]. ®AMS AMERICAN MATHEMATICAL SOCI:ETY W H A T s a Flip? Alessio Corti A flip is a special codimension-2 surgery in alge tracts the exceptional set E toP. If X = ( 2 with co braic geometry. ordinates (x, y), and P = (0, 0), then Flips turn up, for example, in the study of com pactifications of moduli spaces. Constructions in Y = {xm1 - ymo = 0} c ( 2 x 1Jll 1 algebraic geometry depend on parameters (mod where m0 , m1 are homogeneous coordinates on uli). For instance, Riemann surfaces of genus g are 1Jll 1. The function m = m1 / mo is well defined on in natural 1-to-1 correspondence with the points the chart {m 0 I= 0}, which is identified with the set of an algebraic variety Mw Usually, the moduli {y = mx} c ( 3 . The point at infinity corresponds space is noncompact, making it unsuitable for the to the vertical line {x = 0}. study of enumerative and topological questions. Doing this construction inside real algebraic Several meaningful compactifications are possi geometry produces the picture of a helix; topo ble, and they are related by flips. Understanding the logically, one cuts out a small disk and replaces it 'different compactifications in terms of flips can with a Mobius strip. lead to beautiful and difficult combinatorial ques In the language of algebraic geometry, a surgery tions. Among the first examples of this point of view is called a birational map. By definition, a bira is the work of Thaddeus on stable pairs on curves; tional map cp: Y ··X is an isomorphism a recent variation on this theme is the treatment cp : y " E - X " F, exceptional sets E of 3-fold flops by Bridgeland, which I describe where the c Y and F c X are algebraic subvarieties. below (a flop is a kind of flip). In the case of a flip, the exceptional sets E Y Flips are steps in Mori's minimal model pro c and F X are small, that gram. Starting with a nonsingular projective vari c is, they have codimension ety X, the minimal model program is an analog of 2: 2. By contrast, in the blow-up f: Y - X of a nonsingular E Y the geometrization program in topology; its aim is point, the exceptional set c is of to perform surgery on X until the canonical line codimension 1. bundle Kx = /\ topT* X has global positivity prop Topological surgery arises in nature when we erties. cross a critical value of a c oo Morse function The simplest example of surgery in algebraic h: M - IRL As we cross a critical value to, the level 1 1 geometry is the blow-up f: Y - X of a nonsingu set h- (t0 - E) is surgically modified into h- (to + E). lar point P of a surface X. The surface Y is formed By the Morse lemma, a local model of this situa by removing P E X and sticking the projectivized tion isM= ~n x ~m with coordinates (x, y) such tangent space E = IP:'TpX in its place. The morphism that f: Y- X identifies Y "E with X"- {P} and con- (x,y)- h(x,y) = -llxll 2 + [[y[[ 2 • Alessio Corti is Reader at the University of Cambridge, UK. We see that, as t crosses to, the level set undergoes His email address is a. co rti @dpmms. cam. ac. uk. a surgery in which sn- l X Dm is replaced by 1350 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Dn X sm-l (where sn and Dn denote the n-dimen - fc c1 (Kx- ) ~ 0 on curves C contracted by p - , and sional sphere and ball). Integrating along the gra Kx+ is nef over Z . dient of h, we get an action of the additive group Usually, p - : x- ~ Z is given, and the problem IR{ on M; the level sets h- 1(t) fort = t0 ± E are dif is to show that p +: x + ~ Z exists. The flip can feomorphic to the quotients M±I !R{, where exist only in very restricted conditions, and the few M- = M "- {x = 0} and M + = M "- {y = 0}. known existence results are very difficult to es I use an analog of this construction over the com tablish. Mori proved that if x- is a 3-fold with ter plex numbers to give an example of a flip. Consider minal singularities, then the flip exists. The exam the action of the multiplicative group (X on B = ([4 ple above is one of these flips considered by Mori. with weights (-2, -1, 1, 1): In the case of flops, where Kx- = K x+ = 0, Bridgeland shows that x + is the moduli space of (xl,Xz,Yl.Yz) ,_. (A - 2xl,A- 1xz,Ayl,Ayz). certain sheaves on x- (more precisely, complexes The quotient topology by this action is not Haus of coherent sheaves in the derived category), thus dorff. Indeed, a general orbit is asymptotic to an providing a construction of x +. This idea has since orbit in {y = 0} as A ~ 0 and to an orbit in {x = 0} been applied, with mixed success, to the problem as A ~ oo. There are two meaningful ways to get a of existence of flips. Hausdorff topological space, and they are related Flips are fundamental in algebraic geometry in by a flip. Indeed, consider open subsets dimension ~ 3 ; the best place to start learning B- = B " {x = 0} and B+ = B " {y = 0} . Then about them is [1] . x - = B- I (X and x + = B+ 1(X are Hausdorff topo For many applications, it is desirable to have ex logical spaces with a natural structure of algebraic plicit equations of all 3-fold flips. A paper of Mori varieties, and the obvious birational map [2], which is a great place to look for examples of cp: x- •X + is a flip. Note that x- is covered by flips, classifies the important special case of semi charts{x1 obO} ~ 112(1,1,1)(thequotientof([3 by stable flips. a reflection of all coordinates) and {x 2 ob 0} ~ ([3 • In his work [3], Shokurov proves the existence This example also illustrates Wlodarczyk's view of flips in dimension 4. His work is based on an of a flip as a birational cobordism, which leads to important extension of the Mori category, the cat the proof by him, with Abramovich, Karu, and Mat egory of log terminal pairs (X, B) of a variety X and suki, of the factorization theorem, stating that a hi a boundary Q-divisor B = 2: b;B;. In this notation, rational map between nonsingular varieties is a the B; c X are irreducible subvarieties of codi composition of blow-ups and blow"downs along mension 1 and the coefficients 0 < b; :o; 1 are ra nonsingular centres. tional numbers. Initially at least, B is psychologi The few nineteenth-century birational geometers cally a boundary, in the sense that one's emotional who ventured into higher dimensions were on some investment is in the complement X " B. The proof level aware of codimension-2 surgery. However, uses the graded ring R = Elln~of(X, n(Kx +B)) of flips were only discovered recently as steps of the global holomorphic differentials satisfying growth minimal model program. If X is a projective vari conditions at the boundary. For an introduction, see ety, the minimal model program performs surgery A Corti, 3-fold flips after Shokurov, http: ll www. on X until the canonical line bundle Kx is nef, that dpmms. cam. ac. uk/ ~ corti /flips. html. is, degKx1c = cl(Kx) ~ 0 References L [1]]. KOLLAR, Flips, Flops, Minimal Models, etc., Surveys in for all algebraic curves C c X (c1 denotes the first Differential Geometry (Cambridge, MA, 1990), 11 3-199, Lehigh Univ., Bethlehem, PA, 1991. Chern class). To achieve this, it is necessary to [2] S. MoRJ, On Semistable Extremal Neighborhoods, Higher allow X to have mild (to be precise, terminal) sin Dimensional Birational Geometry (Kyoto, 199 7), gularities, for example certain orbifold singulari 157-184, Adv. Stud. Pure Math., 35, Math. Soc. Japan, ties, for which Kx still makes sense. Tokyo, 2002. The formal definition of flip requires a diagram [3] V. V. SHOKUROV, Prelimiting flips, Proc. Steklov Inst. Math. 240 (2003), 75-213. x------~ -- .._ x+ The "WHAT IS ... ?" column carries short (one- or two-page) nontechnical articles aimed at graduate students. Each article focuses on a single mathe matical object rather than a whole theory. The Notices where p± are small birational morphisms with com welcomes feedback and suggestions for topics. Mes sages may be sent to noti ces-whati s@ams. org. pact fibres, such that -Kx- is nef over Z, that is, DECEMBER 2004 NOTICES OF THE AMS 1351 Book Review Strange Curves, Counting Rabbits, and Other Mathematical Explorations Reviewed by Harold R. Parks Strange Curves, Counting Rabbits, and Other distribution, Stirling's Mathematical Explorations formula, coin-weigh Keith Ball ing problems, testing Princeton University Press, 2003 of pooled blood sam Hardcover, 296 pages, $29.95 ples, Fibonacci and ISBN 0-691-11321-1 Lucas numbers, par tial fractions, Pade According to its preface, the genesis of this approximation, and book was a lecture given to the math club at a the irrationality of e school where a friend of the author was a teacher. and rr. A number of That lecture and subsequent lectures on "recre other topics are used ational" or "popular" mathematics in schools and as motivation, men to school students, together with a few other top tioned in passing, ics, formed the basis for the book. The schools used as illustrations, mentioned above were in the United Kingdom, not and so on. the United States, so the "math club" was a "maths The author's writ club," and if you have formed an impression of the ing style is informal, inviting, and clear. Some de level of this book, you need raise it substantially: tails of some arguments are stated as problems, but The author's lectures would probably be appro the solutions are provided. Not all problems are priate for the math club at a college or university there to fill in gaps; some are there to give the in the United States and would be way over the top reader a little more to think about (solutions are for any U.S. high school students other than the provided for those also). Every chapter has some most advanced, talented, and enthusiastic. Even problems stated for the reader to work on, as few though the library of Congress classification of this as three, and as many as eight, but usually five. As book is "QA93 Popular works," a sound knowl in all human endeavors, there are some errors; as edge of calculus is a prerequisite for many parts an existence proof, I note that the word "number" of the book. on page 194, line 10, should not be there. The er The "strange curves" of the title are space-filling rors are remarkably few, and the author is to be curves (orPeano curves), the "counting rabbits" of the congratulated on a very careful job. title refers to the Fibonacci sequence, and the "other The first chapter, "Shannon's Free Lunch," is mathematical explorations" cover quite a bit of about codes. There are essentially no prerequisites ground. Let us now list the major topics discussed until just before the end. The author begins with in the book: Hamming codes, Shannon's theorem, a discussion of the check-digit in the ISBN code. The idea of having check-digits is well known among Pick's theorem, Fermat's Little Theorem, space filling curves, the probability of shared birthdays, mathematicians, but there are a lot of nonmathe maticians who have never heard of such a thing. the normal approximation to the binomial Everything in this chapter would be news to them. The first ISBN example is self-referential: The ex Harold R. Parks is professor of mathematics at Oregon State University in Corvallis. His email address is ample is 0-691-11321-1, the ISBN of Strange Curves, [email protected]. Counting Rabbits, and Other Mathematical 1352 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Explorations itself. That seems a tricky thing to conjecture in hand, the author leads the reader arrange; I was very surprised by that example. through a proof. In the course of proving the pre The issue in this chapter is the transmission of ceding facts it emerges that, for primes other than data on a noisy channel. The best possible rate of 2 or 5, lQP- l - 1 is divisible by p. Consequently, for transmission on a noisy channel was character all primes p, lOP- 10 is divisible by p. Since 10 is ized by Claude Shannon in 1948. The author refers not particularly special, the reader has been led to to this characterization as "Shannon's free lunch". Fermat's Little Theorem: If pis a prime and a is an I don't quite agree with the choice of metaphor. integer, then aP is congruent to a modulo p. Shannon's theorem tells us that there is necessar The fourth chapter, "Strange Curves," is about ily a trade-off: If your channel gets noisier, your space-filling curves. The author constructs exam maximum rate of transmission gets slower. To me ples of such curves using geometric recursion illus a free lunch would be no slowing in transmission trated with nice figures: He starts with a basic rate. The first time Shannon's theorem appears, it pattern in the unit square and then proceeds to is not really stated, as "stated" is understood by a subdivide the square and put a scaled, and possibly mathematician. Presumably, the first chapter is rotated, version of the basic pattern in each sub meant to be accessible, so a precise statement square. The actual curve is the limit of appropriate would be too off-putting. Later, the author does give parametrizations of those recursively constructed a precise statement of Shannon's theorem. curves. Since the author wants to assume that the The second chapter, "Counting Dots," is about reader does not know the basic theorems about uni Pick's theorem. This is also a very accessible chap form convergence of continuous functions, there is ter. Pick's theorem tells us that, for a simple poly a considerable bit of hand-waving. A credible job is gon all the vertices of which are integer lattice done, and it might be a good refresher for a student points, the area of the polygonal region enclosed who has taken advanced calculus but who has not by the polygon is I+ B 12 - 1, where I is the num thought about it lately. The first example of a space ber of lattice points in the interior of the polygo filling curve was constructed by Peano in 1890. nal region and B is the number of lattice points lying Peano's paper, [PG], has no figures. It is a nice feature on the boundary of the polygonal region, i.e., on that the author shows us Peano's original construc the polygon itself. The result dates to 1899 and, we tion in a pictorial form (attributed to Moore and are told, is a staple of recreational mathematics. It Schonflies). was, in fact, the subject of that first lecture the au The next chapter, "Shared Birthdays, Normal thor gave to school students, the lecture that ulti Bells," begins a series of three chapters relating to mately led to this book being written. As an ap probability theory. The chapter starts with the plication, the author uses Pick's theorem to give an shared birthday problem. The question is "Given elegant proof of the fact that, for relatively prime a group of n people, what is the probability that at p and q, there exist integers a and b so that least two have the same birthday, i.e., celebrate their ap - bq = 1. That Pick's theorem cannot hold in birthdays on the same day of the year?" To solve three dimensions is shown by a tetrahedral coun this problem sensibly one must shift to finding the terexample. The author tells us that there are some probability of the complement. At this point the useful things that can be said about lattice points reader must know about logarithms and how to use in polyhedra and that there is some current re calculus to estimate them. The average person is search on this topic, but, regrettably, he gives us now out of the readership. no entree to this current research. The theme of the chapter then shifts a bit to coin The third chapter, "Fermat's Little Theorem and tossing, the normal approximation to the binomial Infinite Decimals," begins with a look at decimal distribution (with equal probabilities of success expansions of rational numbers. As we know, such and failure), and the Central Limit Theorem. High decimal expansions either terminate or are infinitely lights are a wonderful figure showing the annual recurring. The question one might not have thought rainfall at Kew Gardens, in London, for the years about is "What is the period of recurrence in such 169 7-198 7 and a method for computing the Gauss a decimal expansion?" The most interesting cases ian integral that was new to me. No attempt is will be those in which the denominator is prime, made to prove the Central Limit Theorem, but a con so we are led to consider the decimal expansion of vincing case is made for the normal distribution kjp where pis prime and l .::s; k ::s; p- 1. Since 2 and providing a good approximation to the binomial 5 are divisors of 10, they are special and, for these distribution. purposes, anomalous. But the other primes are Now that the gauntlet of calculus has been seen, by example, to fit a nice pattern: For a given thrown down, the chapter "Stirling Works" tackles prime p, other than 2 or 5, the decimal expansion a derivation of Stirling's formula. The arguments of k/p has the same period, independent of k, and feel natural and are very nicely presented. They the number of different types of decimal expan might be heavy going for the popular reader, even sions is p - 1 divided by that period. With a the popular reader who did well in calculus. DECEMBER 2004 NOTICES OF THE AMS 1353 In chapter 7, "Spare Change, Pools of Blood," the fractions and matrices, tools that will continue to level of mathematical sophistication eases up a be used as we approach the proofs of irrationality bit. The main point of the chapter is solving a prac in the last chapter. tical medical problem: Given a blood test for a The penultimate chapter, "Chasing the Curve," relatively rare condition, could one test a group of has nothing to do with the earlier strange curves in patients more efficiently by applying the test to chapter 4. The topic here is, rather, Pade approxi pooled samples of blood? By pooling the blood to mation. While a Taylor approximation is a polynomial be tested, there is the chance of ruling out, with chosen so that it and its first few derivatives agree just one test, the presence of the condition in the with the given function at the given point, a Pacte entire group of patients whose blood was in that approximation is a rational function chosen so that pooled sample. Such a blood test was, in fact, it and its first few derivatives agree with the given developed by the author's brother-in-law, and that function at the given point. Now, one thing the Tay test is sensitive enough to detect the condition in lor approximation has going for it is that finding a pooled sample from 100 patients. the next one is not that much more work. Before addressing the medical problem, the au At first glance, that seems not to thor explores the coin-weighing problem often seen be the case with Pade approxima tion, in recreational mathematics, since the ideas from but, for certain examples, when one thinks in solving the coin-weighing problem turn out to be terms of continued fractions, the situation looks bet relevant to the pooled-blood-sample problem: The ter. The continued fraction for tan xis developed in coin-weighing problem here is to determine the some detail. For the exponential function and for minimum number of weighings needed to find a the arctangent function, the treatment is lightly coin of greater weight in a group of other coins all sketched. These continued fractions are seen again of which have the same weight. The solution of the in the next chapter. coin-weighing problem very nicely motivates the The final chapter, "Rational and Irrational," is de "binary protocol" for the blood testing: First test voted to proofs of irrationality. It is a bit ironic, after a pooled sample from all the patients. If that test all the reader has been through up to this point, is negative, you are done. If the test is positive, form to see the classical Pythagorean proof of the irra two equally sized groups and test each of those tionality of .J2 given in full detail. But that is a mere pooled samples. Any negative test tells you that that moment. The author's main method for showing group does not have the condition. Any positive test the irrationality of a given number a is to show tells you to divide the group into halves and test that if there is a sequence of rational numbers the halves. A slight refinement of the analysis Pn I qn =I lX which converges too rapidly to a, then shows that one ought to divide the group to be lX is irrational. For instance, if Pn I qn converges to tested into subgroups of size 1 I p, where p is the IX, never equals IX, and (Pn l qn - a)qn ~ 0, then lX probability of the condition, before running any is irrational. To see this, one argues by contradic tests. With this improvement, the author shows tion. Supposing a = P I Q, then we see that that the expected number of tests required for N patients is Np[1 +log2(11p)], and he shows that, PnQ- qnP (Pn l qn - P IQ)qn = Q even if the preceding value could be improved by using a different protocol, it cannot be improved by any more than a factor of two. For simplicity, must converge to 0 but never equal 0. Since the nu the issue of false test results is not addressed. merator is an integer and the denominator is fixed, Subsequent chapters do not rely on any topics we have a contradiction. The author applies the pre from this chapter. ceding argument to show that e is irrational. A Chapter 8, "Fibonacci's Rabbits Revisited," is generalization of that approach, combined with about the Fibonacci numbers, no surprise there, and the continued fraction expansion for tanx, is used the Lucas numbers. Of course, we have all read to show that rr is irrational. some things about the Fibonacci numbers. Typically In summary, this book gives a lively and care there is a heavy dose of examples from nature. fully written treatment of a number of interesting Nature is fine, but in this chapter the author gives topics. The material should be fully accessible to us some meatier mathematics of the Fibonacci mathematics majors. Those who have taken cal numbers. For instance, we see in what sense the culus (and remember some of it) should be able to Fibonacci ratios (i.e., the ratios of successive follow the ideas, if not all the details. The range of Fibonacci numbers) are best approximations to the topics is wide, so even the experienced mathe Golden Ratio. Another gem is the discussion of matician may learn something new. the fact that, for a prime number p, the pth Lucas number minus 1 is divisible by p, a fact that turns References out to be an analogue of Fermat's Little Theorem. [PG] Sur une courbe, qui remplit toute une aire plane, fn this chapter, the author introduces continued Mathematische Annalen 36 (1890), 157- 160. 1354 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Mathematicians' Group to Provide Advice on Math Standards In July 2004, during the Park City Mathematics In Instead, curricula are chosen at the state and local stitute (PCMI), a group of thirteen mathematicians levels. Starting in 1989, the NCTM issued anum met to discuss state mathematics standards doc ber of reports providing principles and guidelines uments and offer advice on school mathematics for developing school mathematics standards. standards. Roger Howe of Yale University, former These reports were enormously influential and chair of the AMS Committee on Education, is the sparked the creation of mathematics standards in leader of the group. Its goal is to prepare a docu all fifty states, as well as standards in other acad ment that will comment generally on standards and also highlight a small number of topics the emic disciplines. group believes are central in school mathematics During the meeting at the PCMI, mathematics curricula. standards documents were brought in from the fifty The formation of the group came about partly states, as well as from the District of Columbia and as a way of contributing to a project of the National Department of Defense schools. Groups of the Council of Teachers of Mathematics (NCTM) and the meeting attendees were assembled to examine the Association of School Supervisors of Mathematics standards by grade level, and they pored over the (ASSM) to analyze state standards. Johnny Lott of documents and compiled information about sim the University of Montana, past NCTM president, ilarities and differences. Lott explained that the aim is heading the NCTM-ASSM effort. After discus is simply to get a "snapshot" of the content of cur sions last year between Howe, Lott, and PCMI di rent standards and to see to what extent the states rector C. Herbert Clemens of Ohio State University, might be moving toward common standards. In par two companion proposals were submitted to the ticular, this is not an effort to see whether the National Science Foundation (NSF) for two meetings to take place at the PCMI. One of these was the meet ing of the group of mathematicians led by Howe. Committee of Mathematicians Because the funding decision came very late, many Jerome Dancis, University of Maryland, College Park fewer mathematicians could participate than were Jerry Dwyer, Texas Tech University invited. Solomon Friedberg, Bostoh College The other meeting was organized by Lott and the Bert Fristedt, University of Minnesota past president of the ASSM, Kathleen Nishimura of Daniel Goroff, Harvard University the Hawaii State Department of Education. This Roger Howe, Yale University meeting brought together about seventy-five peo Harvey Keynes, University of Minnesota ple, including representatives of the NCTM and W. James Lewis, University of Nebraska, Lincoln the ASSM and several mathematicians, some of Andy Magid, University of Oklahoma whom were also in Howe's group. The goal of this Frank Quinn, Virginia Polytechnic Institute meeting was to explore the question, To what ex and State University tent does the United States have a de facto na James Milgram, Stanford University tional curriculum for school mathematics? Unlike Alan Tucker, State University of New York, Stony Brook many countrie~ around the world, the United States Steve Wilson, Johns Hopkins University does not have a national mathematics curriculum. DECEMBER 2004 NOTICES OF THE AMS 1355 A.\I ERI CAN 1\IATH E,\IAT ICAL Soc 1 ETY New Journal state standards align with the ·principles set forth in the NCTM standards reports. Distributed The information gleaned during the meeting is in the process of being analyzed, and Lott said that the aim is to prepare a draft report sometime bytheAMS during the fall of 2004 and the final report by April 2005, when the NCTM annual meeting will take Ukrainian Mathematical Bulletin place. Plans call for sessions about the report to be held during conferences later in 2005 and UMB is a new refereed possibly also at the Joint Mathematics Meetings in mathematics journal January 2006. published quarterly by At the end of the meeting during which the stan dards documents were analyzed, in a discussion the Institute of Applied led by Lott, the suggestion was made that Howe's Mathematics and group should offer a mathematical perspective on Mechanics, National important issues in creating standards. While per Academy of Science of haps not unprecedented, this kind of direct inter action between mathematicians Ukraine in cooperation and people from groups such as the NCTM and ASSM has been rare, with the Ukrainian at least in the recent history of mathematics edu Mathematical Society cation reform. "It's a new stage, it's a new devel and distributed by the American opment," Howe said. What the group Mathematical Society.* UMB is devoted of mathematicians will do is to write a document that first outlines some general to the publication of original research arti principles for standards and then focuses more cles in all active areas of pure and closely on a small number of mathematical ideas applied mathematics. that it believes could help improve school mathe matics instruction. The group also intends to produce an annotated set of problems that exemplify those ideas. They do not plan to cover the whole of K-12 mathematics. "We are selecting only a set of focused issues where we feel we have something definite to contribute," Howe explained. "Writing good mathe matics standards is a complex task, and we have a long way to go before we can develop ideal stan dards. We hope to provide useful guidance and advice for the next generation of standards writers." The work of the group of mathematicians will pro ceed on a parallel but separate track from the work headed by Lott to analyze existing state standards. Sponsored by the Institute for Advanced Study in Princeton, the PCMI is a yearly event in Park City, Utah, that brings together mathematicians, Special Introductory Offers: graduate students, postdocs, mathematics edudt tors, and teachers for three weeks of activities de The AMS will begin signed to promote connections between teaching and research. Further meetings focused on school taking orders for subscriptions in mathematics standards may take place at the PCMI 2005. in the summer of 2005. The report of the mathe * The AMS distributes this journal in the following countries: maticians' group will be posted on the PCMI web North America (USA, Canada, and Mexico), the European site and may be produced in hard copy. "If our Union, Norway, Switzerland, Japan, Australia, Taiwan, document is seen as being interesting, there might Israel, South Korea, and New Zealand. be a follow-up meeting, and then we will talk about next steps," Howe said. "I'm hoping it will have a positive effect on standards development in the future." - Allyn jackson 1356 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Deligne Receives 2004 BalzanPrize The International Balzan Foundation has an congruences (the so-called "Riemann conjecture nounced the winners of the 2004 Balzan Prizes. The over finite fields" is part of them). These conjec prize in mathematics went to PIERRE DELIGNE of the tures were both exceptionally hard to settle (the Institute for Advanced Study in Princeton. The best specialists, including A. Grothendieck, had prize ceremony will take place on November 18, worked on them) and most interesting in view of 2004, in Rome. the far-reaching consequences of their solution. The Also receiving 2004 Balzan Prizes are Nikki R. proof, subject matter of two celebrated papers to Keddie (Islamic studies), Colin A. Renfrew (prehis talizing some 150 pages of the Publ. Math. IHES toric archaeology), and Sir Michael Marmot (epi (1974 and 1980), was to make use in a remarkably demiology). Each prizewinner receives 1 million ingenious way of a large combination of very dif Swiss francs (about US$800,000), half of which ficult techniques; a real tour de force, which earned must be devoted to research projects involving its author the Fields Medal in 1978. young researchers in the prizewinner's field. The The first achievement of Pierre Deligne was fol community of Sant'Egidio, Italy, received a special lowed by several others of similar importance. prize of 2 million Swiss francs for humanity, peace, They all have in common the extreme variety as well and brotherhood among peoples. as the difficulty of the techniques involved and the Deligne is receiving the prize "for major contri inventiveness of the methods. butions to several important domains of mathemat As for the results themselves, some are "elemen ics (like algebraic geometry, algebraic and analytic number theory, group theory, topology, Grothen tary", in that the main statements can be understood dieck theory of motives), enriching them with new by almost any professional mathematician. For in and powerful tools and with magnificent results such stance: the irreducibility of the space of curves of as his spectacular proof of the 'Riemann hypothesis given genus (an early joint paper with D. Mumford, over finite fields' (Weil conjectures)." 1969), the definition and application of "buildings" of generalized braid groups (1972), a new solution Laudatio (also in the early 1970s) of Hilbert's 21st problem, During a press conference on September 7, 2004, an epoch-making paper written in common with in Milan, Balzan Prize committee member jacques G. Lusztig on linear representations of finite simple Tits of the College de France made the following groups of Lie type (Annals of Mathematics, 1974), remarks. the construction of a remarkable central extension Pierre Deligne became famous in the mathe of the group of rational points of a reductive group matical world at an early age through his brilliant over a field F by the group K z(F) (a construction first proof of the "Weil conjectures", which concern the described in an unpublished seminar in 19 77-19 78 number of solutions of systems of polynomial and further investigated in a 1996 paper in the Pub I. DECEMBER 2004 NOTICES OF THE AMS 1357 Math. IHES), the study with G. Mostow of the mon received the Fields Medal. He is a foreign member odromy of hypergeometric functions (1986). of the Academie des Sciences of Paris, a foreign hon Other results are more technical but equally orary member of the American Academy of Arts profound, creating new and powerful tools; let us and Sciences, and a member of the Academie Royale just mention a few titles: "La theorie de Hodge" II de Belgique. and III (two fundamental papers in the Publ. Math. IHES, 1971 and 1974; number I was just an an About the Balzan Prize nouncement), "Le symbole modere" (ibid. 1991), The Balzan Prize is among the most important hu "Faisceaux pervers" (in Asterisque, vol. 100, 1982, manistic and scientific awards in the world. The pp. 5-171, joint work with A. A. Beilinson and winners are selected by a General Prize Commit ]. Bernstein), "Categories Tannakiennes" (in The tee made up of prominent European scientists and GrothendieckFestschrift, vol. II, 1990), "A quoi ser academics. The committee evaluates candidate vent les motifs?" (in Motives, AMS, 1994; motives proposals from universities and academies all over are a conjectural notion, created by A. Grothendieck the world. The prizes are interdisciplinary in na in the late 1960s, rich in implications and often ex ture, and the prize categories range over litera emplified by Deligne). ture, moral science and art, medicine, and physi A remarkable feature of Deligne's thinking is cal, mathematical, and natural sciences. The that, when confronted with a new problem or a new Italian-Swiss Balzan Foundation, which has head theory, he understands and, so to speak, makes his quarters in Milan and Zurich, was started in 1956 own its basic principles at a tremendous speed with funds from the daughter of Eugenio Balzan, and is immediately able to discuss the problem or who inherited a large estate from her father and use the theory as a completely familiar object. decided to use it to honor his memory. Eugenio Thus, I often observed that he readily adopts the Balzan was born in 1874 and was a proofreader, language of the persons he is talking to when en reporter, and manager for Carriere della Sera, the gaged in discussions. This flexibility is one of the most important Italian daily newspaper. He also be reasons for the universality of his mathematical came a shareholder in the paper, lived parsimo work. niously, and invested his earnings shrewdly. In Alone or in collaboration, Pierre Deligne has 1933, he settled in Switzerland, mostly because of written about a hundred papers, most of them of his opposition to fascism. He died in 1953 in sizeable length. Because of the conciseness of his Lugano. style and of his habit of never writing the same Among previous recipients of the Balzan Prize thing twice (in fact, quite a few of his best ideas are the following mathematical scientists: Andrej have never been written!), the volume of his pub Kolmogorov (1962), Enrico Bombieri (1980), Jean lications is a true measure of the richness of his Pierre Serre (1985), Otto Neugebauer (1986), scientific production. Armand Borel (1992), Sir Robert May (1998), and Mikhael Gromov (2000). Biographical Sketch -Allyn Jackson Pierre R. Deligne was born on October 3, 1944, in Etterbeek, Belgium. He studied mathematics at the University of Brussels from 1962 untill966. Dur ing the academic year 1965-66 he was concurrently a foreign student (pensionnaire etranger) at the Ecole Normale Superieure in Paris. In 1968 here ceived the licence en mathematiques and the doc tarat en mathematiques from the University of Brussels, and in 1972 he received the doctorat d'Etat des Sciences Mathematiques from the Uni versite de Paris-Sud. In 1968 he went to the Institut des Hautes Etudes Scientifiques as a visitor and in 19 70 was appointed as a permanent member. In 1984, he assumed his present position as a professor at the Institute for Advanced Study in Princeton. Deligne received the Francois Deruyts prize of the Belgium Royal Academy (197 4), the Henri Poin care medal of the Academie des Sciences of Paris (19 74), and the Crafoord Prize of the Royal Swedish Academy of Sciences (1988). At the International Congress of Mathematicians in Helsinki in 1978, he 1358 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Mathematics People bestowed by the U.S. government on outstanding young Bjorken and Callan Awarded scientists, mathematicians, and engineers who are in the 2004 Dirac Medals early stages of establishing their independent research careers. The 2004 Dirac Medals of the Abdus Salam International Three scholars who work in the mathematical sciences Centre for Theoretical Physics (ICTP) have been awarded were honored for 2003. They are KoNSTANTINA TRIVISA, Uni to ]AMEs D. BJORKEN of Stanford University and CuRTIS G. versity of Maryland, College Park; RA vr VAKIL, Stanford Uni- · CALLAN of Princeton University for their work in the use of versity; and HARRY DANKOWICZ, Virginia Polytechnic Institute deep inelastic scattering for shedding light on the nature and State University. of strong interactions. The recipients were selected from nominations made The award citation reads: "Bjorken was the first to re by eight participating federal agencies. Each awardee re alize the importance of deep inelastic scattering and the ceives a five-year grant ranging from $400,000 to nearly first to understand the scaling of cross sections, an insight $1 million to further his or her research and educational that ultimately bore his name-the Bjorken scaling of efforts. cross sections. Callan, together with Kurt Symanzik (now deceased), reinvented the perturbative renormalization -From an NSF announcement group (in a form that now bears the name Callan-Symanzik equations) and recognized these groups as measures of scale invariance anomalies. Callan has applied these tech Prizes of the Acadenne des niques to analyses of deep inelastic scattering and has made substantial contributions to particle physics and, more Sdences recently, string theory." The ICTP awarded its first Dirac Medal in 1985. Given The Academie des Sciences, Paris, has announced the in honor of P. A. M. Dirac, the medal is awarded annually awarding of several prizes for 2004. on Dirac's birthday, August 8, to an individual or individ The Grand Prix Sophie Germain was awarded to HENRI uals who have made significant contributions to theoret BERESTYCKI of l'Ecole des Hautes Etudes en Sciences So ical physics and mathematics. The medalists also receive ciales (EHESS), Paris, for "fundamental contributions to the a prize of US$5,000. An international committee of dis analysis of nonlinear partial differential equations, espe tinguished scientists selects the winners from a list of cially in models arising in physics, chemistry and biology," nominated candidates. The Dirac Medal is not awarded to according to the prize citation. Other prizes in mathe Nobel Laureates or Wolf Foundation Prize winners. matics were as follows: the Prix Jaffe to CoLETTE MOEGLIN of Institut de Mathematiques de ]ussieu des Sciences; -From an ICTP announcement the Prix Paul Doistau-Emile Bluter to LAURENT STOLOVITCH, Laboratoire Emile Picard at Toulouse; and the Prix Servant to GUY DAVID, Universite Paris-Sud, Orsay. The Prix Ayme Poirson, for applications of science PECASE Awards Announced to industry, was awarded to BIJAN MoHAMMAD!, Universite Fifty-seven young researchers were chosen to receive the de Montpellier. ALBERT CoHEN, Universite Pierre et Marie 2003 Presidential Early Career Awards for Scientists and Curie, received the Prix Blaise Pascal du Gamni-Smai. The Engineers (PECASE). This award is the highest honor Prix Jacques Herbrand was awarded to NIKITA NEKRAssov, DECEMBER 2004 NOTICES OF THE AMS 1359 Mathematics People Institut des Hautes Etudes Scientifiques, Bures-sur-Yvette, with the MAA MathFest in Providence, Rhode Island, Au and the Prix Leconte went to REMr MoNASSON, Laboratoire gust 12-14, 2004. Each awardee received a prize of $150. de Physique Theorique de l'Ecole Normale Superieure, The Pi Mu Epsilon awards for best presentations are Paris. sponsored by the AMS. Seven students were chosen for this award. Their names, institutions, and titles of their talks -From an Academie des Sciences announcement follow: STEPHANIE BARILLE, Mount Union College, "Catch the Wave"; NATHAN EDINGTON, Hood College, "Computer Imple mentations of Five Important Approximations to Pi"; JEREMY HAMILTON, Youngstown State University, "Fun with NDSEG Fellowships Awarded Incircles"; CoLLEEN HuGHES, Denison University, "Intrinsic Thirteen young mathematicians have been awarded Na Linking of K5"; THEODORE STADNIK, Youngstown State Uni tional Defense Science and Engineering Graduate (NDSEG) versity, "Bivariate Normal Estimation of Digitally Imaged Fellowships by the Department of Defense (DoD). As a Data"; RYAN STERNBERG, Worcester Polytechnic Institute, means of increasing the number of U.S. citizens trained in "Cartesian Products of Triangles as Unit Distance Graphs"; disciplines of military importance in science and engi and ALYSSA WooD, St. Norbert College, "Mathematical neering, DoD awards fellowships to individuals who have Espionage: Breaking the 'Unbreakable' Enigma Code". demonstrated ability and special aptitude for advanced The prize for best research presentation, sponsored by training in science and engineering. The fellowships are the Council on Undergraduate Research, went to NrcoLE sponsored by the United States Army, Navy, and Air Force. CUNNINGHAM, Youngstown State University, for her paper Following are the names of the fellows in mathematics "Comparing the Eigenvalues of Products of Matrices". The SIAM award for best presentation on environmental issues and the offices that awarded the fellowships. SAMUEL ISAAC was given to MICHAEL CORTEZ, Hope College, for his paper soN, Air Force Office of Scientific Research (AFOSR); TIFFANY "A Mathematical Model of Tri-Trophic Interactions". PsEMENEKI, AFOSR; NITIN SAKSENA, AFOSR; BRYAN SMITH, AFOSR; PAUL VALIANT, AFOSR; WILLIAM FoNG, Army Research Office -Elaine Kehoe (ARO); ]AYCE GETZ, ARO; PAUL HAND, ARO; PHILIP MATCHETT, · ARO; ]OHN WoRKMAN, ARO; MEGAN GUICHARD, Office of Naval Research (ONR); BERNARD MAREs, ONR; and DAVID SMYTH, ONR. -From an NDSEG announcement National High School Calculus E MATHEMATICS Student Award RYAN WILLIAMS, a student at Miami Springs High School, Full-time, tenure-track assistant professorship to begin August 2005. Area of expertise in real or functional analysis. The Florida, has won the fourth annual National High School department, consisting of 20 faculty members and approximately Calculus Student Award. Williams has qualified three times 200 undergraduate majors, offers B.A. and B.S. degrees in for the USA Mathematical Olympiad (USAMO), has twice mathematics and B.S.Ed and M.Ed. degrees in mathematics education. Duties include an annual 24-hour teaching load, been the Florida state calculus champion, was the Florida including a variety of undergraduate mathematics service Mathematics League individual champion in 2003-2004, courses, scholarly activity, student advisement, supervision of and received the first-ever perfect score on the David student research, curriculum development and committee work. Essner Exam, given by the University of Miami. He will Ph.D. (or completion by time of reappointment to the second year) in mathematics with specialization in real or functional attend Stanford University. The $1,000 prize is awarded analysis is required. Must exhibit evidence of strong by Ca 1 cul us. org, based at the University of California commitment to excellence in teaching and continued scholarly at Davis, Williams College, and Wake Forest University. activity. Must be prepared to teach a broad spectrum of undergraduate mathematics courses and have potential to contribute to the department's programs. Must complete a -Calculus.org successful interview and teaching demonstration. Evidence of teaching effectiveness is a primary consideration. Salary/benefits are competitive. Send application letter, vita, copies of undergraduate and Pi Mu Epsilon Student Paper graduate transcripts and three letters of reference (at least two of which attest to recent teaching effectiveness) to Dr. Zhoude Shao, Search Committee/AMS, Department of Mathematics, Presentation Awards Millersville University of Pennsylvania, P.O. Box 1002, Millersville, PA 17551-0302. Completed application must be Pi Mu Epsilon (PME), the U.S. honorary mathematics soci received by January 21, 2005 to assure full consideration. E ety, makes annual awards to recognize the best papers by mail applications will not be accepted. undergraduate students presented at a PME student-paper An EOIAA Institution • www.millersville.edu session. This year the PME held a session in conjunction 1360 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Mathematics Opportunities program designed to strengthen the ability of women and NDSEG Fellowships minority students to successfully complete graduate pro As a means of increasing the number of U.S. citizens grams in the mathematical sciences. trained in disciplines of military importance in science and The summer program consists of two core courses in engineering, the Department of Defense (DoD) awards Na analysis and algebra/linear algebra, a minicourse in a cur tional Defense Science and Engineering Graduate (NDSEG) rent area of mathematical research, short-term visitors Fellowships each year to individuals who have demon from academia and industry, guest lectures, graduate stu strated ability and special aptitude for advanced training dent mentors, and problem sessions. In addition, a follow in science and engineering. The fellowships are awarded up mentoring program and support network will be es for a period of three years for study and research leading tablished with the participants and their respective to doctoral degrees in mathematical, physical, biological, graduate programs. Applicants to the program should be women who either ocean, and engineering sciences. The number of fellowships (1) have been accepted to a graduate program in the math awarded depends on available funding. ematical sciences or (2) have just completed their first year The NDSEG Fellowship Program is open only to appli of graduate school in the mathematical sciences. All ap cants who are citizens or nationals of the United States. plicants should have completed standard junior- or senior NDSEG Fellowships are intended for students at or near the level undergraduate courses in analysis and abstract al beginning of their graduate studies in science or engi gebra and have a desire to earn the doctorate degree. neering. Applicants must have received or be on track to Women who have taken time away from formal education receive their bachelor's degrees by fall of 2005. Applications as well as women from minority groups who fit into one are encouraged from women, persons with disabilities, of the above two categories are encouraged to apply. Final and minorities, including members of ethnic minority acceptance to the program is contingent on acceptance to groups such as African American, American Indian and a graduate program in the mathematical sciences. Alaska Native, Asian, Native Hawaiian and other Pacific In 2005 the eighth session of the EDGE Program will be Islander, Hispanic, or Latino. held at North Carolina Agricultural and Technical State Uni Complete applications must be submitted electroni versity, Greensboro, North Carolina. The tentative dates for cally or postmarked by January 7, 2005. Application ma the summer program are June 6-July 1, 2005. It will be co terials are available from, and completed applications directed by Sylvia Bozeman (Spelman College), Rhonda should be returned to, the American Society for Engi Hughes (Bryn Mawr College), and local coordinator Janis neering Education (ASEE) at NDSEG Fellowship Program, Oldham (North Carolina A&T). A stipend of $2,000, plus c/ o American Society for Engineering Education, 1818 N travel and room and board will be awarded to partici Street, N.W. #600, Washington, DC 20036; telephone 202- pants. Applicants chosen to participate in the program will 331-3516; fax 202-265-8504; email: ndseg@asee. org. For be notified by April 15, 2005. further information, see the website http: I /www. Applications should consist of the following: (1) a com asee.org/ndseg/preface.cfm. pleted application form; (2) a statement describing the ex pected value of this program to the applicant's academic -From an NDSEG announcement goals; (3) two letters of recommendation from mathe matical sciences faculty familiar with the applicant's work; (4) a transcript and current resume; and (5) a list of grad EDGE Summer Program uate programs to which the applicant has applied, to gether with a ranked list of her two or three top choices. The Enhancing Diversity in Graduate Education (EDGE) Pro The application deadline is March 1, 2005. Applica gram is a postbaccalaureate summer enrichment tions should be sent to: EDGE Program, P.O. Box 63, DECEMBER 2004 NOTICES OF THE AMS 1361 Mathematics Opportunities Swarthmore, PA 19081. Actual conduct of the EDGE Pro originality, innovation, and significant impact on the field. gram in 2005 is contingent upon continued funding. For The deadline for nominations for the award is November 30, more information visit the program's website at 2004. Supporting references must be submitted by http:llwww.edgeforwomen.orgl. December 31, 2004. For more detailed information con cerning the nomination procedures, see the website -EDGE Program announcement http:llwww.nsf.govlpubsl2004lnsf045llnsf045l.pdf. -From an NSF announcement CMI liftoff Program for Summer 2005 News from the Mittag-Leffler The Clay Mathematics Institute (CMI) is currently accept Institute ing nominations for the 2005 liftoff Program. Through this program, CMI will employ recent Ph.D. recipients as Liftoff The Mittag-Leffler Institute, Djursholm, Sweden, has Fellows to carry out mathematics research for one month announced its program for the academic year 2005-2006. during the summer of 2005. This program provides a tran The fall term will be devoted to wave motion. The orga sition for young mathematicians from student to faculty nizing committee consists of Adrian Constantin (chair), member or to a postdoctoral position. Funds for travel to Lund; Constantine Dafermos, Providence; Helge Holden, conferences or to visit collaborators are also available to Trondheim; Kenneth H. Karlsen, Oslo; and Walter Strauss, Liftoff Fellows. Providence. The spring term will be devoted to algebraic Nominations should be made by university mathemat topology. The organizing committee consists of Bjorn ics departments; candidates may not apply directly. Criteria Jahren (chair), Oslo; Kathryn Hess, Lausanne; and Bob for selection are the quality and significance of mathe Oliver, Paris. matical research already achieved by the candidate and The application deadline for postdoctoral fellowships the potential of the candidate to become a leader in is January 31, 2005. Applications should be sent to Marie mathematical research. Louise Koskull, Institut Mittag-Leffler, Auravagen 17, Nominations can be sent electronically to the attention SE-182 60 Djursholm, Sweden; email: kosku11 @m1 . kva. se. of Maria McLaughlin at nomi nati ons@c1 aymath. org or For further information see the institute's website, by mail to Clay Mathematics Institute, One Bow Street, http://www.m1.kva.se/grants. 4th Floor, Cambridge, MA 02138. The deadline for nomi nations to be received is February 15, 2005. For more -Institut Mittag-Leffler announcement information and nomination procedures, see the website http: I I c1 aymath. orglfasl1 i ftoff_fe 11 owsl; tele phone 617-995-2600; email: nomi nati ons@c1 aymath. org. News from The Fields Institute -From a CMI announcement The Fields Institute for Research in the Mathematical Sci ences and the Perimeter Institute for Theoretical Physics will hold a thematic program on the geometry of string theory from January through July of 2005. The aim of the Call for Nominations for program is to discuss new results and put new insights Waterman. Award gained from physics into the general mathematical framework. Specialized workshops and minicourses will Congress established the Alan T. Waterman Award in August be held. The program will end with the Strings 2005 Con 1975 to mark the twenty-fifth anniversary of the National Sci ference in July. A list of activities and dates for the ence Foundation (NSF) and to honor its first director. The winter and spring programs follows. Winter 2005: Gradu annual award recognizes an outstanding young researcher ate Course on Symplectic Geometry and Topology. in any field of science or engineering supported by the NSF. Instructor: B. Khesin. To Be Announced: Coxeter Lecture In addition to a medal, the awardee receives a grant of Series. Speaker: Rob bert Dijkgraaf. january 10-14, 2005: $500,000 over a three-year period for scientific research Workshop on Topological Strings with Emphasis on or advanced study in the mathematical, physical, medical, Gromov-Witten Invariants and Open-Closed Duality. biological, engineering, social, or other sciences at the Organizers: E. Getzler, K. Hori, S. Katz. March 21-25, institution of the recipient's choice. Candidates must be 2005: Workshop on N = 1 Compactifications. Organizers: U.S. citizens or permanent residents and must be thirty-five M. Douglas, K. Hori, S. Sethi. March 28-April1, 2005: Work years of age or younger or not more than seven years be shop on String Phenomenology. Organizers: ]. Louis, yond receipt of the Ph.D. degree by December 31 of the R. Myers, G. Shiu. April4-7, 2005: Distinguished Lecture year in which they are nominated. Candidates should have Series. Lecturer: Edward Witten. May 2-6, 2005: Workshop demonstrated exceptional individual achievements in on Gravitational Aspects of String Theory. Organizers: scientific or engineering research of sufficient quality to C. Johnson, P. Kraus, D. Marolf, A. Peet. june 20-july 8, place them at the forefront of their peers. Criteria include 2005: Summer School Program on Strings, Gravity, and 1362 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Mathematics Opportunities Cosmology. Organizers: A. Buchel, R. Myers, M. Rozali. A workshop on Career Options for Women in july 11-16, 2005: Strings 2005 Conference. Mathematical Sciences (February 4-6, 2005) is intended to For more information, including funding opportuni familiarize women in the mathematical sciences with pro ties, see the Fields website at http: I lwww. fields. fessional opportunities in industry and government labo utoronto.calprogramslscientificl04-05l ratories and to suggest strategies for not merely surviving string-theory1. but thriving. The workshop is being organized jointly by The 2005-2006 thematic program will be on renor the IMA and the Association for Women in Mathematics malization and universality in mathematics and mathe (AWM) and is geared primarily toward graduate students matical physics and on holomorphic dynamics, laminations, and Ph.D.'s in the early stages of their postgraduate careers, and hyperbolic geometry. The fall program will concentrate although researchers at all stages of professional devel on the physical aspects of renormalization: statistical opment are welcome. physics, conformal field theory, the underlying Hopf A two-part symposium, Experiments in Physical Biology, algebraic structure, and renormalization in PDE. The spring will be held May 2-6 and May 16-20,2005. The symposium program will feature holomorphic and smooth dynamics, will give leaders in experimental quantitative biology an KAM theory and renormalization of Hamiltonian flows, opportunity to present key aspects of structural biology conformal invariance and universality in 2D stochastic and single molecule biophysics in a tutorial fashion and processes, and the recent breakthrough in the geometriza characterize the types of mathematical models needed to tion program based on the dynamics of the Ricci flow and analyze experimental data. Other spring programs include its connection to the concept of renormalization. two 5-day workshops geared primarily for mathematical The Fields Institute invites applications for postdoctoral audiences. Dates and titles are: fellowship positions at the institute during the 2005-2006 April 11-15, 2005: Workshop on Atomic Motion to academic year. These fellowships provide an opportunity Macroscopic Models: The Problem of Disparate Temporal to spend at least one year engaged in research and partici and Spatial Scales in Matter. This workshop addresses pating in the research activities of the institute. Deadline techniques for modeling materials and macromolecular sys for applications is December 10, 2004. Applicants seeking tems with multiple time and length scales. postdoctoral fellowships funded by other agencies (such june 8-11, 2005: Workshop on Effective Theories for as NSERC and international fellowships) are encouraged to Materials and Macromolecules. This will be an informal request The Fields Institute as their proposed location of workshop on the development and analysis of effective tenure and should apply to The Fields Institute for a letter theories that reduce the degrees of freedom and bridge of invitation. For further information, see http: I l www. time and space scales in physics, chemistry, and biology. fields.utoronto.calproposalslpostdoc.html. Two programs for graduate students will be offered dur ing the summer: - Fields Institute announcement june 13-july 1, 2005: The Participating Institution Sum mer Program for Graduate Students: Stochastic Partial Dif ferential Equations and Environmental and Geophysical the IMA Modeling will be hosted by the University of Wyoming News from and will introduce students to the stochastic analysis of The theme of the 2004-2005 academic year at the Institute nonlinear PDEs, with applications to petroleum, ground for Mathematics and its Applications (IMA), in Minneapolis, water, and renewable resource modeling. Minnesota, is Mathematics of Materials and Macromolecules: August 1-10, 2005: The 2005 Workshop on Mathematical Multiple Scales, Disorder, and Singulaitties (http: I lwww. Modeling in Industry will give graduate students and qual i ma. umn. edulmatte r 1). The program synthesizes a broad ified advanced undergraduates firsthand experience in in spectrum of problems and methodologies at the interface dustrial research, working in teams of approximately six between mathematics, materials science, condensed mat students under the guidance of a mentor from industry. ter physics, and biology. The 2005 Summer Program on Wireless Communica The IMA will offer several intensive, informal workshops tions (June 22-July 1, 2005) will focus on the interplay of that will bring mathematicians together with researchers the physical, link, and network layers in wireless networks, from industry and experimental biology. The winter pro emphasizing stochastic calculus, information theory, sig gram features two 3-day workshops that focus on indus nal processing, optimization, and control theory. The pro trial applications, combining mathematical tutorials, gram will consist of a 3-day tutorial intended for junior presentations by industrial scientists, and extensive group researchers new to the area, followed by a 5-day workshop. discussions. The dates and titles are: Two "Hot Topics" workshops will be held during the February 7- 9, 2005: Workshop on Composites: Where summer: Mathematics Meets Industry. The workshop focuses on july 25-29, 2005: The Hot Topics Workshop on Mixed multiscale modeling. Integer Programming will highlight recent advances in March 28-30, 2005: Workshop on New Paradigms in theoretical and computational aspects of MIP and explore Computation. This workshop addresses fast multipole the role of MIP in network design, computational biology, methods, level set methods, and multiscale computation. medical treatment planning, and cryptography. DECEMBER 2004 NOTICES OF THE AMS 1363 Mathematics Opportunities August 5-6, 2005: The Hot Topics Workshop on New able on the web at http: I lwww . ams . o rgl gove rnmentl Directions in Probability Theory, organized jointly by the MentoringWorkshop.html and send a check payable to IMA and the Institute of Mathematical Statistics (http: I I the American Mathematical Society, 15 2 7Eighteenth Street, www. i mstat. org), is intended for a general probability NW, Washington, DC 20036. Agenda, materials, and loca audience. Session topics are Flows and Random Media; tion information will be sent to all registered attendees Probability, Combinatorics, and Statistical Mechanics; prior to the workshop. Stochastic Integration; Stochastic Partial Differential Equa Space is limited to forty participants. Funding from the tions; and Random Walk in Random Environment. The NSF will cover participant hotel expenses for up to two 2005 New Directions Short Course, Quantum Computation nights' stay and dinner Friday evening (December 3), as well (http:llwww.ima.umn.edulnew-directionsl as breakfast and lunch on Saturday (December 4). 2005NDshort-coursel), to be held August 15-26, 2005, will introduce quantum mechanics and quantum compu - AMS announcement tation, then pursue two tracks: quantum algorithms and error correction, and topological quantum computation. The course combines general lectures, topical lectures by Newton Fellowship Program guest speakers, and problem-solving sessions. The theme of the 2005-2006 thematic program is Imag The Math for America Foundation (MfA) sponsors the New ing (http: I lwww. i rna. umn. eduli magi ng). The program ton Fellowship Program which seeks mathematically will explore image formation (the use of data from sensors sophisticated individuals to become high school mathe to form images), image interpretation (the extraction of in matics teachers in New York City. The five-year fellowship formation from images), and the interplay between these provides an aggregate stipend of $90,000 over five years, areas. Opportunities for participation include fellowships a full tuition scholarship for a Master's level teaching pro (application deadline is January 5, 2005), general member gram at one of MfA' s partner universities, and ongoing sup de ships (visits of a month or more; no application deadline), port mechanisms including mentoring and professional and New Directions Visiting Professorships for established velopment. The application deadline is February 4, 2005. and deadlines can be mathematicians seeking to branch into new directions and Complete application requirements increase the impact of their research (application deadline found at http: I l www. mathforameri ca. org. with a mission to sub March 1, 2005). Descriptions of and application forms MfA is a nonprofit organization stantially improve the quality of mathematics education for these IMA membership programs can be found at in our country's public schools. MfA works with teachers http:llwww.ima.umn.edul docslmembership.html. school administrators, and other stakeholders through ~ Further information and registration forms for all IMA variety of approaches to accomplish this important ob workshops and tutorials are available at http: 1lwww . jective. MfA launched its first initiative, the Newton Fel edu. i rna. umn. lowship Program, in 2004 with a group of thirteen fellows. MfA will award approximately forty fellowships in 2005. -From an IMA announcementement Jim Simons, who received the AMS Veblen Prize in 1975 and was on the faculty at the State University of New York at Stony Brook, serves as chairman of the MfA, and Irwin AMS Mentoring Workshop Kra, Distinguished Service Professor Emeritus at SUNY Stony Brook, is the executive director. The AMS is hosting a National Science Foundation (NSF) The Newton Fellowship Program is designed to attract workshop on mentoring and nurturing students on De mathematically talented recent college graduates and mid cember 3-4, 2004, at the Four Points by Sheraton Hotel in career professionals into high school teaching. Candidates Tucson, Arizona. The workshop will begin at 1:00 p.m. on must have a bachelor's degree with substantial coursework Friday, December 3, and last all day on Saturday, Decem in mathematics and should be able to demonstrate a strong ber 4. interest in teaching. Applicants also must be willing to com participants with This workshop is designed to provide mit to a five-year fellowship term in New York City. Indi and methods that will aid in the development of nur ideas viduals who are currently teaching, are certified to teach, turing environments for students. This will be done by con or have completed an education degree program are not centrating on mentoring mathematical sciences students eligible. through four critical stages in their academic careers: (1) Freshman-sophomore level mathematics courses, (2) Fresh - MfA announcement man-sophomore level mathematics to junior-senior level mathematics, (3) Undergraduate mathematical sciences major to the first two years of graduate school in mathe matics, or to employment, or to graduate and professional schools (other than mathematics), and (4) Writing a dis sertation in the mathematical sciences. A registration fee of $40.00 is required. Those interested in attending should complete the registration form avail- 1364 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Inside the AMS AMS Email Support for Frequently Asked Questions The following is an updated list of non-user-specific email addresses for contacting AMS staff. This list is also avail able on the AMS website at http: I /www. ams. org/ ams/emai l. html. [email protected] [email protected] for questions regarding a particular abstract. to submit classified advertising for the Notices. [email protected] [email protected] to contact the AMS Acquisitions Department. for general information about AMS products (including elec tronic products); tci send address changes, place credit card [email protected] orders for AMS products, or conduct any general to contact the Society's headquarters in Providence, Rhode correspondence with the Society's Customer Services Island. Department. 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[email protected]: for questions regarding a paper to Each submission must be accompanied by the journal appear in the journal Bulletin. template. A copy of the template is available by sending [email protected]: for questions regarding a paper to email to ejour-submit@ams. org. Put the word TEMPLATE appear in the journal journal of the AMS. in the subject field of the email message. To get additional help, put the word HELP in the subject field in a separate [email protected] mail message. to request information about membership in the AMS or about dues payments, or to ask any general membership [email protected] questions; may also be used to submit address changes. for information on AMS employment and career services. [email protected] [email protected] for information or questions about the AMS-ASA-IMS-MAA for technical questions regarding AMS electronic prod Annual Survey of the Mathematical Sciences or to request ucts and services. reprints of Survey reports. 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[email protected] to request examination copies or to inquire about using [email protected] AMS publications as course texts. to send correspondence to the managing editor of the [email protected] Notices, including items for the news columns. The editor (noti ces@math. ou. edu) is the person to whom to send ar for general information or for assistance in accessing and ticles. Requests for permission to reprint from the Notices using the AMS website. should be sentto [email protected] (see below). Deaths of AMS Members [email protected] to submit paid display ads electronically for the Notices. ]AMES T. CuLBERTSON, retired emeritus, California Polytech (Hard copy of the ad should also be faxed or sent via nic State University, died on July 27, 2004. Born on De postal mail.) cember 25, 1911, he was a member of the Society for 22 years. [email protected] LAWRENCE STANLEY EvANs of La Grange, IL, died on May 22, to submit suggestions for books to be included in the 2004. Born on October 21, 1943, he was a member of the Book List in the Notices. Society for 11 years. WALTER FEIT, of Yale University, died on July 29, 2004. [email protected] Born on October 26, 1930, he was a member of the Soci to submit letters and opinion pieces to the Notices. ety for 51 years. [email protected] A. W. GooDMAN, emeritus professor, the University of to comment on or send suggestions for topics for the South Florida, died on July 30, 2004. Born on July 20, WHAT IS ... ? column to the Notices. 1915, he was a member of the Society for 60 years. RoDNEY T. HooD, emeritus professor, Franklin College, [email protected] Frankin, IN, is reported to have died several years ago. Born to contact the AMS Public Awareness Office. on September 29, 1924, he was a member of the Society [email protected] for about 40 years. to contact the president of the American Mathematical ARNO JAEGER, emeritus professor, Ruhr University, Society. Bochum, Germany, died on February 24, 2004. Born in August 1911, he was a member ofthe Society for 63 years. [email protected] JoEL SCHNEIDER, of the Sesame Workshop TV show, died to send correspondence about AMS professional programs on September 12, 2004. Born on April 8, 1943, he was a and services. member of the Society for 38 years. Smzuo KAKUTANI, of New York City, died on August 16, [email protected] 2004. Born on August 28, 1911, he was a member of the to send correspondence to the AMS Publication Division. Society for 51 years. [email protected] AMBIKESHWAR SHARMA, emeritus, University of Alberta, to submit accepted electronic manuscripts to AMS publi died on December 22, 2003. Born on July 2, 1920, he was cations (other than Abstracts). See www. ams. o rg/ a member of the Society for 42 years. 1366 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Reference and Book List The Reference section of the Notices Upcoming Deadlines December 1, 2004: Nominations is intended to provide the reader with November 30, 2004: Nominations for for the Ferran Sunyer i Balaguer frequently sought information in Alan T. Waterman Award. See "Math Prize. See http: I lwww. c rm. esl an easily accessible manner. New ematics Opportunities" in this issue. FerranSunyerBalaguer/ffsb.htm. information is printed as it becomes December 1, 2004: Applications December 10, 2004: Applications available and is referenced after the for AMS Centennial Research Fellow for East Asia and Pacific Summer In first printing. As soon as information ships. See http: I lwww. ams. orgl stitutes. See http: I lwww. nsf. gov I pubsl2003lnsf03608lnsf03608. is updated or otherwise changed, it employmentlcentflyer.html or write to the Membership and Programs December 10, 2004: Applications will be noted in this section. Department, American Mathematical for postdoctoral fellowships for Contacting the Notices Society, 201 Charles Street, Providence, 2005-2006 Fields Institute thematic RI 02904-2294; telephone: 401-455- program. See "Mathematics Opportu The preferred method for contacting 4107;email: [email protected]. nities" in this issue. the Notices is electronic mail. The editor is the person to whom to send Where to Find It articles and letters for consideration. A brief index to information that appears in this and previous issues of the Articles include feature articles, Notices. memorial articles, communications, AMS Bylaws-November 2003, p. 1283 opinion pieces, and book reviews. The AMS E-mail Addresses-December 2004, p. 1365 editor is also the person to whom to AMS Ethical Guidelines-]une/]uly 2004, p. 673 send news of unusual interest about AMS Officers 2002 and 2003 (Council, Executive Committee, other people's mathematics research. Publications Committees, Board of Trustees)-May 2004, p. 566 The managing editor is the person AMS Officers and Committee Members-October 2004, p. 1082 to whom to send items for "Mathe Conference Board of the Mathematical Sciences-September 2004, matics People", "Mathematics Op p. 921 portunities", "For Your Information", Information for Notices Authors-]unej]uly 2004, p. 668 "Reference and Book list", and "Math Mathematics Research Institutes Contact Information-August 2004, ematics Calendar". Requests for p.SlO permissions, as well as all other National Science Board-january 2004, p. 54 inquiries, go to the managing editor. New journals for 2003-]une/]uly 2004, p. 670 The electronic-mail addresses are NRC Board on Mathematical Sciences and Their Applications-March 2004, noti ces@math. ou. edu in the case of p. 350 the editor and noti ces@ams. o rg in NRC Mathematical Sciences Education Board-April 2004, p. 446 the case of the managing editor. The NSF Mathematical and Physical Sciences Advisory Committee-February fax numbers are 405-325-7484 for 20d4,p.242 the editor and 401-331-3842 for the Program Officers for Federal Funding Agencies-October 2004, managing editor. Postal addresses p. 1078 (DoD, DoE); December 2004, p. 1368 (NSF) may be found in the masthead. 1367 DECEMBER 2004 NOTICES OF THE AMS Reference and Book List December 20, 2004: NSA grants june 30, 2005: Nominations for Thomas Russell in quantum computing algorithms. the 2005 Fermat Prize. See http: I I 703-292-4863 See http:llwww.nas.govlmspl www.ups-tlse.friACTUALITESI [email protected] msp00002. cfm. Sciences1Prix_Fermat_2004l December 31, 2004: Supporting Aregl ement. html. Ken Shaw references for nominations for Alan T. january 1, 2006: Applications for 703-292-4859 Waterman Award. See "Mathematics ICM 2006 Travel Grants. See http: I I [email protected] Opportunities" in this issue. www. i cm2006. org or email: grants@ january 1, 2005: Entries for Cryp i cm2006. org. Michael Steuerwalt tologia undergraduate paper compe titions. See http: I lwww. dean. usma. NSF Division of Mathematical 703-292-4860 edulmathlpubslcryptologial. Sciences [email protected] january 5, 2005: Applications for Listed below are names, email ad fellowships for the IMA 2005-2006 dresses, and telephone numbers for Henry Warchall thematic program. See "Mathematics the program directors for the coming 703-292-4861 Opportunities" in this issue. academic year in the Division of Math [email protected] january 7, 2005: Applications for ematical Sciences of the National Sci National Defense Science and Engi ence Foundation. Computational Mathematics neering Graduate Fellowships. See Leland Jameson Algebra, Number Theory, and "Mathematics Opportunities" in this 703-292-4883 issue. Combinatorics Tomek Bartoszynski [email protected] january 10,2005: Applications for 703-292-4885 AAUW Selected Professions Fellow [email protected] Thomas Russell ships. See http: I lwww. aauw. o rgl 703-292-4863 fgalfellowships_grantsl [email protected] selected. cfm or contact the AAUW Donald James 703-292-4877 Educational Foundation, 1111 Six Junping Wang teenth St., N.W., Washington, DC [email protected] 703-292-4488 20036; telephone 800-326-2289 [email protected] (AAUW); fax 202-872-1425; email: Tie Luo i nfo@aauw. org. 703-292-8448 january 31, 2005: Applications for [email protected] Geometric Analysis, Topology, and postdoctoral fellowships at the Mittag Foundations Leffler Institute. See "Mathematics Kathleen O'Hara Tomek Bartoszynski Opportunities" in this issue. 703-292-8491 703-292-4885 February 1, 2005: Applications for [email protected] [email protected] AWM Travel Grants and AWM Men taring Travel Grants. See the AWM Alvin Thaler Joanna Kania-Bartoszynska website, http: I lwww. awm-math. 703-292-8039 703-292-4881 orgltravel grants. html; telephone: [email protected] [email protected] 301-405-7892; email: awm@math. umd. edu. Analysis Benjamin Mann (on leave) February 15, 2005: Nominations John B. Conway 703-292-4867 703-292-4872 for Clay Mathematics Institute Liftoff [email protected] Program. See "Mathematics Opportu [email protected] nities" in this issue. Stewart Priddy March 1, 2005: Applications for · Joe Jenkins 703-292-4878 EDGE Summer Program. See "Mathe 703-292-4870 [email protected] matics Opportunities" in this issue. [email protected] March 1, 2005: Applications for New Directions visiting professor Wing Suet Li Christopher Stark ships at IMA. See "Mathematics Op 703-292-8104 703-292-4869 portunities" in this issue. [email protected] [email protected] May 1, 2005: Applications for AWM Travel Grants. See the AWM website, Applied Mathematics Infrastructure http:llwww.awm-math.orgl Mary Ann Horn John B. Conway travel grants. html; telephone: 301- 703-292-4879 703-2Q2-4872 405-7892; email: awm@math. umd. edu. [email protected] [email protected] 1368 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Reference and Book list Lloyd Douglas science, and engineering. listed below Lee Zia 703-292-4862 is contact information for those EHR 703-292-5140 [email protected] program officers whose fields are in [email protected] the mathematical sciences or mathe Statistics and Probability matics education. These individuals Division of Human Resource Keith Crank (on leave) can provide information about the Development 703-292-4880 programs they oversee, Roosevelt Johnson [email protected] as well as in formation about other EHR programs 703-292-8640 of interest to mathematicians. Shulamith Gross The postal address is: Directorate for Math and Science Partnership 703-292-4868 Program [email protected] Education and Human Resources, National Science Foundation, 4201 Diane Spresser 703-292-5188 Wilson Boulevard, Arlington, VA Xuming He [email protected] 703-292-4876 22230. The EHR webpage is http: I I [email protected] www. nsf. govlehr. Office of Assistant Director for Division of Elementary, Secondary, Education and Human Resources Wen Masters and Informal Education James Ughtbourne 703-292-4871 William Frascella, 703-292-4628 [email protected] Division Director 703-292-8628 [email protected] [email protected] Robert Serfling 703-292-4884 Book List [email protected] John (Spud) Bradley The Book List highlights books that 703-292-8620 have mathematical themes and are The administrative staff includes: [email protected] aimed at a broad audience potentially Division Director including mathematicians, students, William Rundell Monica Mitchell and the general public. When a book 703-292-4850 703-292-8613 has been reviewed in the Notices, a · [email protected] [email protected] reference is given to the review. Gen erally the list will contain only books Executive Officer Monica Neagoy published within the last two years, Deborah Lockhart 703-292-8613 though exceptions may be made in cases 703-292-4858 [email protected] where current events (e.g., the [email protected] death of a prominent mathematician, coverage of a certain piece of mathe Mark Saul Assistant Program Director matics in the news) warrant drawing 703-292-8614 readers' attention to older books. Sug Dean Evasius [email protected] 703-292-8132 gestions for books to include on the list [email protected] may be sent to noti ces-bookl i st@ Division of Research, Evaluation, ams .org. and Communication Administrative Officer *Added to "Book List" since the Tyzcer Henson John Cherniavsky list's last appearance. 703-292-4852 703-292-5136 [email protected] [email protected] Abel's Proof: An Essay on the Sources and Meaning ofMathematical Division Secretary Finbarr (Barry) Sloane Unsolvability, by Peter Pesic. MIT Press, Jennifer Connell 703-292-5146 May 2003. ISBN 0-262-16216-4. 703-292-5301 [email protected] (Reviewed March 2004.) [email protected] Across the Board: The Mathematics of Chessboard Division of Undergraduate Problems, by John J. Watkins. Princeton Education University Press, NSF Mathematics Education April2004. ISBN 0-691-11503-6. Staff John Haddock Adam Spencer's Book of Numbers, (contact information The Directorate for Education and unavailable) by Adam Spencer. Four Walls Eight Human Resources (EHR) of the Na Windows, January 2004. ISBN 1-568- tional Science Foundation (NSF) spon Elizabeth Teles 58289-7. sors a r;ange of programs that support 703-292-4643 Alan Turing: Life and Legacy of a educational projects in mathematics, [email protected] Great Thinker, edited by Christof DECEMBER 2004 NOTICES OF THE AMS 1369 Reference and Book List Teuscher. Springer, 2004. ISBN 3-540- December 2003. ISBN 9-812-38259-3. John Wiley & Sons, January 2003. ISBN 20020-7. Four Colors Suffice: How the Map 0-471-08601-0. Alpha & Omega: The Search for the Problem Was Solved, by Robin Wilson. Linked: The New Science of Net Beginning and End of the Universe, by Princeton University Press, March works, by Albert-Laszlo Barabasi. Charles Seife. Viking, July 2003. ISBN 2003. ISBN 0-691-11533-8. (Reviewed Perseus Publishing, May 2002. ISBN 0-6 70-03179-8. February 2004.) 0-738-20667-9. (Reviewed February Automated Reasoning and the Dis From Newton to Hawking: A History 2004.) covery of Missing and Elegant Proofs, of Cambridge University's Lucasian · Masters of Theory: Cambridge and by Larry Wos and Gail Pieper. Rillton Professors of Mathematics, edited by the Rise of Mathematical Physics, by Press, December 2003. ISBN 1-58949- Kevin C. Knox and Richard Noakes. Andrew Warwick. University of 023-1. Cambridge University Press, Novem Chicago Press, July 2003. ISBN 0-226- Beyond Coincidence, by Martin Plim ber 2003. ISBN 0-521-66310-5. 87375-7. mer and Brian King. Icon Books, March Gamma: Exploring Euler's Constant, Math through the Ages: A Gentle 2004. ISBN 1-840-46534-4. by Julian Havil. Princeton University History for Teachers and Others, by Beyond the Limit: The Dream of Press, May 2003. ISBN 0-691-09983-9. WilliamP. Berlinghoff and Fernando Q. Sofya Kovalevskaya, by Joan Spicci. (Reviewed August 2004.) Gouvea. Oxton House, 2002. ISBN 1- Forge, August 2002. ISBN 0-765- Geometry: Our Cultural Heritage, 881929-21-3. (Reviewed October 2004.) 30233-0. (Reviewed January 2004.) by Audun Holme. Springer, April The Mathematical Century: The 30 The Changing Shape of Geometry: 2002. ISBN 3-540-41949-7. (Reviewed Greatest Problems of the Last 1 00 Celebrating a Century of Geometry May 2004.) Years, by Piergiorgio Odifreddi, trans and Geometry Teaching, edited by Godel's Proof, by Ernest Nagel and lated by Arturo Sangalli. Princeton Chris Pritchard. Cambridge Univer James R. Newman. New York Univer University Press, May 2004. ISBN 0- sity Press, January 2003. ISBN 0-521- sity Press, revised edition, February 691-09294-X. 53162-4. 2002. ISBN 0-8147-5816-9. (Reviewed Mathematical journeys, by Peter D. Cogwheels of the Mind: The Story of March 2004.) Schumer. Wiley-lnterscience, Febru Venn Diagrams, by A. W. F. Edwards. The Golden Ratio: The Story ofPhi, ary 2004. ISBN 0-471-22066-3. Johns Hopkins University Press, April the World's Most Astonishing Number, A Mathematician's Survival Guide: 2004. ISBN 0-801-87434-3. by Mario Livio. Broadway Books, Graduate School and Early Career De Constantin Caratheodory: Mathe October 2002. ISBN 0-767-90815-5. velopment, by Steven G. Krantz. AMS, matics and Politics in Turbulent Times, A Handbook of Mathematical Dis August 2003. ISBN 0-8218-3455-X. by M. Georgiadou. Springer, Septem course, by Charles Wells. Infinity (ReviewedApril2004.) ber 2004. ISBN 3-540-44258-8. Publishing Company, 2003. ISBN 0- The Constants of Nature: From 7414-168 5-9. (Reviewed September Mathematicians as Enquirers: Alpha to Omega-the Numbers That 2004.) LearnLng about Learning Mathematics, Encode the Deepest Secrets of the Uni How Economics Became a Mathe edited by Leone Burton. Kluwer, April verse, by John D. Barrow. Jonathan matical Science, by E. Roy Weintraub. 2004. Hardbound, ISBN 1-4020-7853- Cape, September 2002. Pantheon Duke University Press, June 2002. 6; paperback, ISBN 1-4020-7859-5; Books, January 2003. ISBN 0-375- ISBN 0-822-32856-9. eBook, ISBN 1-4020-7908-7. 42221-8. (Reviewed November 2004.) Infinity: The Quest to Think the Un Mathematics and Culture I, edited Count Down: Six Kids Vie for Glory thinkable, by Brian Clegg. Carroll & Graf, by Michele Emmer. Springer, January at the World's Toughest Math Compe December 2003. ISBN 0-786-71285-6. 2004. ISBN 3-540-01770-4. tition, by Steve Olson. Houghton Mif Information: The New Language of Mathematics and War, edited by Bern flin, April2004. ISBN 0-618-25141-3. Science, by Hans Christian von Baeyer. helmBooss-Bavnbek andJens H0yrup. (Reviewed August 2004.) Weidenfeld & Nicolson, October 2003. Birkhauser, December 2003. ISBN 3- The Curious Life of Robert Hooke, ISBN 0-297-60725-1 (hardcover), 0-753- 764-31634-9. the Man Who Measured London, by 81782-9 (paperback). Mathematics, Art, Technology, and Lisa Jardine. HarperCollins, February just Six Numbers: The Deep Forces Cinema, edited by Michele Emmer and 2004. ISBN 0-060-53897-X. That Shape the Universe, by Martin Mirella Manaresi. Springer, 2003. ISBN Everything and More: A Compact Rees. Basic Books, May 2001. ISBN 0- 3-540-00601-X. History of Infinity, by David Foster 465-03673-2. (Reviewed November Mathematics in Nature: Modeling Wallace. W. W. Norton, October 2003. 2004.) Patterns in the Natural World, by John ISBN 0-393-00338-8. (Reviewed Karl Pearson: The Scientific Life in Adam. Princeton University Press, June/July 2004.) a Statistical Age, by Theodore M. Porter, November 2003. ISBN 0-691-11429-3. The Fabric of the Cosmos, by Brian Princeton University Press, February The Mathematics of juggling, by Greene. Knopf, February 2004. ISBN 2004. ISBN 0-691-11445-5. Burkard Polster. Springer, November 0-375-41288-3. Kepler's Conjecture: How Some of 2002. ISBN 0-387-95513-5. (Reviewed Fields Medalists' Lectures, edited the Greatest Minds in History Helped January 2004.) by Sir Michael Atiyah and Daniel Iagol Solve One of the Oldest Math Prob Meta Math! The Quest for Omega, nitzer. World Scientific, 2nd edition, lems in the World, by George G. Szpiro. by Gregory J. Chaitin. April 2004. 1370 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Reference and Book List Available at http: I /www. cs. Shooting the Sun, by Max Byrd. umaine.edu/~chaitin/omega.html. Bantam, December 2003. ISBN 0-553- More Mathematical Astronomy 80208-9. Morsels, by Jean Meeus. Willmann-Bell Signs of the Inka Khipu: Binary Cod Inc., 2002. ISBN 0-943396-743. ing in the Andean Knotted-String The Music of the Primes: Searching Records, by Gary Urton. University of to Solve the Greatest Mystery in Texas Press, August 2003. ISBN 0-292- 78540-2. Mathematics, by Marcus Du Sautoy. ',, '" ww ...... , _ ....; HarperCollins, April 2003. ISBN 0- Six Degrees: The Science of a Con 066-21070-4. nected Age, by Duncan J Watts. W. W. Newton's Apple: Isaac Newton and Norton, February 2003. ISBN 0-393- the English Scientific Renaissance, by 04142-5. (Reviewed February 2004.) Peter Aughton. Weidenfeld&Nicolson, Strange Curves, Counting Rabbits, October 2003. ISBN 0-297-84321-4. and Other Mathematical Explorations, The Number rr, by Pierre Eymard by Keith Ball. Princeton University and Jean-Pierre Lafon. AMS, 2004. Press, November 2003. ISBN 0-691- ISBN 0-8218-3246-8. 11321-1. (Reviewed in this issue.) On the Nature of Human Romantic Sync: The Emerging Science ofSpon Interaction, by Karl Iagnemma. Dial taneous Order, by Steven Strogatz. Press, April2003. ISBN 0-385-33593-8. Hyperion, February 2003. ISBN 0-786- Phase Change: The Computer Rev 86844-9. (Reviewed March 2004.) olution in Science and Mathematics, by Douglas S. Robertson. Oxford University Press, March 2003. ISBN 0-195-15748-6. Portraits of the Earth: A Mathemati cian Looks at Maps, by Timothy G. Feeman. AMS, September 2002. ISBN 0- 8218-3255-7. Predicting Presidential Elections and Other Things, by Ray C. Fair. Stanford University Press, August 2002. ISBN 0- 804-7 4509-9. Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem, by John Derbyshire. Joseph Henry Press, March 2003. ISBN 0-309-08549-7. Probability Theory: The Logic ofSci ence, by E. T. Jaynes, edited by G. Larry Bretthorst. Cambridge University Press, April2003. ISBN 0-521-59271-2. Proofs from The Book, by Martin Aigner and Gtinter M. Ziegler. Springer l~ '* .iA ~ Verlag, third edition, December 2003. .... ISBN 3-540-40460-0. The Reader of Gentlemen's Mail: Herbert 0. Yardley and the Birth of American Codebreaking, by David ~~ Kahn. Yale University Press, March 2004. 1 ~ u.l L • • J~ ISBN 0-300-09846-4. The Riemann Hypothesis: The ~ Greatest Unsolved Problem in Mathe l "-~ matics, by Karl Sabbagh. Farrar Straus & Giroux, April 2003. ISBN 0-374- L ••J l.~ 25007-3. The Saga of Mathematics: A Brief History, by Marty Lewinter and William Widulski. Prentice Hall, January 2002. ISBN 0-130-34079-0. DECEMBER 2004 NOTICES OF THE AMS 1371 From the AMS Secretary Statistics on Women Invited Hour Address Speakers Mathematicians Compiled by at AMS Meetings (1994-2003) Male: 487 87% theAMS Female: 76 13% Unknown: 0 0% At its August 1985 meeting the Council of the AMS Total checked: 563 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, speak at AMS Meetings (1999-2003) ers at Special Sessions at AMS meetings, percentage of women speakers in AMS Special Sessions by gender of or Male: 10,059 78% ganizers, and members of editorial boards of AMS journals. Female: 1,801 14% It was subsequently decided that this information would Unknown: 1,052 8% be gathered by determining the sex of the individuals in Total checked: 12,912 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 be collected Percentage of Women Speakers using the AMS-IMS-MAA Annual Survey. Since name iden in AMS Special Sessions tification was used, the information for some categories ne by Gender of Organizers (2003) cessitated the use of three classifications: Special Sessions Male: names that were obviously male with at Least One Woman Organizer Female: names that were obviously female Unknown: names that could not be identified as clearly Total number of speakers: 604 male or female (e.g., only initials given, non-gender-specific Male: 468 77% names, etc.) · Female: 130 22% The following is the nineteenth reporting of this infor Unknown: 6 1% mation. Updated reports will appear annually in the Notices. Special Sessions with No Women Organizers Total number of speakers: 1,686 Male : 1,426 85% Female: 223 13% Unknown: 37 2% 2003 Members of the AMS Trustees and Council Members Residing in the U.S. 2000 2001 2002 2003 Male : 12,675 68% Total: 50 49 47 48 Female: 3,305 18% Male: 37 74% 37 76% 33 70% 36 75% Unknown: 2,619 14% Female : 13 26% 12 24% 14 30% 12 25% Total checked: 18,599 Members of AMS Editorial Committees 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 Total: 176 194 198 213 213 230 219 224 230 224 Male: 161 91% 175 90% 177 89% 189 89% 182 85% 198 86% 186 85% 190 85% 195 85% 189 84% Female: 1 5 9% 19 10% 21 11% 24 11% 31 15% 32 14% 33 15% 34 15% 35 15% 35 16% Ph.D.'s Granted to U.S. Citizens 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 Total: 469 567 493 516 586 554 537 494 418 499 Male: 345 74% 426 75% 377 76% 368 71% 423 72% 367 66% 379 71% 343 69% 291 70% 341 68% Female : 124 26% 141 25% 116 24% 148 29% 163 28% 187 34% 158 29% 151 31% 127 30% 1 58 32% 1372 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Mathematics Calendar The most comprehensive and up-to-date Mathematics Calendar information is available one-MATH at http://www.ams.org/mathcal/. December 2004 1 3-1 7 The 9th Asian Technology Conference in Mathematics (ATCM2004), Nationallnstitute of Education, Singapore. (Apr. 2004, 5-16 International Workshop on Nonlinear Partial Differential p. 461) Equations, IPM, Tehran, Iran. (Aug. 2003, p. 850) *5-8 International Conference on Mathematical Inequalities and 1 3-1 7 Recent Advances in Core Model Theory, AIM Research their Applications, I, Victoria University, Melbourne, Australia. Conference Center, Palo Alto, California. (Jun/Jul. 2004, p. 690) Aim: To stimulate researchers from all fields of science to collab 1 3-1 8 Joint Conference: The 2004 NZIMA Conference in Com orate and present new results and applications in mathematical binatorics and Its Applications and The 29th Australasian inequalities. Conference in Combinatorial Mathematics and Combinatorial Information: http: I /rgmia. vu. edu. au/conference/. Computing (29th ACCMCC), Copthornes-Manuels, Lake Taupo, New Zealand. (Jun/Jul. 2004, p. 690) '' 6-8 OSDI '04 - 6th Symposium on Operating Systems Design and Implementation, Renaissance Pare 55 Hotel, San Francisco, 14-16 Sixth IMA International Conference on Mathematics in California. Signal Processing, The Royal Agricultural College, Cirencester, UK. Description: OSDI brings together professionals from academic (Nov. 2004,p. 1263) and industrial backgrounds in what has become a premier forum 1 5-1 7 Arithmetic, Geometry and Topology, Conference on the for discussing the design, implementation, and implications of Occasion of Larry Breen's Sixtieth Birthday, Institut Galilee, systems software. Universite Paris 13, France. (Jun/Jul. 2004, p. 690) Information: http: I /www. usenix . erg/ events/ osdi04/. 16-1 9 International Conference on History and Heritage of 6-1 0 Ill joint Meeting Japan-Mexico in Topology and Its Appli Mathematical Sciences, Govt. Model Autonomous Holkar Science cations, Oaxaca, Mexico. (Jun/Jul. 2004, p. 690) College, Indore, India. (Jun/Jul. 2004, p. 690) 6-1 0 Compa.ct Moduli Spaces and Birational Geometry, AIM 1 7-1 94th WSEAS International Conference on Signal Processing, Research Conference Center, Palo Alto, California. (Jun/Jul. 2004, Computational Geometry & Artificial Vision (ISCGAV'04), Puerto p. 690) De La Cruz, Tenerife, Canary Islands, Spain. (Jun/Jul. 2004, p. 691) 9-1 1 Discrete Mathematics and Its Applications, Amrita Vishwa 1 7-19 International Conference on Smarandache Algebraic Vidyapeetham,Ettimadai, Coimbatore, TamilNadu,India. (Aug. 2004, Structures, lndian Institute of Technology, liT Madras, Chennai, p. 832) Tamil Nadu, India. (Aug. 2003, p. 850) 1 3-1 5 Pseudospectra and Structural Dynamics, University of 17-22 The Third International Congress of Chinese Mathe Bristol, Bristol, UK. (Oct. 2004, p. 1095) maticians, The Chinese Univ. of Hong Kong, Shatin, Hong Kong, This section contains announcements of meetings and conferences respect to participation in the meeting, this fact should be noted. of interest to some segment of the mathematical public, including ad All communications on meetings and conferences in the mathematical hoc, local, or regional meetings, and meetings and symposia devoted sciences should be sent to the Editor of the Notices in care of the American Mathematical Society in Providence or electronically to notices@ams . org to specialized topics, as well as announcements of regularly scheduled · or mathcal@ams. erg. meetings of national or international mathematical organizations. A complete list of meetings of the Society can be found on the last page of In order to allow participants to arrange their travel plans, organizers of each issue. meetings are urged to submit information for these listings early enough 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 for papers and specifies the place, date, subject (when applicable), and the meeting in question. To achieve this, listings should be received in Providence eight months prior to the scheduled date of the meeting. the speakers; a second announcement will be published only if there are changes or necessary additional information. Once an announcement The complete listing of the Mathematics Calendar will be published 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 : I /www. information. In any case, if there is any application deadline with ams. erg/. DECEMBER 2004 NOTICES OF THE AMS 1373 Mathematics Calendar P.R. China. (Dec. 2003, p. 1443) 24-July 22 Developments in Quantitative Finance, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK. (Aug. 2004, 1 8-20 Recent Advances in Mathematics & Its Applications (ISRAMA 2004), Kolkata (Calcutta), lndia. (Jun/Jul. 2004, p. 691) p. 833) 26-30 Front Propagation 20-23 Sharp Thresholds for Mixing Times, AIM Research Con and Nonlinear Stochastic PDEs for Combustion and Other Applications, Centre de ference Center, Palo Alto, California. (Jun/Jul. 2004, p. 691) Recherches Mathematiques, Universite de Montreal, Montreal, Quebec, Canada. 29-31 6th WSEAS International Conference on Mathematical (Aug. 2004, p. 833) Methods and Computational Techniques in Electrical Engineer 27-29 IMAC-XXIII Preconference ing (MMACTEE 2004), Vouliagmeni, Athens, Greece. (Jun/ Jul. 2004, Courses, Rosen Plaza Hotel, p. 691) Orlando, Florida. (May 2004, p. 5 76) 31-February 1 DIMACS Workshop on Bounded Rationality, DI january 2005 MACS Center, CoRE Bldg, Rutgers University, Piscataway, New 5-8 joint Mathematics Meetings, Hyatt Regency Atlanta &Atlanta Jersey. (Oct. 2004, p. 1095) Marriott Marquis, Atlanta, Georgia. (Sept. 2002, p. 1001) '' 31-February 2 IPAM Workshop: Mathematics of the Ear and 6-9 24th Nordic and 1st Franco-Nordic Congress of Mathe Sound Signal Processing, UCLA, Los Angeles, California. maticians, University of Iceland, Reykjavik, Iceland. (Nov. 2004, Organizers: Jack Xin, Li Deng, Stanley Osher, Yingyong Qi, James p. 1263) Sneyd. Information: http: I lwww. ipam. ucla . edulprogramsl 7-8 2004-05 ASL Winter Meeting (with Joint Mathematics es2005l. Meetings), Atlanta, Georgia. (Jun/ Jul. 2004, p. 691) 31-February 3 IMAC-XXIII: A Conference on Structural Dynamics, 8-1 5 Geometry: Interactions with Algebra and Analysis, Napier, Rosen Plaza Hotel, Orlando, Florida. (May 2004, p. 5 76) New Zealand. (May 2004, p. 576) February 2005 9-11 2005 Hawaii International Conference on Statistics, Math ematics and Related Fields, Sheraton, Waikiki Hotel, Honolulu, 3-4 (NEW DATE) DIMACS Workshop on Markets as Predictive De Hawaii. (Aug. 2004, p. 832) vices (Information Markets), DIMACS Center, Rutgers University, Piscataway, New Jersey. (Jun/ Jul. 2004, p. 691) 10-14 4th Symposium on Levy Processes, University of Man chester, Manchester, England. (Oct. 2004, p. 1095) 7-91MATutoriai/Workshop:Where Mathematics Meets Industry, University of Minnesota, Minneapolis, Minnesota. (Jun/ Jul. 2004, 1 0-1 4 Braid Groups, Clusters and Free Probability, AIM Research p. 691) Conference Center, Palo Alto, California. (Jun/ Jul. 2004, p. 691) 14-1 8 Geometry: Interactions with Algebra and Analysis, Uni 1 0-14 International Symposium on "Variational Methods and versity of Auckland, Auckland, New Zealand. (May 2004, p. 576) Nonlinear Differential Equations on the Occasion of the 60th Birthday of Antonio Ambrosetti", University of Rome 3, Rome, 1 5-1 7 International Symposium on Stochastic Models in Relia Italy. (Nov. 2004, p. 1264) bility, Safety, Security and Logistics (SMRSSL'05), Negev Academic College of Engineering (NACE), Beer Sheva, Israel. (Apr. 2004, p. 461) • 1 0-14 Multiscale Processes in Fusion Plasmas, IPAM at UCLA, 460 Portola Plaza, Los Angeles, California. 1 7-21 CERM.4 (Fourth Congress of the European Society for Focus: Multiscale Processes in Fusion Plasmas is a five-day workshop Research in Mathematics Education), Sant Feliu de Guixols, Spain focussing on five physical phenomena in fusion plasmas. (Oct. 2004, p. 1095) Information: http: I lwww. ipam. ucla. edulprogramslfus2005l. '' 21-26 Mathematical Methods in Quantum Mechanics, Cas a Della Gioventli, Bressanone, Italy. 1 0-1 4 Workshop on Topological Strings, The Fields Institute, Aim: To present the state of the art in some challenging open Toronto, Ontario, Canada. (Apr. 2004, p. 461) problems in Quantum Mechanics from the point of view of 12-14 Second Joint IMS/ISBA International Conference, Bormio, Mathematical Physics. It is mainly addressed to young people Italy (Italian Alps). (Aug. 2004, p. 833) interested in working on the subject. Topics: Scattering for linear and nonlinear Schrodinger equation, 1 7-July 1 5 Model Theory and Applications to Algebra and Anal many-body problems, derivation of macroscopic equations from ysis, Isaac Newton Institute for Mathematical Sciences, Cambridge, quantum dynamics, Born-Oppenheimer approximation, England. (Apr. 2003, p. 500) classical behavior in quantum systems. Three short courses will be given '24-28 IPAM workshop: Probabilistic Models of Cognition-The in a series of lectures scheduled in the morning of each day. Mathematics of Mind, UCLA, Los Angeles, California. Some invited talks will be given in the afternoon followed by short Organizers: Alan Yuille, Josh Tenenbaum. contributed talks given by participants. Information: http: I lwww. ipam. ucla. edulprogramsl cog2005l. Courses: M. Pulvirenti (Roma, La Sapienza), Introduction to quantum kinetic theory; G. Velo (Bologna), Basic mathematical aspects of ' 24-29 RTNS2005: Recent Trends in Nonlinear Science 2005 nonlinear Schrodinger equations; J. Yngvason (Wien), The Bose (winter school), Castellon, Spain. Einstein condensation. Goal: The goal of these winter schools is to train participants to Invited Speakers: S. Albeverio (Bonn), L. Erdos (Munich),]. Frohlich* theory and applications in the field of nonlinear science. This will (ETH, Zurich), A. Joye (Grenoble), S. Teufel (Warwick), K. Yajima be done in an atmosphere of informal discussion and interchange (Tokyo)* to be confirmed. of ideas. These courses have received official recognition in the Organizers: G. Dell' Antonio (Roma La Sapienza), R. Figari (Napoli), doctorate programs of Universitat Autonoma de Barcelona and S. Graffi (Bologna), V. Grecchi (Bologna), A. Sacchetti (Modena), A. Universitat Politecnica de Catalunya. Teta (L'Aquila). Courses: (http: I lwww. rtns2005 . uj i. esl courses. html). Information: http: I lwww. MMQM. unimore. it; email: info. mmqm© Registration: (http: I lwww. rtns2005. uj i. es/registration.) unimo. it. html. NOTE: The number of available places in the school is limited. Final admissions will be by the registration order. * 22-26 IPAM Workshop: Mathematical Issues and Challenges Information: Second Winter School of the Spanish Network DANCE in Data Assimilation for Geophysical Systems-Interdisciplinary (http: I lwww. dance-net . org/). Perspectives, UCLA, Los Angeles, California. 1374 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Mathematics Calendar Organizers: Christopher Jones, Kayo Ide, Robert Miller, Douglas Program: These are tutorials to introduce mathematicians to the Nychka. main issues and problems of current interest in astrophysics, and to Information: http://www. ipam . ucla. edu/programs/da2005/. introduce astrophysicists to the principal mathematical techniques relevant to doing computations in astrophysics. '' 2 3-2 5 Graph Asymmetries, Massey University, Palmerston North, Information: http://www. ipam. ucla. edu/programs/pcatut/. New Zealand. Topics: The topics to be discussed at the workshop comprise 14-l 8 Deterministic and stochastic Navier-Stokes equations, but are not limited to: Endomorphism monoids of classes of AIM Research Conference Center, Palo Alto, California. (Oct. 2004, graphs such as paths, trees, or bipartite graphs; Graphs whose p. 1095) endomorphism monoids have prescribed properties; Semigroups l 8-l 9 AMS Southeastern Section Meeting, Western Kentucky whose Cayley graphs have prescribed properties; Graphs from University, Bowling Green, Kentucky. (May 2004, p. 5 76) other algebraic structures; Aut- and End-vertex transitive Cayley graphs of semigroups; Graph grammars and their relationship to 1 9,-20 Twenty-Eighth Annual Texas Partial Differential Equa graph morphisms; Asymmetric designs and graph families; Graph tions Conference, University of Texas, Pan American, Edinburg, asymmetries in computer- or life science. Texas. (Oct. 2004, p. 1095) Deadlines: Abstract submission: january 7, 2005. Author noti 1 9-22 2005ASLAnnual Meeting,Stanford,California.(Jun/ Jul. 2004, fication: january 28, 2005. Final abstract deadline: February 11, p. 692) 2005. Information: Workshop Page: http: //wga. massey. ac. nz/wga05/; 21-25 Extensions of Hilbert's Tenth Problem, AIM Research RolandKaschek, email: R. H. Kaschek@massey. ac. nz;UlrichKnauer, Conference Center, Palo Alto, California. (Sept. 2004, p. 970) email:[email protected]. 21-2 5 Workshop on N= 1 Compactifications, The Fields Institute, Toronto, Ontario, Canada. (Mar. 2004, p. 361) March 2005 22-26 Conference on Algebra and its Applications, Center of l-2 DIMACS Short Course: A Field Guide to GenBank and NCBI Ring Theory and Its Applications, Department of Mathematics, Molecular Biology Resources, DIMACS Center, Rutgers University, Ohio University, Athens, Ohio. (Oct. 2004, p. 1095) Piscataway, New jersey. (Jun/ Jul. 2004, p. 692) 24-27 Geometric Representation Theory, University of Arizona, 2-5 Representing Unresolved Degrees of Freedom for the Tucson, Arizona. (Aug. 2004, p. 833) Atmosphere and Ocean, Centre de Recherches Mathematiques, 27-31 The 3rd International Conference on Sciences of Elec Universite de Montreal, Montreal, Quebec, Canada. (Aug. 2004, tronic, Technologies of Information and Telecommunications p. 833) (SETIT 2005), Susa, Tunisia. (Nov. 2004, p. 1264) 3-5 International Conference on Environmental Fluid Mechanics 28-30 IMA Tutorial/Workshop: New Paradigms in Computation, (ICEFM'05), Indian Institute of Technology Guwahati, Guwahati, University of Minnesota, Minneapolis, Minnesota. (Jun/Jul. 2004, India. (Sept. 2004, p. 971) p. 692) 6-l 2 International Conference on Algebras, in Memory of Kostia 28-April 1 Generalized Kostka Polynomials, AIM Research Con Beidar, National Cheng Kung University, Tainan, Taiwan. (Nov. 2004, ference Center, Palo Alto, California. (Jun/Jul. 2004, p. 692) p. 1264) * 28-April 1 Topology and geometry of the moduli space of 7-9 DIMACS Working Group on Order Theoretic Aspects of curves, AIM Research Conference Center, Palo Alto, California. Epidemiology, DIMACS Center, Rutgers University, Piscataway, Organizers: Ravi Vakil and Ulrike Tillmann. New Jersey. (Jun/Jul. 2004, p. 692) Workshop topics: This workshop, sponsored by AIM and the NSF, 7-11 Third International Conference on Pattern Avoiding Permu will be devoted to bringing the communities of topologists and tations, University of Florida, Gainesville, Florida. (Jun/Jul. 2004, algebraic geometers together. The aim is to have an active exchange p. 692) of results, techniques and ideas on the cohomology of the moduli spaces of curves. Specific topics to be addressed include: Integral *?-June l 0 IPAM Long Program: Grand Challenge Problems in cohomology, stable and unstable. Tautological cohomology of the Computational Astrophysics, UCLA, Los Angeles, California. compactified moduli space. Applications to Gromov-Witten theory. Desscription: This long-term program will involve a community Deadline: December 15, 2004. of senior and junior researchers. The intent is for long-term Information: http : //aimath. org/ ARCC/workshops/ participants to have an opportunity to learn about computational modspacecurves .html. astrophysics from the perspectives of many different fields mathematics, science and astronomy. In addition to these activities, 28-April 1 Workshop on String Phenomenology, The Perimeter there will be opening tutorials, four workshops, and a culminating Institute, Waterloo, Ontario, Canada. (Apr. 2004, p. 461) workshop at Lake Arrowhead. Full and partial support for long-term participants is available, and those interested are encouraged to 2 9-April l 14th International Workshop on Matrices and Statis fill out an online application at the website above. Support for tics, Massey University, Albany Campus, Auckland, New Zealand. individual workshops will also be available, and may be applied (Nov. 2004,p. 1264) for through the online application for each workshop. Funding for participants is available at all academic levels, though recent April 2005 PhD's, graduate students, and researchers in the early stages of 1-July 8 Special Semester on "Modern Methods of Time their career are especially encouraged to apply. Frequency Analysis", Erwin Schroedinger Institute (ESI) for Math Organizers: Willy Benz, Philip Colella, Richard Klein, James ematical Physics, Vienna, Austria. (Apr. 2004, p. 461) McWilliams, Joseph Monaghan, Mark Morris, Stanley Osher, Chi 2-3 AMS Eastern Section Meeting, University of Delaware, Newark, Wang Shu, Harold Yorke. Delaware. (May 2004, p. 576) Information: http://www. ipam. ucla. edu/programs/pca2005/. 4-8 Stiff Sources and Numerical Methods for Conservation '' 8-ll IPAM Program in Grand Challenge Problems in Computa Laws, AIM Research Conference Center, Palo Alto, California. (Nov. tional Astrophysics-Tutorials, UCLA, Los Angeles, California. 2004, p. 1264) DECEMBER 2004 NOTICES OF THE AMS 1375 Mathematics Calendar * 4-9 IPAM Workshop: Astrophysical Fluid Dynamics, UCLA, Los 28-30 Barrett Lectures: New Developments in Nonlinear Par Angeles, California. tial Differential Equations, University of Tennessee, Knoxville, Organizers: Richard Klein, Willy Benz, Philip Colella, James Tennessee. (Sept. 2004, p. 972) McWilliams, Joseph Monaghan, Michael Norman, Robert Rosner, Chi-Wang Shu, Jim Stone, Marco Velli. May 2005 Information: http : I lwww. ipam. ucla. edulprogramslpcaws11. 2-6 IMA Workshop: Experiments in Physical Biology, Part I, University of Minnesota, Minneapolis, Minnesota. (Jun/Jul. 2004, 6-1 0 Extracting Macroscopic Information from Molecular Dy p. 693) namics, Centre de Recherches Mathematiques, Universite de Montreal, Montreal, Quebec, Canada. (Aug. 2004, p. 833) * 2-61PAM Workshop: Relativistic Astrophysics, UCLA, Los Angeles, California. 8-1 0 AMS Central Section Meeting, Texas Tech University, Lub bock, Texas. (May 2004, p. 576) Organizers: Richard Matzner, Curt Cutler, Michael Holst, Richard Klein, Joseph Monaghan, Ewald Mueller, Tsvi Piran, Stuart Shapiro. '' 9-1 0 Third Annual Graduate Student Topology Conferen.ce, Information: http : I lwww. ipam . ucla. edulprogramslpcaws31. Northwestern University, Evanston, Illinois. Description: The purpose of this conference is to gather graduate 2-6 Workshop on Gravitational Aspects of String Theory, The students in topology and provide them the opportunity to give Fields Institute, Toronto, Ontario, Canada. (Apr. 2004, p. 461) talks, communicate recent advances, exchange new ideas, and meet other students in their field. The schedule will consist of keynote 5-6 DIMACS Workshop on Security of Web Services and E talks by Mike Hopkins (MIT) and Paul Seidel (Univ. Chicago), and Commerce, DIMACS Center, CoRE Bldg, Rutgers University, Piscat many student talks. Talks should be accessible to an audience of away, New Jersey. (Oct. 2004, p. 1096) graduate students of varying levels and need not be about original 6-9 Statistical Inferences on Shape Manifolds, AIM Research research, but simply something the speaker enjoys and wishes to Conference Center, Palo Alto, California. (JuniJul. 2004, p. 693) share. We hope to build upon the success of the first conference at Notre Dame University and the second conference at the University 11-1 5 Integrative Multiscale Modeling and Simulation in Mate of Minnesota. rials Science, Fluids and Environmental Science, Centre de Re Keynote Speakers: Mike Hopkins (MIT) and Paul Seidel (Univ. cherches Mathematiques, Universite de Montreal, Montreal, Quebec, Chicago). Canada. (Aug. 2004, p. 834) Organizers: Paul Pearson and Valentina Joukhovitski. 1 3-14 Sixth Mississippi State-UAB Conference on Differen Information: http: I lwww. math. northwestern. edul-pearsonpl tial Equations & Computational Simulations, Mississippi State conference. html;email: pearsonp@math. northwestern. edu or email: University, Mississippi State, Mississippi (Oct. 2004, p. 1096) [email protected]. 1 4-1 5 Conference in Honor of Heydar Radjavi's 70th Birthday, * 1 0-1 5 2005 USENIX Annual Technical Conference, Marriott Hotel Golf, Bled, Slovenia. (Aug. 2004, p. 834) Anaheim, Anaheim, California. 1 5-l 8 HPCS 2005: The New HPC Culture in Canada, The 19th Description: USENIX has always been the place to present ground Annual Symposium on High Performance Computing Systems breaking research and cutting-edge practices in a wide variety of & Applications, University of Guelph, Guelph, Ontario, Canada. technologies and environments and 2005 is no exception. Topics: An extensive Training Program; covering crucial topics 1 5-18 OSCAR'OS: The 3rd Annual Symposium on Open Source and led by highly respected instructors; General Session Refereed Cluster Application Resources (OSCAR), University of Guelph, Papers, discussing original work on topics in modern computing; Guelph, Ontario, Canada. (Nov. 2004, p. 1264) FREENIX/Open Source Refereed Papers, showcasing the latest 1 5-21 43rd International Symposium on Functional Equations, developments and interesting applications of open source software; Batz-sur Mer, France. (Nov. 2004, p. 1265) Guru Is In Sessions, where you can ask noted experts your most burning technical questions and get practical solutions. 1 5-21 ICMI Study 1 5: The Professional Education and Develop Information: http : I lwww. usenix. orgleventslusenix05l. ment of Teachers of Mathematics, Aguas de Lind6ia, Sao Paulo, Brazil. (Jun/Jul. 2004, p. 693) 11-1 5 IMA Workshop: Atomic Motion to Macroscopic Models: 16-20 IMA Workshop: Experiments in Physical Biology, Part II, The Problem of Disparate Temporal and Spatial Scales in Matter, University of Minnesota, Minneapolis, Minnesota. (Jun/Jul. 2004, University of Minnesota, Minneapolis, Minnesota. (Jun/Jul. 2004, p. 693) p. 692) 14-1 5 DIMACS Workshop on Intellectual Property Protec * 16-20 IPAM Workshop: Transport Phenomena in Computational tion, DIMACS Center, Rutgers University, Piscataway, New Jersey. Astrophysics, UCLA, Los Angeles, California. (Jun/Jul. 2004, p. 692) Organizers: Rolf-Peter Kudritzki, Adam Burrows, Jim Morel, Mark Morris, Chi-Wang Shu, William Watson, Harold Yorke 1 6-1 7 AMS Western Section Meeting, University of California, Information: For further information: http : I lwww. ipam. ucla. Santa Barbara, California. (May 2004, p. 5 76) edulprogramslpcaws41. * 1 8-22 IPAM Workshop: N-body Problems in Astrophysics, UCLA, Los Angeles, California. 16-20 Stability Criteria for Multi-dimensional Waves and Pat Organizers: Ben Moore, Sverre Aarseth, Willy Benz, Geoff Bryden, terns, AIM Research Conference Center, Palo Alto, California. (Nov. Hugh Couchman, Piet Hut, Ben Leimkuhler, Joseph Monaghan, 2004, p. 1265) Matthias Steinmetz. 1 7-20 Graph Theory with Altitude, University of Colorado at Information: http : I I www. ipam . ucla. edulprogramslpcaws21. Denver, Denver, Colorado. (Jun/Jul. 2004, p. 693) 1 8-July 1 3 Time at Work, Institut Henri Poincare, Paris, France. 19-21 CTS Conference on Combinatorics and Its Applications (Aug. 2004, p. 833) in Honor of Frank K. Hwang's 65th Birthday, National Chiao Tung University (NCTU), Hsin Chu, Taiwan. (Sept. 2004, p. 973) 27-May 1 Multiscale Modeling in Solids, Centre de Recherches Mathematiques, Universite de Montreal, Montreal, Quebec, Canada. 22-25 ICCS 2005: International Conference on Computational (Aug. 2004,p. 834) Science, Atlanta, Georgia. (Oct. 2004, p. 1096) 1376 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Mathematics Calendar 23-25 DIMACS Workshop on The Epidemiology and Evolution Geometry around Hypergeometric Functions, Galatasaray Uni of Influenza, DIMACS Center, CoRE Bldg, Rutgers University, versity, Ortakoy, Istanbul, Turkey. (Aug. 2004, p. 834) Piscataway, New Jersey. (Oct. 2004, p. 1096) 1 6-19 Second Joint International Meeting with the Deutsche · 29-June 35th Conference on Stochastic Analysis, Random Fields Mathematiker-Vereinigung (DMV) and the Oesterreichische and Applications and Minisymposium on Stochastic Methods in Mathematische Gesellschaft (OMG), Mainz, Germany. (May 2004, Financial Models V, Centro Stefano Franscini, Ascona, Switzerland. p. 576) Benaim (Neuchatel), T. Ko Confirmed invited speakers: M. 19-24 33rd Canadian Operator Symposium (COSy), dedicated morowski (Lublin), S. Meleard (Paris X), D. Nualart (Barcelone), to George Elliott's 60th birthday, University of Ottawa, Ottawa, enopole Evry), M. Scheutzow E. Perkins (Vancouver), B. Prum (G Ontario, Canada. (Nov. 2004, p. 1265) (TU-Ber lin), F. Viens (Purdue), N. Bouleau (ENPC Paris), R. Carmona (Princeton), P. Malliavin (Academie des Sciences Paris); W. Schmidt 1 9-24 First Announcement: Conference on Applied Mathematics (HfB Frankfurt). and Scientific Computing 4: On the occasion of Professor Organizers: R. Dalang (EPF Lausanne), M. Dozzi (Nancy), F. Russo Aganovic's 70th birthday, Brijuni, Croatia. (Nov. 2004, p. 1265) is 13). (Par 1 9-24 Conference on Applied Mathematics and Scientific Com Information: Contact: Mrs. E. Gindraux, lnstitut de Mathematiques, puting 4: On the occasion of Professor Aganovic's 70th Birthday, EPFL, CH-1 01 5 Lausanne, Switzerland; e mail: erika. gindraux@ Brijuni, Croatia. (Nov. 2004, p. 1265) epfl .ch. '' 20- 22 DIMACS Workshop on Detecting and Processing Regular june 2005 ities in High Throughput Biological Data, DIMACS Center, CoRE Bldg, Rutgers University, Piscataway, New Jersey. 1- 5 Stochastic Modeling in Financial Mathematics (joint with Description: The biological community is being innundated with SAMSI), Centre de Recherches Mathematiques, Universite de Montreal, a large amount of data and understanding this data is lagging Montreal, Quebec, Canada. (Aug. 2004, p. 834) behind the process of acquiring it. It is believed n ature has 4-8 International Conference on Scientific Computing (ICSCOS), left vital clues hidden in this data a nd there is a need for Nanjing, P. R. China. (Oct. 2004, p. 1096) techniques and methodologies to work effectively in detecting these. Biological information processing exploits these regularities 6-8 DIMACS Workshop on Polyhedral Combinatorics of Random to gain understanding of the underlying model or phenomenon. Utility, DIMACS Center, CoRE Bldg, Rutgers University, Piscataway, The workshop aims to contribute significantly to the research effort New Jersey. (Oct. 2004, p. 1096) by bringing together researchers from the many different groups 6- 8 SEM Annual Conference & Exposition on Experimental engaged in biological projects having the study of regularities in and Applied Mechanics, Marriott Portland Downtown, Portland, the data as an underlying theme. Oregon. (May 2004, p. 5 76) Organizer: LaxmiParida, IBM; T. J. Watson Research, email: par ida@ us. ibm. com. ' 6- 1 0 International Mediterranean Congress Of Mathematics Local Arrangements: Maria Mercado, DIMACS Center, email: Almeria 2005, Almeria, Spain. mer cado@dimacs,rutger s . edu, 732-445-5928. Main Speakers: Fabrizio Catanese (Univ. Bayreuth, Germany), Alfio http: I / dimacs. r utgers . edu/ Workshops/ Quarteroni (E. P. F. Lausanne, Switzerland). Efim Zelmanov (Univ. Information: San Diego, San Francisco, U.S.A.). Detecting/. ts Representations, Geometry Thematic Sessions: Algebras and i 20- 24 Second Conference on Self-Similarity and Applications, d Topology, Approximation, Special Functions and Numerical an INSA Toulouse, Toulouse, France. (Aug. 2004, p. 834) Analysis, Functional Analysis and its Applications, General Topology and its Applications, Probabilistic Spaces, Copulae and T-norms. 20-2 5 Asymptotic and Probabilistic Methods in Geometric Group Applications, Random Models and Design of Experiments, Financial Theory, Geneva, Switzerland. (Jun/ Jul. 2004, p. 693) Mathematics and Mathematical Economics, Mathematics Education. '' 20- 2 5 Title FPSAC'OS: 17th Annual Conference on Formal Power Information: http: I /www . ual . es/congresos/CIMMA2005. Series and Algebraic Combinatorics, Taormina, Sicily (Italy). other 6- 1 0 Moduli Spaces of Properly Embedded Minimal Surfaces,AlM Topics: All aspects of combinatorics and their relations with Research Conference Center, Palo Alto, California. (Jun/ Jul. 2004, parts of mathematics, physics, computer science and biology. p. 693) Information: http : I /www. unime. i t/fpsac05; email: fpsac05@ unime . i t . 7-1 0 SIAM Conference on Mathematical and Computational Issues in the Geosciences, Palais des Papes, The International * 20-26 Sixth International Conference "Symmetry in Nonlin Conference Center, Avignon, France. (Nov. 2004, p. 1265) ear Mathematical Physics", lnstitute of Mathematics, National 7- 1 7 Fields Institute Summer School on Operator Algebras, Academy of Sciences of Ukraine, Kyiv (Kiev), Ukraine. University of Ottawa, Ottawa, Ontario, Canada. (Nov. 2004, p. 1265) Topics: Syrmnetries of differential equations, lntegrable and super integrable systems, Symbolic computations in syrmnetry analysis, '' 8- 1 0 Eleventh Conference on Integer Programming and Com Dynamical systems, solitons, Supersyrmnetry and its generaliza binatorial Optimization (IPCO XI), Berlin, Germany. tions, Quantum field theory, Lie groups and algebras, representation Deadline: November 15, 2004. theory and special functions, q-algebras, quantum groups and non Information: http: I I www . math. tu-berlin. de/ipco05. commutative geometry, Gravitation, cosmology, quantum gravity, Condensed matter and statistical physics, Nonlinear phenomena 8-11 IMA Workshop: Effective Theories for Materials and and quantum chaos. Macromolecules, University of Minnesota, Minneapolis, Minne Deadline: May 20, 2005. sota. (Jun/ Jul. 2004, p. 693) Information: Conference address: AnatolyNikitin; Institute ofMath 12- 24 Foliations 2005, Lodz, Poland. (Sept. 2004, p. 973) ematics, National Academy of Sciences of Ukraine, 3 Tereshchenkiv ska Street, Kyiv 4, 01601 Ukraine; http: I / www . i math. k iev . uar Function Theory (CMFT 1 3-18 Computational Methods and appmath/ conf . html; email: appmath@imath. k i ev. ua; fax: +38 044 2005), Joensuu, Finland. (Feb. 2004, p. 279) 235 20 10; phone: +38 044 234 63 22 (office); +38 044 250 08 96 13- 25 CIMPA Summer School AGAHF 2005- Arithmet ic and (home). D ECEMBER 2004 N OTICES OF THE AMS 1377 Mathematics Calendar 20-July 8 (REVISED) Random matrices, random processes, and Auckland, Auckland, New Zealand. (Jun/Jul. 2004, p. 694) integrable systems (C.R.M. Short Program), Centre de recherches 2-9 Mile High Conference on Quasigroups, Loops and Nonas mathemati- sociative Systems, University of Denver, Denver, Colorado. (Nov. ques, Universite de Montreal, Montreal. (Nov. 2004, p. 1265) 2004, p. 1266) 20-August 1 5 Computational Prospects of Infinity, Institute for 3-9 XXIViemes Journees Arithmetiques, Marseilles, France. (Sept. Mathematical Sciences, National University of Singapore, Singapore. 2004, p. 975) (Jun/ Jul. 2004, p. 693) ;, 4-8 8th International Symposium on "Generalized Convexity 21 -2 4 MAM 5-Fifth International Conference on Matrix Analytic and Monotonicity", Insubria University, Varese, Italy. Methods in Stochastic Models, Pisa, Italy. (Sept. 2004, p. 974) Topics: Generalized convexity of functions and sets, general " 26-29 12th International Linear Algebra Society Conference, ized monotonicity of maps, and their applications to mathemat Regina Inn Hotel and Conference Centre, Regina, Canada. ical programming, economics, management science, engineering, Aim and Scope: The 2005 ILAS Conference in Regina will bring stochastics, variational inequalities, etc. together an international group of researchers to present recent Program Committee: N. Hadjisawas (Chair), A. Cambini , R. accounts of their work, to discuss advances in all aspects of linear Cambini, A. Guerraggio, D.T. Luc, L. Martein, ].E. Martinez-Legaz, algebra and its applications, to promote and foster new directions A. Rubinov, S. Schaible, X.Q. Yang. for research, and to provide a forum to ensure that linear algebra Organizing Committee: A. Guerraggio (Chair), N. Hadjisawas, E. remains a prominent and respected discipline within mathematics. Allevi, M. Bianchi, G. Crespi, G. Giorgi, A. Gnudi, D. La Torre, E. Deadlines: Abstract submission: 1:fay 1, 2005; Registration: May Miglierina, E. Molho, L. Pellegrini, R. Pini, M. Rocca, A. Setti. 25, 2005; Accomodation reservation: May 25, 2005. Deadlines: Early registration: March 31, 2005. Late registration: Organizers: S. Fallat, D. Farenick, C-H. Guo, S. Kirkland. Scientific May 31, 2005. Title and abstract of talks: May 31, 2005. Submission Organizers: R. Bhatia, R. Guralnick, D. Hershkowitz, S. Kirkland, V. of manuscripts for publication in the Symposium Proceedings: Mehrmann, B-S. Tam, P. van den Driessche, H. Wolkowicz. September 30, 2005. Information: http : I /www . math. uregina. carilas2005/; email: Information: http: I /www. eco . uninsubria. it/gcm8. [email protected]. * 4-8 Conference on Universal Algebra and Lattice Theory, Uni '' 26-29 The Twentieth IEEE Symposium on Logic In Computer versity of Szeged, Szeged, Hungary. Science (LICS 2005): Call for Workshop Proposals, Chicago, Topics: The program of the conference will consist of 30 minute Illinois. invited and 20 minute contributed talks within the scope of Topic proposals: Researchers and practitioners are invited to universal algebra and lattice theory. Presentations on algorithmic submit proposals for workshops on topics relating logic - broadly aspects such as decidability and complexity questions related to construed - to computer science or related fields. Typically, LICS algebras and lattices are especially welcome. workshops feature a number of invited speakers and a smaller Organizers: Laszlo Zadori, Gabor CzedliBolyaiinstitute, University number of contributed presentations. Proposals should include: A of Szeged. short scientific summary and justification of the proposed topic. Invited Speakers: Ralph Freese (University of Hawaii, Honolulu), This should include a discussion of the particular benefits of George Gratzer (University of Manitoba, Winnipeg), Keith A. Kearnes the topic to . the LICS community. A discussion of the proposed (University of Colorado, Boulder), Emil W. Kiss (Eotvos Lorimd Uni format and agenda and the proposed duration, which may vary versity, Budapest), Benoit Larose (Concordia University, Montreal), from half a day to two days,and preferred dates. Procedures for Ralph N. McKenzie (Vanderbilt University, Nashville), Matthew selecting participants and papers. Expected number of participants. A. Valeriote (McMaster University, Hamilton), Friedrich Wehrung Potential invited speakers. Plans for dissemination (for example, (Universit de Caen, Caen), Ross Willard (University of Waterloo, special issues of journals). Please note that it is expected that LICS Waterloo). workshop organizers should be present to run their workshops. It Information: http: I /www .math. u-szeged. hu/ confer /algebra/. is also assumed that normally workshop organizers (though not necessarily participants) will register for the LICS conference. 9-11 Joint Meeting of the Chinese Society of Probability and Workshop Dates: June 25, 2005 and June 30-July 1, 2005. Statistics (CSPS) and the Institute of Mathematical Statistics Proposal deadline: November 15, 2004 and should be submitted (IMS), Beijing, China. (Aug. 2004, p. 834) electronically to: Philip Scott, Workshops Chair, LICS 2005; email: 1 0-14 12th International Conference on Mathematical Modelling phil@si te . uottawa . ca. and Applications (ICTMA 12), City University, London, England. (Jan. 2004, p. 64) 26-July 1 ERLOGOL-2005: Intermediate Problems of Model The ory and Universal Algebra, State Technical University/Mathematics 1 0-1 5 20th British Combinatorial Conference, University of Institute, Novosibirsk, Russia. (Jun/Jul. 2004, p. 694) Durham, United Kingdom. (Sept. 2004, p. 975) 26-July 1 30th Conference on Stochastic Processes and Their 1 0-1 5 SampTA05 (Sampling Theory and applications), Ondokuz Applications, University of California at Santa Barbara (UCSB), Maws University Samsun, Turkey. (Nov. 2004, p. 975) Santa Barbara, California. (Jun/Jul. 2004, p. 694) 1 0-16 Stochastic Modelling of Complex Systems (SMOCS-05), * 28-July 1 DAYS on DIFFRACTION-2005, St. Petersburg Branch of Daydream Island resort (Whitsundays, Queensland, Australia). (Nov. Steklov's Math. Inst. and St. Petersburg Univ., St. Petersburg, Russia. 2004, p. 1266) Workshop Topics: All topics related to mathematical aspects of 10-23 Cornell Summer School in Probability, Cornell University, wave propagation, scattering and diffraction. Ithaca, New York. (Aug. 2004, p. 834) Organizers: Prof. V. M. Babich (PDMI), Prof. V. S. Buldyrev (SPbU), Euler Int. Math. Inst. * 1 1-14 Sixth SIAM Conference on Control and its Applications, Deadlines: Abstract submission by March 1, 2005. Hilton New Orleans Riverside Hotel, New Orleans, Louisiana. Information: http: I /math . nw . ru/DD/. Topics: This conference, which will be held jointly with the 2005 SlAM Annual Meeting, will showcase a wide range of topics in control july 2005 and systems theory. The topics and applications include real-time optimization and data assimilation, cellular and biological regu 2-7 SRTL-4: The Fourth International Research Forum on Sta lation, control techniques for financial mathematics, cooperative tistical Reasoning, Thinking, and Literacy, The University of control for unmanned autonomous vehicles, biomedical control, 1378 NOTICES OF 1HE AMS VOLUME 51, NUMBER 11 Mathematics Calendar risk sensitive control and filtering, control of smart systems, flow 8-1 3 XX Nevanlinna Colloquium, ETH Lausanne, Lausanne, Switz control and quantum control. erland. (Nov. 2004, p. 1266) Information: http: I lwww. siam. orglmeetingsl ct05l. 8-December 2 3 Global Problems in Mathematical Relativity, Isaac Newton Institute for Mathematical Sciences, Cambridge, England. 11-1 5 Gravitational Lensing in the Kerr Spacetime Geometry, (Aug. 2004, p. 834) AIM Research Conference Center, Palo Alto, California. (Nov. 2004, p. 1266) October 2005 1 1 -1 6 Strings 2005, Toronto, University of Toronto, Toronto, * 8-9 AMS Eastern Section Meeting, Bard College, Annandale-on Ontario, Canada. (Nov. 2004, p. 1266) Hudson, New York. 1 8-22 Algorithms for Approximation V, University College, Information: http : I lwww . ams . orglamsmtgslsectional. html. Chester, UK. (Nov. 2004, p. 1266) '' 1 5-16 AMS Southeastern Section Meeting, East Tennessee State 20-27 The 5th International Algebraic Conference in Ukraine, University, Johnson City, Tennessee. Odessa I. I. Mechnikov National University, Odessa, Ukraine. (Nov. Information: http : I lwww. ams . orglamsmtgslsectional. html. 2004, p. 1266) '' 21-22 AMS Central Section Meeting, University of Nebraska, 24-28 25th European Meeting of Statisticians, University of Oslo, Lincoln, Nebraska. Oslo, Norway. Information: http : I lwww. ams. orglamsmtgslsectional.html. Scientific Programme: The meeting will cover all areas of method ological, applied and computational statistics, probability theory November 2005 and applied probability. There will be 8 speciallecturers, 2 3 ordinary invited sessions and one invited discussion session. '' 12-1 3 AMS Western Section Meeting, University of Nebraska, Organizer: Arnoldo Frigessi, Chairman of the Local Organising Com University of Oregon, Eugene, Oregon. mittee; email: arnoldo. frigessi@medisin. uio. no. The meeting Information: http : I lwww. ams . orglamsmtgslsectional.html. is organised jointly by the University of Oslo and the Norwegian Computing Center. Scientific Programme Committee: Aad van der Vaart, chair (Am sterdam), Ornulf Borgan (Oslo), Ursula Gather (Dortmund), Sylvia The following new announcements will not be repeated until Richardson (London), Gareth Roberts (Lancaster), Tomasz Rolski the criteria in the next to the last paragraph at the bottom of (Wroclaw), Jeffrey Steif (Goteborg). the first page of this section are met. Registration: Registration to the conference and booking of ac December 2005 commodation must be made via http: I lwww. ems2005. no. Conference Dates and Deadlines: Deadline for grant application * 14-1 8 First Joint International Meeting with the Taiwanese is March 1, 2005. Deadline for submission of contributed papers Mathematial Society, Taiwan, Taiwan. and poster: March 31, 2005. Deadline for early registration: May 1, Information: http : I lwww. ams. orglamsmtgslinternmtgs .html. 2005. Deadline for conference registration: June 30, 2005. * 1 5-1 7 International Conference on Computer & Information Contact information: EMS 2005, P.O. Box 114 Blindern, N-0314 Science (ICCIS'2005), Fort Panhala, Kolhapur, India. Oslo, Norway; email: ems2005@nr .no; fax: (+47) 22 69 76 60. Aim: To provide a platform for academics and professionals in com puter science and information technology to meet, communicate, 25-29 IMA Workshop: Mixed Integer Programming, University exchange ideas, and establish professional networks. of Minnesota, Minneapolis, Minnesota. (Jun/ Jul. 2004, p. 694) Sponsors: Technomathematics Research Foundation, India. 28-August 3 Logic Colloquium '05: ASL European Summer Important Dates: Full paper due: April 20, 2005. Proposals for Meeting, Athens, Greece. (Oct. 2004, p. 1097) tutorials and sessions due: February 20, 2005. Notification of acceptance: June 15th, 2005. Camera-ready paper with registration August 2005 fee due: July 20, 2005. 1-December 23 Pattern Formation in Large Domains, Isaac Information: http: I lpune. sancharnet. inlkpr_tmrfliccis05 . Newton Institute for Mathematical Sciences, Cambridge, England. html. (Aug. 2004, p. 834) * 1 5-19 Conference on Low-dimensional Topology, University of 3-5 DIMACS Workshop on Yield Management and Dynamic Virginia, Charlottesville, Virginia. Pricing, DIMACS Center, CoRE Bldg, Rutgers University, Piscataway, Objective: To bring together researchers working on different New Jersey. aspects of low-dimensional topology, including Floer homology, Organizers: James Dana, Northwestern University, email: j-dana@ the Ricci flow program, and more "classical" geometric topology, kellogg. northwestern. edu; Brenda Dietrich, IBM Watson Labs, with the goal of looking for connections and unifying perspectives. email: [email protected]. A theme in several of these areas is that subtle relationships between Local Arrangements: Maria Mercado, DIMACS Center, email: a 4-manifold and its boundary constrain and illuminate both 3- mercado@dimacs . rutgers . edu, 732-445-5928. and 4-dirnensional topology. We propose this as a framework for Information: http : I I dimacs . rutgers . eduiWorkshopsiYieldl. comparing existing approaches and formulating key problems. Organizers: Slava Krushkal (Univ. Va), Frank Quinn (Virginia Tech). ' 7-12 International Conference: Mathematics in Finance, Kruger Information: http: I lwww. math . virginia. edultopologyI. National Park, South Africa. Hosts: Hosted jointly by Potchefstroom University for CHE, The University of Pretoria and The University of the Witwatersrand. Focus: Topics that would be covered include among others: Stochastic models, Modern methods of risk analysis, Quantitative and computational models and methods, Methods of financial mathematics; in particular the role of measure theory, functional analysis and modern stochastics in Finance. Information: email: mfinance@cam . wits. ac. za. DECEMBER 2004 NOTICES OF THE AMS 1379 New Publications Offered by the AMS The book is suitable for graduate students and researchers Analysis interested in operator algebras and applications, including noncommutative geometry. This item will also be of interest to those working in mathemat Operator Algebras, ical physics. Quantization, and Contents: P.R. Halmos, The legend of John von Neumann; Photo of stone: G. W. Mackey, Marshall H. Stone: Mathemati Operator Algebras, Quantization, and Noncommutative cian, statesman, advisor, and friend; W. Arveson, The Noncommutatlve Geometry universal A-dynamical system; P. Baum, On the index of equi A Centennial Celebration Honoring Geometry John von Neumann and Marshall H. Stone variant elliptic operators; B. Blackadar, The algebraization of Roberts. Doran A Centennial Celebration dynamics: Amenability, nuclearity, quasidiagonality, and Richard V. Kadison approximate finite dimensionality; D. P. Blecher, Multipliers, Editors Honoring John von C* -modules, and algebraic structure in spaces of Hilbert Neumann and Marshall space operators; N. Higson, Meromorphic continuation of zeta H. Stone functions associated to elliptic operators; R. V. Kadison, Non commutative conditional expectations and their applications; RobertS. Doran, Texas Christian University, Fort Y. Katayama and M. Takesaki, Outer actions of a discrete Worth, TX, and Richard V. Kadison, University of amenable group on approximately finite dimensional factors I: Pennsylvania, Philadelphia, PA, Editors General theory; P. S. Muhly and B. Solei, On the curvature of a completely positive map; ]. A. Packer, Applications of the John von Neumann and Marshall Stone were two giants of work of Stone and von Neumann to wavelets; R. T. Powers, of the 100th Twentieth Century mathematics. In honor Addition of spatial £ 0 -semigroups; G. L Price, On shifts of anniversary of their births, a mathematical celebration was minimal index on the hyperfinite Ih factor; M. A. Rieffel, organized featuring developments in fields where both men Compact quantum metric spaces; ]. Rosenberg, A selective were major influences. history of the Stone-von Neumann theorem; M. Junge and Z. This volume contains articles from the AMS Special Session, J. Ruan, Decomposable maps on non-commutative Lp·spaces; Operator Algebras, Quantization and Noncommutative Geom A. M. Sinclair and R. R. Smith, A survey of Hochschild coho etry: A Centennial Celebration in Honor of John von Neumann mology for von Neumann algebras; D. P. Williams, From the and Marshall H. Stone. Papers range from expository and Stone-von Neumann theorem to the equivariant Brauer group historical surveys to original research articles. All articles were and beyond. carefully refereed and cover a broad range of mathematical Contemporary Mathematics, Volume 365 topics reflecting the fundamental ideas of von Neumann and , Softcover, ISBN 0-8218-3402-9, LC Stone. December 2004, 422 pages 2004054245, 2000 Mathematics Subject Classification: 01A70, Most contributions are expanded versions of the talks and 19K56, 22D25,46L05,46L07,46L10,46L53,46L65,46L87, were written exclusively for this volume. Included, among 58B34, 58J22, 81R05, All AMS members $87, List $109, Order others, are articles by George W. Mackey, Nigel Higson, and code CONM/ 365N Marc Rieffel. Also featured is a reprint of P.R. Halmos's The Legend of john von Neumann. 1380 NOTICES OF THE AMS VOLUME 51, NUMBER 11 New Publications Offered by the AMS Contents: A. Ballesteros, F- 1- Herranz, F_ Musso, and Differential Equations Q_ Ragnisco, Superintegrable deformations of the Smorodinsky-Winternitz Hamiltonian; F. Calogero and J.- P. Franc;:oise, Isochronous motions galore: Nonlinearly coupled Superintegrability in oscillators with lots of isochronous solutions; T_ L Curtright and C. K. Zachos, Nambu dynamics, deformation quantization, (? CRM Classical and and superintegrability; C. Gonera, Maximally superintegrable ll PROCEEDINGS & ~M LECTURE NOTES Quantum Systems systems of Winternitz type; S. Gravel, Cubic integrals of Untve,.,utdeMontttal~"=~-~-~··~- ... a motion and quantum superintegrability; J- Harnad and ~ Superintegrability P. Tempesta, Scuola Superiore 0. Yermolayeva, Superintegrability, Lax matrices and separa _ in Classical and Internazionale, Trieste, Italy, P. tion of variables; F. J. Herranz, A. Ballesteros, M. Santander, - Quantum Systems and T. Sanz-Gil, Maximally superintegrable P.Tempest.a Winternitz and J. Harnad, P.Wtntemttz J. H amad Smorodinsky-Winternitz systems on the N-dimensional sphere W.Mmer. J r. University of Montreal, QC, C. Pogosyan and hyperbolic spaces; A. Kokotov and D. Korotkin, Invariant M. Rodriguez ""'~ Canada, W. Miller, Jr., Wirtinger projective connection and Tau-functions on spaces University of Minnesota, of branched coverings; L. G- Mardoyan, Dyon-oscillator Minneapolis, MN, G. Pogosyan, duality. Hidden symmetry of the Yang-Coulomb monopole; ]oint Institute of Theoretical Physics, Moscow, P. Desrosiers, L. Lapointe, and P. Mathieu, Supersymmetric Calogero-Moser-Sutherland models: Superintegrability struc Russia, and M. Rodriguez, Universidad ture and eigenfunctions; W. Miller, Jr., Complete sets of Complutense de Madrid, Spain, Editors invariants for classical systems; A. G. Nikitin, Higher-order symmetry operators for Schrodinger equation; A. V. Penskoi, Superintegrable systems are integrable systems (classical and Symmetries and Lagrangian time-discretizations of Euler equa quantum) that have more integrals of motion than degrees of tions; L G. Mardoyan, G. S. Pogosyan, and A. N. Sissakian, freedom. Such systems have many interesting properties. This Two exactly-solvable problems in one-dimensional quantum proceedings volume grew out of the Workshop on Superinte mechanics on circle; M. F. Raftada and M. Santander, Higher grability in Classical and Quantum Systems organized by the order superintegrability of a rational oscillator with inversely Centre de recherches mat):lematiques in Montreal (Quebec). quadratic nonlinearities: Euclidean and non-Euclidean cases; The meeting brought together scientists working in the area of F. Finkel, D. G6mez-Ullate, A. Gonzalez-Lopez, finite-dimensional integrable systems to discuss new develop M. A. Rodriguez, and R. Zhdanov, A survey of quasi-exactly ments in this active field of interest. solvable systems and spin Calogero-Sutherland models; Properties possessed by these systems are manifold. In clas M. Sheftel, On the classification of third-order integrals of sical mechanics, they have stable periodic orbits (all finite motion in two-dimensional quantum mechanics; R. G. McLe orbits are periodic). In quantum mechanics, all known superin naghan, R. G. Smirnov, and D. The, Towards a classification tegrable systems have been shown to be exactly solvable. of cubic integrals of motion; K. Takasaki, Integrable systems Their energy spectrum is degenerate and can be calculated whose spectral curves are the graph of a function; algebraically. The spectra of superintegrable systems may also P. Tempesta, On superintegrable systems in E2: Algebraic have other interesting properties, for example, the saturation properties and symmetry preserving discretization; of eigenfunction norm bounds. A. V. Turbiner, Perturbations of integrable systems and Articles in this volume cover several (overlapping) areas of Dyson-Mehta integrals; Y. Uwano, Separability and the Birk research, including: hoff-Gustavson normalization of the perturbed harmonic oscillators with homogeneous polynomial potentials; J. Berube - Standard superintegrable systems in classical and quantum and P. Winternitz, Integrability and superintegrability without mechanics. separability; T. Wolf, Applications of CRACK in the classifica - Superintegrable systems with higher-order or nonpolynomial tion of integrable systems; G. A. Griinbaum and M. Yakimov, integrals. The prolate spheroidal phenomenon as a consequence of bispectrality; Q_ Yermolayeva, On a trigonometric analogue of - New types of superintegrable systems in classical mechanics. Atiyah-Hitchin bracket; A. Zhalij and R. Zhdanov, Separation - Superintegrability, exact and quasi-exact solvability in stan- of variables in time-dependent Schrodinger equations; dard and PT-symmetric quantum mechanics. M. Znojil, New types of solvability in PT symmetric quantum - Quantum deformation, Nambu dynamics and algebraic theory. perturbation theory of superintegrable systems. CRM Proceedings & Lecture Notes, Volume 37 - Computer assisted classification of integrable equations. December 2004, 347 pages, Softcover, ISBN 0-8218-3329-4, The volume is suitable for graduate students and research 2000 Mathematics Subject Classification: 81-06, 81R12, 37]15, mathematicians interested in integrable systems. 22E70, All AMS members $87, List $109, Order code CRMP/ 37N This item will also be of interest to those working in mathemat ical physics. DECEMBER 2004 NOTICES OF THE AMS 1381 New Publications Offered by the AMS homotopy theoretic ideas are becoming important, such as General Interest algebraic K-theory and algebraic geometry. The authors' approach is to define the notion of a homo topical category, which is more general than that of a model Combined category, and to consider model categories as special cases of Membership List this. A homotopical category is a category with only a single distinguished class of maps, called weak equivalences, subject 2004-2005 to an appropriate axiom. This enables one to define "homo topical" versions of such basic categorical notions as initial The Combined Membership List (CML) and terminal objects, colimit and limit functors, cocomplete is a comprehensive directory of the ness and completeness, adjunctions, Kan extensions, and membership of the American Mathe universal properties. matical Society, the American Mathematical Association of Two-Year There are two essentially self-contained parts, and part II logi Colleges, the Association for Women in cally precedes part I. Part II defines and develops the notion of Mathematics, the Canadian Mathemat- a homotopical category and can be considered as the begin ical Society, the Mathematical nings of a kind of "relative" category theory. The results of Association of America, and the Society for Industrial and part II are used in part I to obtain a deeper understanding of Applied Mathematics. model categories. The authors show in particular that model categories are homotopically cocomplete and complete in a It includes a complete alphabetical list of all individual sense stronger than just the requirement of the existence of members in all six organizations. For each member, the CML small homotopy colimit and limit functors. provides an address, title, department, institution, telephone number (if available), and electronic address (if provided) and A reader of part II is assumed to have only some familiarity also indicates membership in the six participating societies. In with the above-mentioned categorical notions. Those who read addition, the CML lists academic, institutional, and corporate part I, and especially its introductory chapter, should also members of the six participating societies providing addresses know something about model categories. and telephone numbers of mathematical sciences depart Contents: Model categories: An overview; Model categories and ments. their homotopy categories; Quillen functors; Homo topical The CML is an invaluable reference for keeping in touch with cocompleteness and completeness of model categories; Homo colleagues and for making connections in the mathematical topical categories: Summary of part II; Homotopical categories sciences community in the United States and abroad. and homotopical functors; Deformable functors and their approximations; Homotopy colimit and limit functors and December 2004, 336 pages, Softcover, ISBN 0-8218-3620-X, homotopical ones; Index; Bibliography. Individual member $42, List $70, Institutional member $56, Order code CML/2004/ 2005N Mathematical Surveys and Monographs, Volume 113 December 2004, 181 pages, Hardcover, ISBN 0-8218-3703-6, LC 2004059481, 2000 Mathematics Subject Classification: 18A99, Geometry and Topology 18D99, 18G55, 55U35, All AMS members $47, List $59, Order code SURV /113N -- Homotopy Limit Mathematical Physics Ho~otopy Limit Functors on Model Functors on Model Categories Categories and and l!lomotopical ~~ ~athematic:s Proc:eedings Strings and Categories Homotopical I Geometry William G. Dwyer Categories Philip S. Hirschhorn Daniel M. Kan Strings and Michael Douglas, Rutgers Jaffrey H. Smith William G. Dwyer, University Geometry of Notre Dame, IN, Philip S. University, Piscataway, N], Michael Douglas Jerome Gauntlett, University of Hirschhorn, Wellesley College, Jerome Gauntlett Mark Gross London, England, and Mark MA, Daniel M. Kan, Editors Massachusetts Institute of Technology, Cambridge, Gross, University of California MA, and Jeffrey H. Smith, Purdue University, West San Diego, La Jolla, CA, Editors Lafayette, IN This volume is the proceedings of the 2002 Clay Mathematics Institute The purpose of this monograph, which is aimed at the grad School on Geometry and String Theory. This month-long uate level and beyond, is to obtain a deeper understanding of program was held at the Isaac Newton Institute for Mathemat Quillen's model categories. A model category is a category ical Sciences in Cambridge, England, and was organized by together with three distinguished classes of maps, called weak both mathematicians and physicists: A. Corti, R. Dijkgraaf, M. equivalences, cofibrations, and fibrations. Model categories Douglas, J. Gauntlett, M. Gross, C. Hull, A. Jaffe and M. Reid. have become a standard tool in algebraic topology and homo The early part of the school had many lectures that intro logical algebra and, increasingly, in other fields where duced various concepts of algebraic geometry and string 1382 NOTICES OF THE AMS VOLUME 51, NUMBER 11 New AMS-Distributed Publications theory with a focus on improving communication between these two fields. During the latter part of the program there New AMS-Distributed were also a number of research level talks. This volume contains a selection of expository and research Publications articles by lecturers at the school and highlights some of the current interests of researchers working at the interface between string theory and algebraic geometry. The topics covered include manifolds of special holonomy, supergravity, Algebra and Algebraic supersymmetry, D-branes, the McKay correspondence and the Fourier-Mukai transform. Geometry The book is suitable for graduate stud~nts and research math ematicians interested in relations between mathematical Elements de Ia physics and algebraic geometry. Seminaires This item will also be of interest to those working in algebra & Congres theorie des systemes and algebraic geometry. Co ll e ct i o n SMF ,,...... ~. differentiels Titles in this series are published by the AMS for the Clay Mathematics Institute (Cambridge, MA). ~ geometriques ELEMENTS DE LA THEORIE Contents: M. R. Douglas, The geometry of string theory; DES SYST:EMES DIFFERENTIELS GEOMtTRIQUES Cours du C.I.M.P.A. Ecole B. S. Acharya, M theory, Gz-manifolds and four dimensional COORS DU C.I.M.P.A. ECOLE D'ETi DE SEviLLE (1996) d'ete de Seville (1996) physics; S. K. Donaldson, Conjectures in Kahler geometry; PHILI PPE MAISONOBE AND J. P. Gauntlett, Branes, calibrations and supergravity; W ISNARVAEZMACARRO. EDITORS Philippe Maisonobe, S. Gukov, M-theory on manifolds with exceptional holonomy; SOCttri: MAniEMATIQUE DE PRANCE Universite de Nice, France, and N. Hitchin, Special holonomy and beyond; D. Joyce, Constructing compact manifolds with exceptional holonomy; Luis Narvaez Macarro, A. Kovalev, From Fano threefolds to compact Gz-manifolds; Universidad de Sevilla, Spain, Editors A. Craw, An introduction to motivic integration; A. Ishii, · The theory of geometric differential systems consists of the Representation moduli of the McKay quiver for finite Abelian study of coherent modules on the ring of differential opera subgroups of SL(3, (();F. Kirwan, Moduli spaces of bundles tors on a complex analytic or algebraic manifold. It is used in over Riemann surfaces and the Yang-Mills stratification revis various branches of mathematics: algebraic geometry, arith ited; C. Madonna and V. V. Nikulin, On a classical metics, Lie groups and Lie algebras, algebraic topology of correspondence between K3 surfaces II; B. Szendroi, Contrac singularities, etc. This book contains articles from lectures tions and monodromy in homological mirror symmetry; given at the Centre International de Mathematiques Pures et N. Dorey, Lectures on supersymmetric gauge theory; Appliquees (C.I.M.P.A.) summer school. It offers a complete A. Kapustin, The geometry of A-branes; R. C. Myers, Low survey of the theory, taking into account the most recent energy D-brane actions; List of Participants. advances. Clay Mathematics Proceedings, Volume 3 The volume is suitable for graduate students and researchers January ZOOS, approximately 384 pages, Softcover, ISBN 0- interested in algebra and algebraic geometry. 8218-3715-X, 2000 Mathematics Subject Classification: 81T30, A publication of the Societe Mathematique de France, Marseilles (SMF), 83E30, 53C29, 32Q25, 14J32, 83ESO, 14E15, 53C80, 32S45, distributed by the AMS in the US, Canada, and Mexico, Orders from 14DZO, All AMS members $55, List $69, Order code CMIP/3N other countries should be sent to the SMF, Members of the SMF receive a 30% discount from list. Contents: Ph. Maisonobe and T. Torrelli, Image inverse en theorie des D-modules; L. N. Macarro, The local duality theorem in D-module theory; F. J. Castro-Jimenez and M. Granger, Explicit calculations in rings of differential opera tors; L. N. Macarro and A. R. Leon, Continuous division of linear differential operators and faithful flatness of D'X over Dx; J. Brianc;on, Extensions de Deligne pour les croisements normaux; z. Mebkhout, Le theoreme de positivite, le theoreme de comparaison et le theoreme d'existence de Riemann; Ph. Maisonobe and Z. Mebkhout, Le theoreme de comparaison pour les cycles evanescents; B. Malgrange, On irregular halo nomic D-modules; Y. Laurent, Geometric irregularity and D-modules. Seminaires et Congres, Number 8 July 2004, 430 pages, Softcover, ISBN 2-85629-151-1, 2000 Mathematics Subject Classification: 12-XX, 13N10, 13P10, 14Bxx, 16S32, 32C38, 32S40, 32S60, 35A27, 35Nl0, Individual member $94, List $104, Order code SEC0/ 8N DECEMBER 2004 NOTICES OF THE AMS 1383 Classified Advertisements Positions available, items for sale, services available, and more http: I /www _math_ uab _edu. UAB is an · consideration, all materials should be re ALABAMA AA/ EO employer. ceived by November 1, 2004. Late appli 000153 cations will be reviewed until the position UNIVERSITY OF ALABAMA _ is closed. Women and minorities are en AT BIRMINGHAM UNIVERSITY OF ALABAMA IN couraged to apply. The University of Al Department of Mathematics HUNTSVILLE abama in Huntsville is an Affirmative Ac Department of Mathematical Sciences tion, Equal Opportunity Institution. Applications are invited for two tenure 000143 track positions at the level of assistant The Department of Mathematical Sciences professor or higher to begin August 15, at the University of Alabama in Huntsville 2005. Applicants should have demon invites applications for a tenure-track po CALIFORNIA strated strong potential in research and a sition at the rank of assistant professor, commitment to excellent teaching. Post beginning spring semester 2005 or fall se CALIFORNIA INSTITUTE OF doc experience is desirable. Candidates mester 2005. In exceptional cases, more whose research is compatible with the de advanced appointments may be consid TECHNOLOGY partment's research expertise- which lies ered. A Ph.D. degree in mathematics or ap Department of Mathematics in differential equations, differential geom plied mathematics is required. Applicants etry, dynamical systems, mathematical The Division of Physics, Mathematics and must have a strong commitment to teach Astronomy at the California Institute of physics and topology and includes the ing and show evidence of excellent teach Technology invites applications for a pos computational aspects of these research ing ability. Applicants should also show sible tenure-track position in mathemat areas- are encouraged to apply. We are es evidence of outstanding research potential ics at the assistant professor level. We are pecially interested in applicants with ex in an area that matches the interests of the particularly interested in the following re pertise in geometric or harmonic analysis, department _Preference will be given to search areas: algebraic geometry/ number inverse problems, or numerical analysis. applicants whose research areas are prob theory, analysis/ dynamics, combinatorics, Applications should include a curriculum ability/ stochastic processes or numerical finite and algebraic groups, geom vita with publication list, a statement of fu analysis. Applicants should send a cur etry/topology, logic/ set theory, and math ture research plans, and at least three let riculum vita with the AMS standard cover ematical physics, but other fields may be ters of recommendation. The AMS Stan sheet, transcripts, and three letters of rec considered. The term of the initial ap dard Cover Sheet should be completed ommendation (with at least one letter ad pointment is normally four years for a online at http: I j www- math jobs- or g. Ap dressing teaching) to Chairman, Depart tenure-track assistant professor (with a plicants are encouraged to submit all their ment of Mathematical Sciences, University possible to extension to as much as seven materials electronically at http:www.math of Alabama in Huntsville, Huntsville, AL years). Appointment is contingent upon jobs.org. Review of applications will begin 35899. For more information about the completion of the Ph.D. Exceptional can December 1, 2004. For more information department, visit our web site at didates may also be considered at the as about the department please visit http: I jwww _math_ uah _edu. To ensure full sociate or full professor level. We are Suggested uses for classified advertising are positions available, books or March 2005 issue-December 29, 2004; April 2005 issue-anuary 28, 2005; lecture notes for sale, books being sought, exchange or rental of houses, May 2005 issue-February 25, 2005; June/July 2005 issue-April 27, 2005. and typing services. U.S. laws prohibit discrimination in employment on the basis of color, age, The 2004 rate is $100 per inch or fraction thereof on a single column (one sex, race, religion, or national origin. "Positions Available" inch minimum), calculated from top of headline.· Any fractional text of 1/2 advertisements from institutions outside the U.S. cannot be published inch or more will be charged at the next inch rate. No discounts for multi unless they are accompanied by a statement that the institution does not ple ads or the same ad in consecutive issues. For an additional $10 charge, discriminate on these grounds whether or not it is subject to U.S.laws. De announcements can be placed anonymously. Correspondence will be for tails and specific wording may be found on page 13 73 (vol. 44). warded. 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 body copy, unless additional headline copy is specified by the advertiser. 401-455-4084 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 billed Upcoming deadlines for classified advertising are as follows: January upon publication. 2005 issue-October 28, 2004; February 2005 issue-November 22, 2004; 1384 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Classified Advertisements seeking highly qualified applicants who Immigration Services to work in the United mathematicians and statisticians in the are committed to a career in research and States. consortium. teaching. Applicants should write Responsibilities: the successful candi Claremont is situated approximately 3 5 promptly to: SEARCH COMMITTEE, Math date will assume an active role in: (1) Stu miles east of downtown Los Angeles, at the ematics 253-37, California Institute of dent advisement for prospective teachers; foot of the San Gabriel Mountains. The Technology, Pasadena, CA 91125. Please in (2) Teaching, designing and collaborating community is known for its tree-lined clude curriculum vitae, list of publications on courses for pre-service teachers; (3) streets and village charm. It is an easy with those publications appearing in ref Creating and maintaining partnerships drive from Claremont to the cultural at ereed journals so noted, description of re with colleagues in the College of Education tractions of the greater Los Angeles area, search, and ensure that at least three let and mathematics teachers at local schools, as well as the ocean, mountains, and ters of recommendation be sent to the including the new Los Angeles Unified deserts of Southern California. above address. Caltech is an Affirmative School District high school just opened Applicants should send a curriculum Action/Equal Opportunity Employer. on the CSUN campus; (4) Grant activities vitae, a description of their teaching phi Women, minorities, veterans, and disabled to support K-12 projects in the depart losophy and experience, a description of persons are encouraged to apply. ment; (5) Participating in the Carnegie ini their current research program, under 000146 tiative; (6) Continuing scholarly activities graduate and graduate transcripts, and in research and publication in mathemat arrange to have three letters of recom CALIFORNIA STATE UNIVERSITY ics education; (7) A long-term commitment mendation sent to the address that ap to K-12 mathematics education. Appli pears below. Further information about LOS ANGELES cants should send a vita, the AMS standard Department of Mathematics the college and department may be found cover sheet, and three letters of recom athttp://www.math.hmc.edu/.Preference Inquiries are invited for a possible tenure mendation, one of them addressing the will be given to applications completed by candidate's teaching abilities, to the Hir December 17, 2004. track position in mathematics at the level ing Committee, Department of Mathe of assistant professor, starting June or Harvey Mudd College is an Equal Op matics, CSUN, Northridge, CA 91330-8313. portunity Employer and is committed to September 2005. A Ph.D. in mathematics Review of applications will begin on Jan (algebra/number theory) from an accred the recruitment of applicants historically uary 15, 2005, and continue until a can underrepresented on college faculties. ited institution of higher education is re didate is appointed or the search is ter quired. Ability to teach a range of under minated. Email (inquiries only) Address for applications: graduate mathematics classes is essential. math. hi ri ngl@csun. edu. California State Professor Francis E. Su Publications in peer reviewed journals University is an Equal Opportunity, Affir Chair, Search Committee and/or grant activity is required for mative Action employer. Department of Mathematics tenure/promotion. CSULA is on the quar 000160 Harvey Mudd College ter system. Send letter of application, vita, Claremont, CA 91711-5990 three letters of recommendation and of HARVEY MUDD COLLEGE 000055 ficial transcript from institution awarding Department of Mathematics doctorate to Dr. P. K. Subramanian, Chair, STANFORD UNIVERSITY Department of Mathematics, California Harvey Mudd College invites applications Department of Mathematics State University at Los Angeles, 5151 State for a tenure-track position in statistics, University Drive, Los Angeles, CA 90032. biostatistics, or related statistical fields. The department expects to make one or An Equal Opportunity, Title IX, Disabled, The rank will be at the assistant or asso more Szego assistant professor appoint Employer. ciate professor level. Excellence in teach ments. These appointments are for a term 000147 ing is essential, as is evidence of a strong of three years beginning in September and ongoing research program. Preference 2005. Research fields to be considered are: CALIFORNIA STATE UNIVERSITY will be given to candidates familiar with (1) analysis, (2) algebra, number theory, or logic, (3) geometry or topology, (4) com NORTHRIDGE modern data analysis techniques with cross-disciplinary interests. Candidates binatorics, (5) applied mathematics or Department of Mathematics must be willing to supervise undergradu probability, (6) financial mathematics. The Department of Mathematics invites ate research and work with others in de Applicants are expected to show out applications for a tenure-track appoint partmental programs, such as the recently standing promise in research as well as ment at the assistant or associate profes created mathematical biology major or the strong interest and ability in teaching. sor level effective Fall2005. This position industrial projects-based clinic program. They must have received the Ph.D. prior to is affiliated with Teachers for a New Era Harvey Mudd College is a highly selec the start of the appointment, but not be (TNE), an initiative funded in part by the tive undergraduate institution of science, fore 2003. Candidates should send a let Carnegie Corporation of New York. For engineering and mathematics; the median ter of application with a curriculum vitae more information, please visit SAT score is about 1470, a quarter of our and list of publications, a teaching state http://tne.csun.edu. students are National Merit Scholars, and ment and supporting information includ one year of high school calculus is re ing a teaching letter if possible, and three Qualifications: A doctorate in the math quired for admission. Each year there are letters of recommendation to Szego Search ematical sciences or in education with sig about 25 graduates in mathematics, Committee, Department of Mathematics, nificant experience in mathematics. We CS/math, and mathematical biology, with Stanford University, Stanford, CA 94305 by also value experience teaching K-12 math approximately half going to graduate December 15, 2004. Stanford is an Affir ematics, managing and developing teacher school. Over 40% of mathematics alumni mative Action, Equal Opportunity Em preparation programs, familiarity with is from HMC have entered Ph.D. programs. ployer. sues in mathematical education, including The college enrolls about 700 students 000158 standards and classroom practices, and and is a member of the Claremont College any other expertise in preparing students consortium, which consists of four other STANFORD UNIVERSITY to be successful classroom teachers. Po undergraduate colleges, the Claremont Department of Mathematics tential for publication in mathematical ed Graduate University, and the Keck Gradu ucation is expected. At the time of the ap ate Institute of Applied Life Sciences, form The department is considering applica pointment, the successful applicant, if not ing together an academic community of tions for a tenure-track or tenured faculty a U.S. citizen, must have authorization about 5,000 students. There is an active appointment beginning September 2005. from the Bureau of Citizenship and and vital research community of over 40 The research fields to be considered are: DECEMBER 2004 NOTICES OF THE AMS 1385 Classified Advertisements (1) analysis, (2) algebra, number theory, or ing background required. The salary range courses per semester and an engagement logic, (3) geometry or topology, (4) com is $48,900-$53,200. Teaching load for Ad with our research group in topology. binatorics, (5) applied mathematics or juncts is six quarter courses per year. The salary is competitive. Review of ap probability. There are also possibilities for (6) Visiting Instructorships. plications will begin on February 1, 2005, joint appointments with other depart Applicants should complete the appli and will continue until the position is filled. ments. cation located on the website at Send curriculum vitae, a research sum Candidates should send a letter of ap http://www.math.ucla.edu/~search. mary and plan, and at least three letters plication with a curriculum vitae, a list of Preference will be given to applicants of recommendation to: publications, a brief statement of research whose applications are completed by Jan Daniel Ullman, Chair interest, and a cover sheet clearly stating uary 10, 2005. Department of Mathematics the following information: name, area of UCLA is an Equal OpportunityI Affirma The George Washington University specialization, institution, date of Ph.D., tive Action Employer. Under federal law, 1922 F Street NW, Room 102 and Ph.D. advisor. Also the candidate the University of California may employ Washington, DC 20052 should arrange to have at least three let At least one letter of recommendation ters of recommendation (junior candidates only individuals who are legally autho rized to work in the United States as es should comment in some detail about only) or names and addresses of three ref teaching. Applications from women are erences (senior candidates only) and evi tablished by providing documents speci fied in the Immigration Reform and especially encouraged. The George Wash dence of commitment to excellence in ington University is an Equal Opportu teaching sent to Search Committee, De Control Act of 1986. 000106 nityI Affirmative Action employer. partment of Mathematics, Stanford Uni 000155 versity, Stanford, CA 94305 by January 1, 2005. Stanford is an Affirmative Action, THE GEORGE WASHINGTON UNIVERSITY Equal Opportunity Employer. CONNECTICUT Department of Mathematics 000159 Washington, DC YALE UNIVERSITY TABULA, INC. Josiah Willard Gibbs The Department of Mathematics invites Engineer wanted Instructorships/Assistant applications for a tenure-track faculty po Professorships sition in an area of mathematical biology Senior Place & Route Algorithms Engineer, at the assistant professor level beginning job located in Santa Clara, CA. Tabula, Inc., Description: Offered to men and women fall 2005. A strong commitment to re send resume to: email: h r@tabu 1 a. com. with the doctorate who show definite search and excellence in teaching are re 000149 promise in research in pure mathematics. quired. Responsibilities include teaching Applications from women and members of two courses per semester and an active in UNIVERSITY OF CALIFORNIA minority groups are welcome. Appoint volvement with the department's doctoral LOS ANGELES ments are for two/ three years. The teach program. Department of Mathematics ing load is kept light to allow ample time The university is committed to building for research. This will consist of 3 one-se an interdisciplinary strength in quantita The following positions are available for tive biological sciences, including hires in the 2005-06 academic year, subject to mester courses. Part of the teaching duties over the term of the appointment may various departments (biology, chemistry, availability of resources and administrative physics, computer sciences) in the fall of approval. consist of a one-semester course at the graduate level in the general area of the in 2004. The ideal applicant will be able to col (1) Tenure-track/tenured faculty posi laborate with this emerging group, while tions. structor's research. Grant Amount: The 2005-2006 salary will be at least $53,800. also fitting into an area of strength within (2) E.R. Hedrick Assistant Professorships. Deadline: January 1, 2005. Application in the Department of Mathematics, e.g., com Salary is $53,200, and appointments are formation: Inquiries and applications can binatorics and graph theory, complexity for three years. The teaching load is four theory, differential equations, dynamical quarter courses per year, which may in be obtained at the following website: http://www.math.yale.edu.Inquiriesand systems, or topology. See http: I /www. clude one advanced course in a success gwu. edu/ ~home for more information ful candidate's field. application-supporting documents should be sent to the Gibbs Committee, Depart about the department of mathematics, and (3) Research Assistant Professorships in ment of Mathematics, Yale University, via see http: I jwww. bioi nfo rmati cs. gwu for Computational and Applied Mathematics email: [email protected]. information on one aspect of GW's re (CAM). The salary is $53,200, and ap Yale University is an Affirmative Ac search group in quantitative biological sci pointments are for three years. The teach ences. ing load is normally reduced to two or tion/Equal Opportunity Employer. 000065 The salary is competitive. Review of ap three quarter courses per year by research plications will begin on January 15, 2005, funding as available and can include one and will continue until the position is filled. advanced course in a successful candi Send a curriculum vitae, a research sum date's field. DISTRICT OF COLUMBIA mary and plan, a statement of teaching phi (4) Assistant Adjunct Professorships in losophy, and at least three letters of rec the Program in Computing (PIC). Appli THE GEORGE WASHINGTON UNIVERSITY ommendation to: cants for these positions must show very Department of Mathematics Daniel Ullman, Chair strong promise in teaching and research Washington, DC Department of Mathematics in an area related to computing. The teach The George Washington University ing load is four one-quarter programming The Department of Mathematics invites 1922 F Street NW, Room 102 courses each year and one seminar every applications for a contract faculty position Washington, DC 20052 two years. Initial appointments are for one in the area of topology at the assistant At least one letter of recommendation year and possibly longer, up to a maximum professor level beginning fall2005. The ini should comment in some detail about service of four years. The salary is $56,800. tial appointment is for a three-year term, teaching. Applications from women are (5) Assistant Adjunct Professorships and and there is a possibility of renewal. A especially encouraged. The George Wash Research Postdocs. Normally appoint strong commitment to research and ex ington University is an Equal Opportu ments are for one year, with the possibil cellence in teaching are required. Re nityI Affirmative Action employer. ity of renewal. Strong research and teach- sponsibilities include teaching two or three 000156 1386 NoTICEs oF THE AMS VOLUME 51, NUMBER 11 Classified Advertisements address. Screening of applications will preferred. Send letter of application, CV, FLORIDA begin on January 1, 2005. and three letters of recommendation to: Informal inquiries are welcome; please Numerical Analysis Position, Department UNIVERSITY OF WEST FLORIDA see our web page at http: I lwww. mathcs. of Mathematics, Southern illinois Univer Department of Mathematics and emory. edu/News/Ops for further details. sity Carbondale, Carbondale, Illinois Statistics Emory University is an Affirmative Ac 62901-4408. Review of applications will tion/Equal Opportunity Employer. begin November 22, 2004, and continue The University of West Florida, Depart 000144 until position is filled. SIUC is an affirma ment of Mathematics and Statistics, in tive action/equal opportunity employer vites applications for an anticipated GEORGIA INSTITUTE OF TECHNOLOGY that strives to enhance its ability to develop tenure-track position at the assistant pro a diverse faculty and staff and to increase fessor level, beginning August 2005. Ph.D. Beginning with the 2004/05 academic year, its potential to serve a diverse student in mathematics required with preference the School of Mathematics at Georgia Tech population. All applications are welcomed given to candidates in applied mathemat will embark on an ambitious faculty re and encouraged and will receive consid ics. Salary competitive. Candidates should cruitment program, one which will be sus eration. have strong commitment to teaching at tained over the next five years. Building on 000145 the undergraduate and master's levels, past successes, this recruiting effort is in scholarly activity and service. A police tended to make rapid advances in the background screening is required. scope and quality of our research and INDIANA To apply, please go to http: 1lj obs. uwf. graduate education programs. Candidates edu to create your application. Please be will be considered at all ranks, with priority given to those candidates who (1) bring ex INDIANA UNIVERSITY SOUTH BEND prepared to attach the following docu ceptional quality research credentials to Department of Mathematical Sciences ments in digital format: letter of interest Georgia Tech; (2) complement existing The Department of Mathematical Sciences and vita. Interested persons should also strengths in the School of Mathematics; (3) send transcripts and at least three sealed invites applications for a tenure-track, as reinforce bridges to programs in engi sistant professor position in applied math letters of reference to Dr. Kuiyuan U, Chair neering and the physical, computing and person, Department of Mathematics and ematics starting August 2005. The appli life sciences; (4) have strong potential for cant must have completed all requirements Statistics, University of West Florida, 11000 external funding; and (5) have a demon University Parkway, Pensacola, Florida for a Ph.D. in mathematics or a closely re strated commitment to high quality teach lated field by the time of appointment. 32514. Active review of candidates' mate ing at both the undergraduate and gradu rials will begin January 15, 2 00 5, and will Preferred areas of interest include simu ate levels. Consistent with these priorities, lation and stochastic modeling, and ap continue until the position is filled. UWF candidates will be considered in all areas is an Equal Opportunity, Access, Affirma- · plied probability. Responsibilities include of pure and applied mathematics and sta teaching undergraduate and graduate tive Action Employer. tistics. Candidates for positions at the as 000165 courses, research, and service. Salaries and sistant and associate professor levels fringe benefits are competitive. For more should arrange for a resume, at least three information, visit the website http: I jwww. letters of reference, and a summary of fu iusb.edul-sbmathl. GEORGIA ture research plans to be sent to the Hir To apply, send a letter of application, ing Committee, School of Mathematics, curriculum vitae, copies of graduate school EMORY UNIVERSITY Georgia Institute of Technology, Atlanta, transcripts, a statement of research in GA 30332-0160, USA. Candidates for full Department of Mathematics and terests, a statement of teaching philoso professor positions should submit a re phy, and arrange for at least three letters Computer Science sume and a letter outlining their vision Atlanta, Georgia 30322 of recommendation to be sent to: Applied for service as a senior faculty member at Mathematics Search Committee, Depart Georgia Tech. Review of applications will ment of Mathematical Sciences, The Emory University Department of Math begin in September 2004, and the roster ematics and Computer Science invites ap of candidates being considered will be up !USB is an Affirmative Action/Equal Op portunity Employer, and encourages ap plications for an anticipated tenure-track dated on a monthly basis. Georgia Tech, assistant professorship, effective plications from underrepresented groups. an institution of the University System of Applications will be reviewed as they are 2005-2006. The department seeks candi Georgia, is an Equal Opportunity/Affir dates with research interests in the areas received, but full consideration will be mative Action Employer. given to any applications completed by of differential geometry and geometric 000101 analysis. Preference will be given to can January 31, 2005. didates whose research interests mesh 000162 well with those of current faculty. Appli cants must have a Ph.D. in mathematics or ILLINOIS UNIVERSITY OF NOTRE DAME a closely related field, with demonstrated Department of Mathematics promise in research and a strong com SOUTHERN ILLINOIS UNIVERSITY Notre Dame, IN 46556 mitment to teaching in a liberal arts envi CARBONDALE Notre Dame Instructorship in ronment. Department of Mathematics Mathematics Applications, including a letter of ap Numerical Analysis Position plication, a CV, and a brief description of The Department of Mathematics of the Applications are invited for a tenure-track University of Notre Dame invites applica research accomplishments and plans position in numerical analysis at the as tions from recent doctorates for the posi should be sent to: sistant professor level to begin on August tion of Notre Dame Instructor in Mathe Screening Committee, Math Search 16, 2005. Applicants must have a research matics. Candidates in any specialty Department of Mathematics and program in numerical analysis, and must compatible with the research interests of Computer Science demonstrate evidence of, or potential for, the department will be considered. The Emory University excellence both in research and in teach teaching load and salary will be competi Atlanta, Georgia 30322 ing at both undergraduate and graduate tive with those of distinguished instruc Applicants should also arrange for at least levels. Ph.D. in mathematics required by torships at other AMS Group I universities. 3 letters of reference to be sent to this August 15, 2005. Postdoctoral experience This position is for a term of three years DECEMBER 2004 NOTICES OF THE AMS 1387 Classified Advertisements beginning August 22, 2005, is non-renew a letter of application, and a completed Kansas State University able and non-tenure-track Applications, in AMS standard cover sheet, should be sent Manhattan, KS 66506 . eluding a curriculum vitae, a letter of ap to: William G. Dwyer, Chair, at the above The department also requires that the can plication, and a completed AMS standard address. Applicants should also arrange didate arrange for letters to be submitted cover sheet, should be sent to: William G. for at least three letters of recommenda evaluating teachin Dwyer, Chair, at the above address. Ap g accomplishments and tion to be sent to the chair. These letters potential. Offers may begin by December plicants should also arrange for at least should address the applicant's research ac three 1, 2004, but applications for positions will letters of recommendation to be sent complishments and supply evidence that to the be reviewed until February 1, 2005, or until chair. These letters should address the applicant the applicant's research accomplishments has the ability to communi positions are closed. AA/ EOE and supply evidence that the applicant cate articulately and teach effectively. 000137 has the ability to communicate articulately Notre Dame is an Equal Opportunity Em and teach effectively. Notre Dame is an ployer. Women and minorities are urged Equal Opportunity Employer. Women and to apply. The evaluation of candidates will KENTUCKY minorities are urged to apply. The evalu begin December 1, 2004. Information ation of candidates will begin December 1, about the department is available at UNIVERSITY OF LOUISVILLE http://www.science.nd.edu 2004. Information about the department / math. Department of Mathematics is available at http: I jwww. science. 000069 nd. edu/math/ . The Department of Mathematics at the 000067 University of Louisville invites applica IOWA tions for several tenure-track positions at UNIVERSITY OF NOTRE DAME the assistant professor level beginning fall Department of Mathematics UNIVERSITY OF IOWA 2005. Minimum qualifications for these Notre Dame, IN 46556 positions include a Ph.D. degree, or its Regular Position in Algebra Actuarial science tenure-track assistant equivalent, in the mathematical sciences professor starting 8/05. Ph.D. required. and promise of excellence in research and The Department of Mathematics of the Actuarial fellowship or associateship teaching. Preference will be given to ap University of Notre Dame invites applica highly preferred. Industrial experience plicants who strengthen the department's tions for a position in algebra, especially helpful. Duties include teaching and re new Ph.D. program in applied and indus number theory, algebraic geometry, the trial mathematics Langlands program, search in actuarial science and/ or finan and who complement and areas of algebra the existing such as commutative algebra consonant cial mathematics, involvement in Ph.D. strengths in the department. Interested with the research interests of the depart program, and supervision of Ph.D. stu applicants should submit (1) ment. The starting date for the position is dents. Selection begins 12/01/ 04. CV, three the AMS Standard Coversheet; (2) cur August 22, 2005. Candidates at any rank reference letters, and transcript for recent riculum vitae; (3) summary of research in will be considered. The teaching load is one Ph.D.s to Actuarial Search, Statistics & Ac terest; (4) statement of teaching qualifi course one semester and two courses the tuarial Science, Univ. of Iowa, Iowa City, lA cations; and (5) at least four letters of other semester. The salary is competitive. 52242-1409. http: I /www. stat. ui owa. recommendation, including letters which Applications, including a curriculum vitae, edu. discuss at length research and teaching a letter of application, and a completed Women and minorities are encouraged qualifications. To receive full considera AMS standard cover sheet, should be sent to apply. The University of Iowa is an Af tion, material.should be received by De to: William G. Dwyer, Chair, at the above firmative Action, Equal Opportunity Em cember 15, 2004. Applications should be address. Applicants should also arrange ployer. sent to: Search Committee, Department of Mathematics, University for at least three letters of recommenda 000132 of Louisville, tion to be sent to the chair. These letters Louisville, KY 40292. The Department of should address the applicant's research ac Mathematics is committed to building a complishments and supply evidence that culturally diverse faculty and strongly en the applicant has the ability to communi KANSAS courages women, African Americans, and cate articulately and teach effectively. other minorities to apply. AA/ EOE Notre Dame is an Equal Opportunity Em KANSAS STATE UNIVERSITY 000148 ployer. Women and minorities are urged Department of Mathematics to apply. The evaluation of candidates will begin December 1, 2004. Information Subject to budgetary approval, applica about the department is available at tions are invited for tenure-track positions LOUISIANA http://www. math.nd.edu/ math. commencing August 14, 2005; rank and 000068 salary commensurate with qualifications. LOUISIANA STATE UNIVERSITY The department seeks candidates whose Department of Mathematics UNIVERSITY OF NOTRE DAME research interests mesh well with current Department of Mathematics As part of the Louisiana State University faculty. The department has research National Flagship Notre Dame, IN 46556 Agenda, the Department groups in the areas of analysis, algebra, of Mathematics is engaged in a major Regular Position in Numerical Analysis ex geometry/ topology, and differential equa pansion of its professorial faculty. To help tions. Applicants must have strong re The Department of Mathematics guide this expansion, applications are in of the search credentials as well University of Notre Dame invites applica as strong ac vited for a distinguished mathematician tions from an applied mathematician with complishment or promise in teaching. who will take a leadership role in advanc a special interest in numerical analysis. Letter of application, current vita, de ing the national reputation of the Mathe The starting date for the position is August scription of research, and at least three let matics Department. This anticipated full 22 , 2005. Candidates at any rank will be ters of reference evaluating r esearch professor position will have a substantial considered. The teaching load is one should be sent to: salary and a teaching load of one class course one semester and two courses the Louis Pigno each semester. Some additional junior po other semester. The salary is competitive. Department of Mathematics sitions may be available for the appointee Applications, including a curriculum vitae, Cardwell Halll38 to fill. The department will consider 1388 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Classified Advertisements applicants in algebra, analysis, topology, TOWSON UNIVERSITY torics, operations research, theory of al applied mathematics and combinatorics. Tenure-Track Assistant Professor gorithms, numerical analysis, astrophysics, Applicants are expected to have a Ph.D. Position condensed matter physics, computational or equivalent degree in mathematics (or a in Mathematics physics, fluid dynarllics, geophysics, non related area), a record of leadership in re linear waves, theoretical and computa search and a record of excellence in teach Applicants are invited to apply for a tional molecular biology, quantum com ing. Applicants should send a curriculum tenure-track position in pure mathematics puting, quantum field theory and material vitae and the names and addresses of four at the rank of assistant professor begin science, but new hiring may involve other references. Letters of support are welcome ning 2005 Fall Semester. The salary is com areas. Please send curriculum vitae, re but not required for the initial applica petitive. Applicants must have an earned search description, along with three letters tion. doctorate in mathematics. Applicants must of recommendation by January 10, 2005, Applications will be reviewed beginning possess a commitment to teaching, an ac to: Committee on Applied Mathematics, January 3, 2005. We request that appli tive research program, and the ability to Room 2-345, Department of Mathematics, cants use the secure AMS online applica teach a variety of courses, some of which M.I.T., 77 Massachusetts Ave., Cambridge, tion system at http:/ /www.mathjobs. require the use of technology. MA 02139-4307. M.I.T. is an Equal Oppor orgljobs. Applicants may also write to Applicants should submit a letter of ap tunityI Affirmative Action Employer. (For the address below. Minorities and women plication, a resume, a description of re more information about the position and are encouraged to apply. LSU is an equal search, a statement of teaching experience institution: http: I /www-math. mit. edu.) and philosophy, and a copy of both the un opportunity/equal access employer. Sub 000126 mit to: dergraduate and graduate transcripts. They should arrange to have three letters Hiring Committee MASSACHUSETTS INSTITUTE OF Ref: Log #0172 of recommendation, addressing both teaching and research sent to: TECHNOLOGY Department of Mathematics Department of Mathematics Louisiana State University Dr. Leonid Stern, Chairperson Mathematics Search Committee Baton Rouge, LA 70803 The Department of Mathematics may make email: [email protected] Mathematics Department Towson University appointments, at the level of lecturer and 0 0 0154 8000 York Road assistant professor or higher, in pure math Towson, MD 21252-0001 ematics for the year 2005-2006. The teach ing load will be nine hours for the acade Applications or material sent by e-mail or mic year (eight hours for assistant MARYLAND facsimile will not be considered. Priority professor appointments). These positions will be given to applications received on JOHNS HOPKINS UNIVERSITY or before January 20, 2005. are open to mathematicians with doctor ates who show definite promise in re Department of Mathematics The Mathematics Department http: I I search. Applications should be complete www. towson. edu/math/ offers bachelor's Subject to availability of resources and ad degree programs in pure mathematics, ap by January 10, 2005. Applicants should ministrative approval, the following posi plied mathematics, actuarial science and arrange to have sent (a) vita, (b) three let tions are available for the 2005-06 acad risk management, and mathematics edu ters of reference, (c) a description of their emic year. cation. Master's degree programs are of most recent research, and (d) a research 1. One tenure-track or tenured positions fered in applied and industrial mathe plan for the immediate future to: Pure in all areas of pure mathematics. matics, and mathematics education (at Mathematics Committee, Massachusetts 2. One non-tenure-track].]. Sylvester As both the secondary school and middle Institute of Technology, Room 2-263, 77 sistant Professor. school levels). Massachusetts Ave., Cambridge, MA 3. One FRG postdoc position: This is Towson University is an equal opportu 02139-4307. M.I.T. is an Equal Opportunity open to mathematicians who have recently nity/ affirmative action employer and has Affirmative Action Employer. (For more completed or will soon complete a doc a strong institutional commitment to di information about the position or institu torate in mathematics and whose research versity. Women, minorities, persons with tion: http: I /www-math. mit. edu.) interests concern Eigenfunctions of the disabilities, and veterans are encouraged 00012 7 Laplacian. to apply. For questions, send an email to 000141 MASSACHUSETTS INSTITUTE OF math@math. j hu. edu. Applications should TECHNOLOGY be sent to: Appointments Committee, De Department of Mathematics C.L.E. partment of Mathematics, Johns Hopkins MASSACHUSETTS Moore Instructorships in Mathematics University, 404 Krieger Hall, Baltimore, MD 21218-2689, and should include a com MASSACHUSETTS INSTITUTE OF These positions are open to mathemati plete curriculum vitae, at least four letters TECHNOLOGY cians with doctorates who show definite promise in research. The teaching load of recommendation (including a letter con Department of Mathematics will be nine hours for the academic year. cerning teaching), and a description of Applied Mathematics current and planned research. Applica Applications should be complete by Jan tions received by November 1, 2004, will The applied mathematics group at MIT is uary 10, 2005. Applicants should arrange be given priority. Johns Hopkins University seeking to fill possible positions at the to have sent (a) a vita, (b) three letters of is an Affirmative Action/Equal Opportu level of instructor, assistant professor, or reference, (c) a description of the research nity Employer. Minorities and women can higher, beginning September 2005. Ap in their thesis, and (d) a research plan for didates are encouraged to apply. See our pointments will be made based on demon the next year to: Pure Mathematics Com ad online at http: I jwww. mathematics. strated outstanding research qualifica mittee, Massachusetts Institute of Tech jhu.edulmathnewljobs.html. tions. Candidates in all areas of applied nology, Room 2-263, Cambridge, MA 000058 mathematics, including physical applied 02139-4307. M.I.T. is an Equal Opportu mathematics, computational molecular bi nityI Affirmative Action Employer. (For ology, numerical analysis and scientific more information about the position or in computation, will be considered. Current stitution: http: I /www-math. mit. edu.) activities of the group include: combina- 000128 DECEMBER 2004 NOTICES OF THE AMS 1389 Classified Advertisements UNIVERSITY OF MASSACHUSETTS environment for all of its faculty, staff AMHERST and students; as an EEO/ AA employer, NEW HAMPSHIRE Department of Mathematics & Statistics Williams especially encourages applica DARTMOUTH COLLEGE tions from women and minorities. For The Department of Mathematics & Statis john Wesley Young Research more information on the Department of tics (http: I jwww. math. umass. edu) invites Instructorship applications for tenure-track positions at Mathematics and Statistics, visit the assistant professor level. The search http://www.williams.edu/Mathematics. The John Wesley Young Instructorship is will encompass the following areas: analy 000151 a postdoctoral two-year appointment in sis and partial differential equations, ap tended for promising Ph.D. graduates with plied and computational mathematics, al WILLIAMS COLLEGE strong interests in both research and teach gebraic geometry, differential geometry Department of Mathematics ing and whose research interests overlap and topology, representation theory and a department member's. Current research Lie theory, number theory, probability, The Williams College Department of Math areas include applied mathematics, com and statistics. Exceptional promise in re ematics and Statistics invites applications binatorics, geometry, logic, noncommuta search and teaching tive geometry, number theory, operator (at all levels of the cur for one tenure-track position in riculum) is required. Although this search statistics, algebras, probability, set theory and topol focuses on junior level appointments, can beginning fall 2005, at the rank of assis ogy. Instructors teach four 10-week didates for more senior level appointments tant professor (in an exceptional case, a courses distributed over three terms, will be considered. In addition, visiting as more advanced appointment may be con though one of these terms in residence sistant professor/lecturer positions might sidered). We are seeking a highly quali may be free of teaching. The assignments be available. Applicants should send a cur fied candidate who has demonstrated ex normally include introductory, advanced riculum vita, and arrange to have at least cellence in teaching and research, and who undergraduate, and graduate courses. In three letters of recommendation sent to: will have a Ph.D. by the time of appoint structors usually teach at least one course Search Committee, Department of Mathe in their own specialty. This appointment ment. matics & Statistics, University of Massa is for 26 months with a monthly salary of chusetts Amherst, Lederle Graduate Re Williams College is a private, residen $4,350.00 and is not renewable. Salary in search Center, 710 North Pleasant St., tial, highly selective liberal arts college cludes 2-month research stipend for in Amherst, MA 01003-9305. Review of ap with an undergraduate enrollment of ap structors in residence during two of the plications will begin on November 1. Ap proximately 2,000 students. The teaching three summer months in 2006 and 2007. plications will continue to be accepted load is two courses per 12-week semester To be eligible for a 2005-2007 Instruc until all positions are filled. Please include and a winter term course every other Jan torship, candidate must be able to com the AMS Application Cover Sheet. Women plete all requirements for the Ph.D. uary. In addition de and members of minority groups are en to excellence in teaching, gree before September 2005. couraged to apply. The University of Mass an active and successful research program Applications may be obtained at achusetts is an Affirmative Action/ Equal is expected. http://www.math.dartmouth.edu/re Opportunity Employer. To apply, please send a vita and have c rui ti ng / . Or submit a letter of applica p00133 three letters of recommendation on teach tion, curriculum vitae, graduate school ing and research sent to the Hiring Com transcript, thesis abstract, statement of WILLIAMS COLLEGE mittee, Department of Mathematics and research plans and interests, and at least Department of Mathematics Statistics, Williams College, Williamstown, three, preferably four, letters of recom mendation to Donna Black, Department MA 01267. Teaching and The Williams College Department of Math research state of Mathematics, Dartmouth College, 6188 ematics and Statistics invites applications ments are also welcome. Evaluations of Bradley Hall, Hanover, NH 03755-3551. At for one tenure-track position in mathe applications will begin on or after No least one referee should comment on ap matics, beginning fall2005, at the rank of vember 15 and will continue until the po plicant's teaching ability; at least two ref assistant professor (in an exceptional case, sition is filled. Williams College is dedi erees should write about applicant's re a more advanced appointment may be con cated to providing a welcoming intellectual search ability. Applications received by sidered). We are seeking a highly quali environment for all of its faculty, staff January 5, 2005, receive first consideration; fied candidate who has demonstrated ex applications will be accepted until position cellence in teaching and research, and who and students; as an EEO/ AA employer, Williams especially encourages applica is filled. Dartmouth College is committed will have a Ph.D. by the time of appoint to diversity and strongly encourages ap ment. tions from women and minorities. For plications from women and minorities. Williams College is a private, residen more information on the Department of 000103 tial, highly selective liberal arts college Mathematics and Statistics, visit with an undergraduate enrollment of ap http://www.williams.edu/Mathematics. DARTMOUTH COLLEGE proximately 2,000 students. The teaching 000152 Department of Mathematics load is two courses per 12-week semester and a winter term course every other Jan The Department of Mathematics antici uary. In addition to excellence in teaching, pates a tenure-track opening with initial ap an active and successful research program MICHIGAN pointment in the 2005-2006 academic is expected. year. The position is for an applied math To apply, please send a vita and have MICHIGAN STATE UNIVERSITY ematician at the rank of assistant profes three letters of recommendation on teach East Lansing, Ml48824 sor. In extraordinary cases, an appoint ing and research sent to the Hiring Com ment at a higher proMSc rank is possible. mittee, Department of Mathematics and Program in Successful candidate should have demon Statistics, Williams College, Williamstown, Industrial Mathematics strated ability to work across disciplines; MA 01267. Teaching and research state particularly, it is expected that he or she ments are also welcome. Evaluations of Direct your students toward one of the seek out and strike up collaborations applications will begin on or after No professional M.Sc. programs. Industry across campus with departments such as vember 15 and will continue until the po needs business-savvy mathematicians. See biology, physics, computer science; he/ she sition is filled. Williams College is dedi http://www.sciencemasters.com/. should also aggressively seek funding in cated to providing a welcoming intellectual 000001 his/ her area of research. Current applied 1390 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Classified Advertisements interests include (but are not limited to) and arrange for four letters of reference, preferred. We especially emphasize coor imaging, signal processing, computational at least one of which specifically addresses dination with department, college and uni number theory, statistical physics, sto teaching, to be sent to Donna Black, Re versity goals, including undergraduate chastic processes, quantum computing, cruiting Secretary, Department of Mathe teaching in the university's SAGES Pro and computational biology and are re matics, Dartmouth College, 6188 Bradley gram. Areas of preference have been iden ceiving funding from various sources in Hall, Hanover, NH 03755-3551. Applica tified to meet department priorities. For cluding NSF and NIH. Candidates for the tions received by December 15, 2004, will more information and instructions, see position must be committed to outstand receive first consideration. Dartmouth Col http: l/www .case.edul artsci l deanl interaction with students is committed to diversity and strongly ing teaching and lege csOS. html. Indicate at all levels of undergraduate and gradu encourages applications from women and searchesl mathemati ate study. minorities. Inquiries about the progress in which area you wish to be considered. The successful candidate will hold the To create an atmosphere supportive of of the selection process may be directed research, Dartmouth offers new faculty to Dan Rockmore, Recruiting Chair. Ph.D. or equivalent and have, relative to ca members grants for research-related ex 000105 reer stage, a distinguished record of pub penses, a quarter of sabbatical leave for lication, research, service, and teaching. each three academic years in residence, Compensation commensurate with quali and flexible scheduling of teaching re NORTH CAROLINA fications. Electronic applications only, to: sponsibilities. The teaching responsibility James Alexander, math-faculty courses spread posi ti on@cwru. edu, consisting of a letter in mathematics is three NORTH CAROLINA STATE UNIVERSITY over three of four 1 0-week terms. To apply of application, which indicates in which Department of Mathematics for the position, applications may be ob area of preference you wish to be consid tained at http: I lwww. math. dartmouth. We invite applications for an anticipated ered, AMS cover sheet, a c.v., and the edu/recruiting/. Or send a letter of ap tenure track position at the assistant pro names and contact information for four plication, curriculum vitae, and a brief fessor level in probability and applications referees to whom we may write. Visiting statement of research results and interests, beginning fall2005. Applicants must have positions/ instructorships/ lectureships and arrange for four letters of reference, a doctorate in mathematics or a closely re may also be open. Evaluation of applica at least one of which specifically addresses lated area, a strong ongoing research pro tions will begin December 15, 2004. Case teaching, to be sent to Donna Black, Re gram, and a commitment to effective teach cruiting Secretary, Department of Mathe is a recipient of an NSF ADVANCE insti ing at the undergraduate and graduate tutional transformation grant to increase matics, Dartmouth College, 6188 Bradley levels. Candidates in all areas of probability Hall, Hanover, NH 03755-3551. Applica the participation of women in science and theory and related applications who have engineering. Case Western Reserve Uni tions received by December 15, 2004, will of postdoctoral ex had at least one year committed to diversity and is receive first consideration. Dartmouth Col perience will be considered. The depart versity is lege is committed to diversity and strongly ment has strong research programs in an Affirmative Action, Equal Opportunity encourages applications from women and both pure and applied mathematics, and Employer. Applications from women or minorities. Inquiries about the progress significant collaborations with other de minorities are especially encouraged. of the selection process may be directed partments, institutions, and industry. The 000131 to Dan Rockmore, Recruiting Chair. successful candidate will have the oppor 000104 tunity to participate in the programs of the Statistical and Applied Mathematical Sci OREGON DARTMOUTH COLLEGE ences Institute (SAMSI), the Center for Re Department of Mathematics search in Scientific computation, and our UNIVERSITY OF OREGON affiliated programs in biomathematics and The Department of Mathematics antici financial mathematics. Information about Department of Mathematics pates a tenure-track opening with initial ap the department· may be found at pointment in the 2005-2006 academic Applications are invited for three posi http: I l www. math. ncsu. edu. Applicants In extraordinary cases, an appoint e department of mathematics: year. should send a vita, research plan, and tions in th ment at a higher rank is possible. Prefer 1. Assistant or associate professor in ei three letters of recommendation to Sto ence given to candidates working in Department any area of pure or applied mathematics, theory/logic or areas of algebra chastics Search Committee, ther set of Mathematics, NC State University, Box statistics or mathematics education. This with connections to existing research in is a tenure related position. com 8205, Raleigh, NC 27695-8205. North Car terests in the department, including is an Equal Oppor algebra, algebraic and arith olina State University 2. Assistant or associate professor in putational tunity and Affirmative Action Employer. In representation theory, probability, statistics or related area. This metic geometry, NC State welcomes all persons coding theory and algebraic combinatorics. addition, is a tenure related position. must also be without regard to sexual orientation. ADA 3. Paul Olum Visiting Assistant Profes Candidates for the position Dr. Jean-Pierre Fouque, committed to outstanding teaching and Accommodations: sor. This is a two-year postdoctoral posi ncs u. edu, (919) 515-2382. interaction with students at all levels of un fouque@math. tion named in honor of former University dergraduate and graduate study. Complete applications received before De cember 31, 2004, will receive full consid of Oregon President Paul Olum. This po To create an atmosphere supportive of eration. sition is not tenure related. research, Dartmouth offers new faculty 000130 Specific descriptions and qualifications members grants for research-related ex for these positions, and application in penses, a quarter of sabbatical leave for structions, can be found at: http: I I each three academic years in residence, OHIO uoregon.edul-mathlemployment .html. and flexible scheduling of teaching re Application materials may NOT be sub sponsibilities. The teaching responsibility onically. in mathematics is three courses spread CASE WESTERN RESERVE UNIVERSITY mitted electr over three of four 1 0-week terms. To apply Department of Mathematics Closing date for all positions is January for the position, applications may be ob Cleveland, Ohio 5, 2005. Women and minorities are en tained at http: llwww.math.dartmou t h. couraged to apply. The University of Ore edul recruitingl . Or send a letter of ap One or more tenure-track appointments. gon is an EO/ AA/ ADA Institution com plication, curriculum vitae, and a brief Open rank, however, appointment at the mitted to diversity statement of research results and interests, rank of assistant professor is strongly 000150 D ECEMBER 2004 NOTICES OF THE AMS 1391 Classified Advertisements probability and statistics by hiring at the starting with the fall 2005 semester. The PENNSYLVANIA assistant professor level in statistics, in department includes the areas of algebra cluding biostatistics. and discrete mathematics; analysis; com CARNEGIE MELLON UNIVERSITY A successful candidate will demonstrate putational mathematics; mathematics ed CENTER FOR NONLINEAR ANALYSIS great research potential, and have a record ucation; operations research; and proba Department of Mathematical Sciences of successful teaching commensurate with bility and statistics. Targeted recruiting is the position. Applications from new and The Center for Nonlinear Analysis expects for the assistant professor rank, but ap recent Ph.D.'s are welcome. plicants for all ranks will be considered. to make several Post-Doctoral appoint As part of their application, candidates ments for 2005-06 in applied analysis, and Desirable attributes for candidates include should submit: (a) an AMS cover sheet; (b) an interdisciplinary research orientation in potential focus areas include materials a complete vita, including a list of publi science, systems biology, and fluid flow. the mathematical sciences; post-doctoral, cations; (c) a research plan; and (d) at least industrial, or practical experience; collab These will be one- or two-year joint ap four letters of recommendation, at least pointments by the Center and the De orative possibilities with faculty members one of which addresses the candidate's in the department and related disciplines; partment of Mathematical Sciences. Re teaching. cipients will teach at most two courses and an interest in innovative applications. per year. Applicants should send a vita, list Applications received by November 15 Candidates should have strong potential of publications, a statement describing will be assured of full consideration. Ap plication materials should be sent to: or demonstrated capability for effective re current and planned research, and arrange search and teaching. An earned doctorate to have at least three letters of recom Statistics Hiring Committee Department of Mathematics or equivalent is required for the tenure mendation sent to: track positions. Review of applications will Post-Doctoral Appointments Com Lehigh University Bethlehem, PA 18015-3174 begin on November 1, 2004, and will con mittee tinue until the positions are filled. Appli For detailed information see the depart Center for Nonlinear Analysis cations received by December 1, 2004, will ment website: http: I lwww. 1 ehi gh. edul Department of Mathematical Sci receive full consideration. Applicants ences -math. Lehigh University is an Equal Opportu should indicate their research specialties Carnegie Mellon University and interests in their cover letter. Vita and Pittsburgh, PA 15213-3890 nity/Affirmative Action employer. 000139 three reference letters should be sent to The deadline for applications is December the address below. For further information 15, 2004. LEHIGH UNIVERSITY regarding the department and its pro 000164 Department of Mathematics grams, please visit the web site http: I lwww. math. c1 em son. edu. CU is an LEHIGH UNIVERSITY The Lehigh Department of Mathematics AAIEO employer and encourages applica Department of Mathematics seeks to fill two visiting positions. These tions from women and minorities. The Lehigh Department of Mathematics are one-year, non-tenure-track positions Send applications to: Faculty Search seeks to build on its strengths in pure that carry a four course per year teaching Committee, Department of Mathematical mathematics by hiring at the assistant pro load. Sciences, Box 340975, File N, Clemson Uni fessor level in analysis with a preference The department welcomes applicants in versity, Clemson, SC 29634-0975. for fields which complement our existing any fields of pure and applied mathemat 000163 areas of research. ics, including statistics, which complement A successful candidate will demonstrate our existing areas of research. As part of their application, candidates great research potential and have a record TENNESSEE of successful teaching commensurate with should submit: (a) an AMS cover sheet; (b) the position. Applications from new and a complete vita, including a list of publi recent Ph.D.'s are welcome. cations; (c) a research plan; and (d) at least VANDERBILT UNIVERSITY As part of their application, candidates four letters of recommendation, at least Department of Mathematics one of which addresses the applicant's should submit (a) anAMS cover sheet; (b) We invite a.pplications for a non-tenure a complete vita, including a list of publi teaching. Applications received by November 15 track assistant professor position begin cations; (c) a research plan; and (d) at least ning fall 2005. This position is to be filled four letters of recommendation, at least will be assured of full consideration. Ap one of which addresses the candidate's plication materials should be sent to: in the area of analysis such as operator the teaching. Visiting Faculty Hiring Committee ory and holomorphic spaces. It is a two Applications received by November 15 Department of Mathematics year appointment at the non-tenure-track will be assured of full consideration. Ap Lehigh University assistant professor level with a 2-2 teach plication materials should be sent to: Bethlehem, PA 18015-3174 ing load, normally renewable for a third Analysis Hiring Committee For detailed information see the depart year. This position is intended for a recent Department of Mathematics ment website: http: I lwww. 1 ehi gh. edul Ph.D. with demonstrated research poten Lehigh University -math. tial and a strong commitment to excel Bethlehem, PA 18015-3174 Lehigh is an Equal OpportunityI Affir lence in teaching. Submit your application For detailed information see the depart mative Action employer. and supporting materials to the attention 000140 of the "Analysis Hiring Committee." These ment website: http: I lwww. 1 ehi gh. edul -math. materials should include a vita, a publi Lehigh University is an Equal Opportu cation list, a research summary, and the nityI Affirmative Action employer. SOUTH CAROLINA American Mathematical Society Cover 000138 Sheet. Please include an email address and CLEMSON UNIVERSITY fax number if available. Applicants should LEHIGH UNIVERSITY Department of Mathematical Sciences also arrange to have four letters of rec Department of Mathematics ommendation sent to the hiring commit The Department of Mathematical Sciences tee, including one that discusses the can The Lehigh Department of Mathematics at Clemson University invites applications didate's teaching qualifications. Evaluation seeks to build on its strengths in for expected tenure-track faculty positions of the applications will commence on 1392 NOTICES OF THE AMS VOLUME 51 NUMBER 11 Classified Advertisements November 1, 2004, and continue until the These materials should include a vita, a edu/ math for more information about the position is filled. publication list, a research summary and department. Vanderbilt University is an Affirmative the American Mathematical Society Cover To apply, send a letter of application Action/Equal Opportunity Employer. Sheet. Please include an email address and with a curriculum vitae, a list of publica 000135 fax number if available. Applicants should tions, and a research and teaching state also arrange to have four letters of rec ment to: The Faculty Search Committee, VANDERBILT UNIVERSITY ommendation sent to the hiring commit Department of Mathematics, Southern Department of Mathematics tee, including one that discusses the can Methodist University, P.O . Box 750156, 1 326 Stevenson Center didate's teaching qualifications. Evaluation Dallas, Texas 75275-0156. Applicants must Nashville, TN 37240 of the applications will commence on No also arrange for three letters of recom vember 1, 2004, and will continue until the mendation to be forwarded to the Faculty We invite applications for two non-tenure position is filled. For information about the Search Committee. The Search Commit track assistant professor positions in the research group in noncommutative geom tee can be contacted by sending e-mail to areas of noncommutative geometry/topol etry and operator algebras at Vanderbilt mathsearch@mai 1. smu. edu. [Tel: (214) 768- ogy and operator algebras beginning fall University, please consult the Web at 2452; Fax: (214) 768-2355] 2005. These are three-year appointments http://www .math.vanderbilt.edu/-ncgo To ensure full consideration for the po at the non-tenure-track assistant profes a/. Vanderbilt University is an Affirma sition, the application must be postmarked sor level with a 1-1 teaching load, a sum tive Action/Equal Opportunity Employer. by January 7, 2005, but the committee will mer stipend, and an award for research re 000161 continue to accept applications until the lated travel. The positions are supported position is filled. The committee will no by a Research Training Group (RTG) grant tify applicants of its employment decision from the National Science Foundation. TEXAS after the position is filled. They are intended for recent Ph.D.'s who SMU will not discriminate on the basis are U.S. citizens or residents with demon RICE UNIVERSITY of race, color, religion, national origin, sex, age, disability or veteran status. SMU is also strated research potential and a strong Department of Mathematics commitment to excellence in teaching. committed to nondiscrimination on the Postdoctorate Submit your application and support basis of sexual orientation. ing materials to the attention of the "Non Griffith Conrad Evans Instructorships Post 000142 commutative Geometry Hiring Commit doctoral appointments for two to three tee". These materials should include a vita, years for promising research mathemati UNIVERSITY OF HOUSTON-CLEAR LAKE a publication list, a research summary and cians with research interests in common School of Science and the American Mathematical Society Cover with the active research areas at Rice, par Computer Engineering Sheet. Please include an email address and ticularly geometric topology, geometric Faculty Search fax number if available. Applicants should analysis, differential geometry, combina also arrange to have four letters of rec torics, analysis, algebraic geometry, and er The UHCL School of Science and Computer ommendation sent to the hiring commit godic theory. Duties will include research Engineering is conducting a search to fill tee, including one that discusses the can and classroom teaching. Applications re the faculty position listed below. Inter didate's teaching qualifications. Evaluation ceived by December 15, 2004, will receive view by appointment only. If an accom of the applications will commence on No full consideration. Rice University is an modation is needed during an interview, vember 1, 2004, and will continue until the Equal Opportunity Affirmative Action Em please notify the search committee at least position is filled. For information about the ployer and strongly encourages applica one week prior to the scheduled interview. research group in noncommutative geom tions from women and minority group Position Description: Assistant Pro etry and operator algebras at Vanderbilt members. Inquiries and applications fessor for Mathematics University, please consult the Web at should be addressed to Chair, Evans Com The Department of Mathematical Sci http: //www .math.vanderbilt.edu/- ncgo mittee, Department of Mathematics, Rice ences of the University of Houston-Clear a/. Vanderbilt University is an Affirma University, P.O. Box 1892, Houston, TX Lake invites applications for a tenure-track tive Action/Equal Opportunity Employer. 77251-1892. Submitting the AMS Appli opening for an assistant professor or 000049 cation Cover Sheet (available in Notices, higher to begin August 2005. The depart ElMS, or on the AMS website) would be ment seeks candidates whose mathemat VANDERBILT UNIVERSITY greatly appreciated. ical interests complement those of cur Department of Mathematics 000111 rent faculty. A Ph.D. in mathematics by 1 326 Stevenson Center August 2005 is expected. The successful Nashville, TN 37240 SOUTHERN METHODIST UNIVERSITY candidate will be expected to teach un Dedman College dergraduate and graduate courses in math We invite applications for two non-tenure Department of Mathematics ematics, to conduct mathematical research, track assistant professor positions in the and to perform university service. areas of noncommutative geometry/topol Applications are invited for one tenure The University of Houston-Clear Lake is ogy and operator algebras beginning fall track assistant professor position to begin an upper-level institution with an enroll 2005. These are three-year appointments in the fall semester of 2005. Applicants ment of 7,500 located adjacent to the John at the non-tenure-track assistant profes must have a Ph.D., provide evidence of son Space Center. It offers degree pro sor level with a 1-1 teaching load, a sum outstanding research, and have a strong grams at the bachelor And master's level. mer stipend, and an award for research re commitment to teaching at all levels. The The mathematical sciences area offers lated travel. The positions are supported Department of Mathematics' active doc bachelor and master's degrees in mathe by a Research Training Group (RTG) grant toral program is in computational and ap matics, master's degrees in statistics, from the National Science Foundation. plied mathematics. Current research in courses supporting the natural and ap They are intended for recent Ph.D.'s who cludes numerical analysis of ordinary and plied sciences, and courses in support of are U.S. citizens or residents with demon partial differential equations, mathemat the certification of elementary and sec strated research potential and a strong ical software, dynamical systems, fluid dy ondary school teachers. commitment to excellence in teaching. namics, nonlinear optics, and mathemat Apply on-line at http: I jj obs. uhcl . Submit your application and supporting ical biology. Applications in all areas of edu/. Please send three letters of recom materials to the attention of the "Noncom computational and applied mathematics mendation from the references to Chair of mutative Geometry Hiring Committee". are encouraged. Visit http: I /www . smu. Mathematical Sciences Search Committee, DECEMBER 2004 NOTICES OF THE AMS 1393 Classified Advertisements University of Houston-Clear Lake, 2 700 the math department and faculty in re Bay Area Blvd. MC-167, Houston, TX, lated disciplines; and to develop a com TAIWAN 77058. Prelintinary interviews will be held petitive, externally funded research pro at the Joint Winter Meetings in Atlanta gram. Review of completed applications NATIONAL CHIAO TUNG UNIVERSITY (January 2005) but applications will be ac will begin December 15, 2004. Department of Applied Mathematics cepted until the position is filled. A complete application will consist of a The University of Houston-Clear Lake is an Affirmative Action/Equal Opportunity letter of application, a complete CV, a Applications invited for regular or visiting Employer supporting workforce diversity statement of research interests and ac positions at all levels (assistant profes and does not discriminate on the basis of complishments, and a statement of teach sors and above) beginning August 2005. All race, sex, age, religion, national origin, dis ing philosophy. Please forward applica areas of pure and applied mathematics ability, or veteran status. The university tions to: Search Committee on considered. Applicant should hold Ph.D. hires only individuals authorized to work (by August 2005) in mathematics or related Computational Multiphase Flow, Depart field, with strong research potential. Usual in the United States and does not observe ment of Mathematics, University of hiring practices that will result in the dis language of instruction is Mandarin. Wyoming, Laramie, WY 82071-3036. Please Send letter of application, curriculum placement of qualified United States citi have at least three letters of recommen zens or permanent residents. We reserve vitae, research plans, three recommenda dation, one of which should address the the right to extend searches or not fill po tion letters, transcripts of graduate works sitions. candidate's teaching, sent directly to the (for recent graduates) to: 000136 search committee. For further informa Hiring Committee tion please refer to: http: I /math. uwyo. Department of Applied Mathematics edu. UW is an EO/AA Employer. National Chiao Tung University Hsinchu 300, Taiwan VIRGINIA 000097 Full consideration to applications received by February 20, 2005. CHRISTOPHER NEWPORT UNIVERSITY The department is one of the leading re Department of Mathematics PORTUGAL search centers in Taiwan, with 24 faculty members in combinatorics, differential Two tenure-track positions at assistant INSTITUTO SUPERIOR TECNICO professor level to begin August 2005. Must equations, differential geometry, dynam have Ph.D. in mathematics or related field, Center for Mathematical Analysis ical systems, financial mathematics, func with expertise in any area of mathemat Geometry, and Dynamical Systems tional analysis, Lie theory, mathematical physics, number theory, operator theory, ics/statistics & qualifications compatible Departamento de Matematica probability theory, and scientific compu with needs of department, faculty & stu Av. Rovisco Pais tation. Visit website http: I /www. math. dents. Effective language communication 1049-001 lis boa, Portugal nctu. edu/tw/ for details. skills essential. Applicants should show in 000115 terest in student-faculty research & ob Postdoctoral Positions taining grants. Further details (Search The Center for Mathematical Analysis, #8275) at http: I jwww. cnu. edu/admi n/hr. Deadline: 2/1/05. EOE. Geometry, and Dynamical Systems of the 000157 Department of Mathematics of Instituto Superior Tecnico, Lisbon, Portugal, invites applications for postdoctoral positions for WYOMING research in mathematics, subject to bud getary approval. Positions are for one year, UNIVERSITY OF WYOMING with the possibility of extension for a sec Department of Mathematics ond year upon mutual agreement. Selected Tenure-Track Position in candidates will be able to take up their po Computational Fluid Dynamics sition between September 1, 2005, and January 1, 2006. Applications are invited for an assistant Applicants should have a Ph.D. in math professor tenure-track position starting ematics preferably obtained after Decem August 2005. A higher rank is possible ber 31,2002. They must show very strong for persons with outstanding research research promise in one of the areas in qualifications. The minimum qualifica tions are an earned Ph.D., significant which the mathematics faculty of the cen record of accomplishments in research, ter is currently active. There are no teach evidence of a strong commitment to teach ing duties associated with these positions. ing, and appropriate level of communica Applicants should send a curriculum tion skills. Candidates with research em vitae; reprints, preprints and/or disserta phasis in areas such as computational tion abstract; description of research pro multiphase flow (modeling, simulation, ject (of no more than 1,000 words); and parameter estimation, optimization and three letters of reference directly to the di control) as well as computational methods rector at the above address. for free boundaries and fluid discontinu ities (e.g., fluid interfaces, shock waves, To insure full consideration, complete etc.) will be preferred. The position re application packages should be received by quires the ability and interest to advise un January 15, 2005. Additional information dergraduates and supervise master's and about the Center and the positions is avail doctoral students; to teach a variety of able at http://www.math.ist.utl. undergraduate, graduate and outreach pt/cam/. courses; to collaborate with colleagues in 000134 1394 NOTICES OF THE AMS VOLUME 51, NUMBER 11 CAMBRIDGE NEW FROM CAMBRIDGE UNIVERSITY PRESS Mathematical Illustrations A Manual of Geometry and PostScript Bill Casselman $90.00* : Hardback: 0-521-8392 1-1: 336pp $40.00*: Paperback: 0-521-54788-1 Introduction to Circle Packing The Theory of Discrete Analytic Functions Kenneth Stephenson $50.00* : Hardback: 0-521-82356-0: 400pp The Geometry of Efficient Fair Division Julius B. 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US$ 228,95 * ISBN 3-11-017118-X In this volume Kahler's mathematical papers are collected following a "Tribute to Herrn Erich Kahler" by S. S. Chern, an overview of Kahler's life data by A. Bohm and R. Berndt, and a Survey of his Mathematical Work by the editors. E de Gruyter Berlin· New York *for orders placed in USA, Canada, Mexico w ww. d eg ru yt e r. d e Prices are subject to change. Payments may be made online at: www.ams.org/ dues-renewal or call the AMS at: 401-455-4000 (worldwide) or 800-321-4267 (U.S. & Canada) Order exclusively on the AMS Bookstore--titles are conveniently listed by subject category. 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American Mathematical Society, 20 I Charles Street, Providence, Rl 02904-2294, USA (@) AMERICAN MATHEMATICAL SOCIETY 10/04 CMS WINTER MEETING 2004 December 11 ;... 13 decembre Universite McGill University, Montreal, Quebec The Department of Mathematics and Statistics, McGill Unive rsity is happy Le departement de mathematiques et statistiques de I'Universite McGill est to announce the provisional outline for the Canadian Mathematical heureux d'annoncer les details provisoires pour Ia Reunion d'hiver 2004 de Society Winter Meeting 2004, to be held at the Hilton Bonaventure in Ia SMC, qui se tiendra au Hilton Bonaventure au centre-ville de Montreal. downtown Montreal. Look for the First An nouncement in the September Veuillez consulter Ia premiere annonce officielle dans le numero de 2004 issue of the CMS Notes and at septembre des Notes de Ia SMC ainsi que notre site web ww.cms.math.cal Eventslwinter041 for the latest updates. www.cms.math.ca/Reunionslhiver04/ pour les informations les plus ajour. PLENARY LECTURERS I CONFERENCIERS PRINCIPAUX Michael Bennett (UBC) Persi Diaconis (York) Rainer Steinwandt (Karlsruhe) Rostislav Grigorchuk (Texas A&M) PRIZES I PRIX Conferencier Coxeter-James Lecture: lzabella laba (UBC) Prix de doctorat I Doctoral Prize Lecture : Nicolaas Spronk (Waterloo) Prix pour service meritoire de Ia SMC I CMS Distinguished Service Award: Edgar Goodaire (Memorial) Prix Adrien Pouliot Prize: to be announced I avenir Prix G. de B. Robin son Award: to be announced I avenir SESSIONS Algebraic Combinatorics: Fran~o is Bergeron, Riccardo Biagioli, Interactions between Algebra and Computer Science: Peter McNamara, and Christophe Reutenauer (UQAM) Alexei Myasnikov (McGill) and Vladimir Shpilrain (CUNY) Approximation Theory: Richard Fournier Mathematical Methods in Statistics: Russell Steele, Alain Vandal and Paul Gauthier (Montreal) and David Wolfson (McGill) Arithmetic Geometry: Eya l Goren and Adrian lovita (McGill) Mathematics for Future Teachers: Leo Jonker (Queen's) Combinatorial and Geometric Group Theory: lnna Bumagin Number Theory: Andrew Granville (Montreal) (Carleton) and Dani Wise (McGill) Special Metrics and Submanifolds in Riemannian Geometry: Commutative Algebra: Sara Faridi (UQAM), Sindi Sabourin (York), Gordon Craig (McGill) and Spiro Karigiannis (McMaster) Wil l Tra ves (UQAM) and Adam van Tu yl (Lakehead) Universal Algebra and Complexity: J. Hynd man (McGill), Discrete Geometry: Karoly Bezdek (Calgary) and Bob Erdahl (Queen's) B. Larose (Concordia), and Denis Therien (McGill) Dynamical Systems: Michael A. Radin (RIT) Contributed Papers: William Brown (McGill) Groups, Equations, non-commutative Algebraic Geometry: Olga Kharlampovich and Alexei Myasnikov (McGill) Harmonic Analysis: Galia Dafni (Concordia) Meeting Director: Olga Kharlampovich (McGill) History of Mathematics: Thomas Archibald (Acadia), Rich Olander, local Arrangements: William Brown (McGill) Ron Sklar (St. John's) and Alexei Vo lkov (McGill) SYMPOSIUMS Combinatoire algebrique : Fran~ois Bergeron, Riccardo Biagioli, Interactions entre Ia science informatique et l'algebre : Peter McNamara, et Christophe Reutenauer (UQAM) Alexei Myasnikov (McGill) et Vlad imir Shpilrain (CUNY) Theorie d'approximation : Richard Fournier Methodes mathematiques en statistique : Russell Steele, et Paul Gauthier (Montreal) Alain Va ndal et David Wo lfson (McGill) Geometrie arithmetique : Eyal Goren et Adr ian lovita (McGill) Mathematiques pour futur professeur(e)s : Leo Jonker (Queen's) Theorie des groupes combinatoire et geometrique : Theorie des nombres : Andrew Granville (Montreal) lnna Bumagin (Carleton) et Dani Wise (McGill) Distances et sous-varietes speciales de Ia geometrie Algebre commutative : Sara Faridi (UQAM), Sindi Sabourin (York), Riemanienne : Gordon Craig (McGill) et Spiro Karigiannis (McMaster) Will Tra ves (UQAM) et Adam van Tuyl (Lakehead) Algebre universelle et complexite : J. Hynd man (McGill), Geometrie discrete : Karoly Bezdek (Calgary) et Bob Erdahl (Queen's) B. Larose (Concordia), et Denis Therien (McGill) Systemes dynamiques : Michael A. Radin (RIT) Communications libres :William Brown (McGill) Groupes, Equations, geometrie algebrique non-commutative : Olga Kharlampovich et Alexei Myasnikov (McGill) Analyse harmonique : Galia Dafni (Concordia) Directrice de reunion: Olga Kharlampovich (McGill) Histoire des mathematiques : Thomas Archibald (Acadia), logistique locale: William Brown (McGill) Rich Olander, Ron Sklar (St. John's) et Alexei Volkov (McGill) Meetings & Conferences oftheAMS IMPORTANT INFORMATION REGARDING MEETINGS PROGRAMS:AMS SectionalMeetingprograms 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: I lwww. ams . o rglmeeti ngs I. Programs and abstracts will continue to be displayed on the AMS website in the Meetings and Conferences section until about three weeks after the meeting is over. Final programs for Sectional Meetings will be archived on the AMS website in an electronic issue of the Notices as noted below for each meeting. For the latest information on this meeting, see www. ams . Atlanta, Georgia orglamsmtgsl209l_intro.html. Atlanta Marriott Marquis and Hyatt Joint AMS-MAA Sessions Regency Atlanta The AMS Committee on Science Policy-MAA Science Pol ...._f.{J_ oint Mathematics icy Committee Government Speaker has been cancelled January 5-8, 2005 ('!"" ..;, ~""- Meetings on Friday afternoon. Wednesday - Saturday I ATLANTA , GEOR.Gii\ .e1 ]rmuary 5-8, 2005 AMS Program Updates Meeting #1 003 The Invited Address by Steven Zelditch, Friday, 10:05 to ]oint Mathematics Meetings, including the 111 th Annual 10:55 a.m., is titled Random Complex Geometry, or How Meeting of the AMS, 88th Annual Meeting of the Mathe to count universes in string theory. matical Association of America (MAA), annual meetings of The Panel, Friday, 9:30a.m. to 10:55 a.m. This one act play is set in Ballston VA, at the headquarters of mathe the Association of Women in Mathematics (A VVM) and the maticians' favorite federal agency. It is an historical drama National Association of Mathematicians (NAM), the winter based on, and accurately adhering to, actual events, but meeting of the Association of Symbolic Logic (ASL), with ses typical of the genre, it also seeks to entertain while pene sions contributed by the Society for Industrial and Applied trating facets of the human (and, of course, mathemati Mathematics (SIAM). cal) condition. The audience will be challenged to reflect Associate secretary: Lesley M. Sibner on the realities presented and will have a sense of deja vu Announcement issue of Notices: October 2004 at the characters portrayed. The work is written and pro Program first available on AMS website: November 1, 2004 duced by the National Science Foundation, Division of Program issue of electronic Notices: January 2005 Mathematical Sciences; the staff and the cast will consist Issue of Abstracts: Volume 26, Issue 1 of well-known mathematical thespians at this world pre mier performance. This presentation will be moderated by Deadlines William Rundell, National Science Foundation. For organizers: Expired For consideration of contributed papers in Special Sessions: AMS Workshop Expired Department Chairs Workshop, Tuesday, 8:00a.m. to 6:30 For abstracts: Expired p.m. This workshop is intended to stimulate discussion For summaries of papers to MAA organizers: Expired among attending chairs and workshop leaders. Sharing ideas and experiences with peers provides a form of DECEMBER 2004 NOTICES OF THE AMS 1403 Meetings & Conferences department chair therapy, creating an environment that Morgan Prize Session, Friday, 10:00 a.m. to 10:50 a.m. enables attending chairs to address departmental mat The winner and honorable mention recipients of the AMS ters from new perspectives. Workshop leaders will be MAA-SIAM Frank and Brennie Morgan Prize for Outstanding Krishnaswami Alladi, Department Chair of Mathematics, Research in Mathematics by an Undergraduate Student University of Florida; Deanna Caveny, Department Chair will speak about their research: Reid W. Barton (winner), of Mathematics, College of Charleston; Peter March, De Massachusetts Institute of Technology, and Po-Shen Loh partment Chair of Mathematics, The Ohio State University; (honorable mention), California Institute of Technology and and Robert Olin, Dean of Arts and Sciences, University of Cambridge University. Alabama-Tuscaloosa. Past workshop sessions have fo SIGMAA on the Philosophy of Mathematics Invited cused on a range of issues facing departments today, in Speaker, Business Meeting, and Reception, Friday, 5:00 cluding personnel issues (staff and faculty), long range plan p.m. to 6:30 p.m., organized by Bonnie Gold, Monmouth ning, hiring, promotion and tenure, budget management, University, and Satish C. Bhatnagar, University of Nevada, assessments, outreach, stewardship, junior faculty devel Las Vegas. Jonathan Borwein, Dalhousie University, will opment, communication, and departmental leadership. speak on Philosophical Implications of Experimental Math There is a registration fee for the workshop of $75, which ematics. includes lunch and a post-workshop reception. This is SIGMAA on Quantitative Literacy Board Meeting and separate from the Joint Mathematics Meetings registration Reception, Friday, 5:15p.m. to 7:00p.m., organized by Judy fee. If you would like to attend the workshop, please com Moran, Trinity College, and Caren Diefenderfer, Hollins plete the RSVP form located at http: I /www. ams. org/ University. government/ChairsWorkshop2005 . RSVPForm.pdf and return it along with your check as outlined on the form. Other Organizations The RSVP form also includes space for your input in help Blumenthal Session, Friday, 9:00 a.m. to 9:45 a.m. The ing to identify important and timely topics that should be Leonard M. and Eleanor M. Blumenthal Award for the Ad addressed at this workshop. Agenda, materials, and loca vancement of Research in Pure Mathematics will be given tion information will be sent to all registered attendees at the Joint Prize Session on Thursday afternoon. The win prior to the meeting. ner of this award, Manjul Bhargava, Princeton University, MAA Program Updates will speak on his research at this Friday morning session. SIGMAA on Research in Undergraduate Mathematics Ed Social Events ucation Business Meeting and Guest Lecture, Thursday, University of Illinois at Urbana-Champaign Reception, 5:45p.m. to 7:45p.m., organized by Barbara E. Edwards, Thursday, 6:00 p.m. to 7:30 p.m. Oregon State University. Michigan Alumni Get-Together, Friday, 5:00p.m. to 7:00 MAA Student Research Programs, Friday, 9:00 to 10:30 p.m. This reception is sponsored by the University of a.m., organized by William Hawkins Jr., MAA and the Uni Michigan Department of Mathematics Alumni, who are in versity of the District of Columbia and Robert E. Meg vited for hors d'oevres and a cash bar. ginson, MSRI and the University of Michigan. The MAA sup The Ohio State University Friends and Alumni Re ported undergraduate minority student research at six sites in the summer of 2004 as part of its National Research ception, Friday, 6:00 p.m. to 8:00 p.m. Experiences for Undergraduates Program (NREUP). NREUP Association of Christians in the Mathematical Sci has funding from the NSF and NSA. Presenters will discuss ences (ACMS) Banquet, Friday, 6:30p.m. This annual din how their projects were organized and the work of their ner will feature a talk by Thomas Banchoff, Brown Uni students. There will be ample time for discussion and versity, on Dali: The Christian Dimension. Tickets are $3 5 questions. Panelists will include Nathaniel Dean, Texas ($25 for ACMS members and students) and may be pur Southern University, and David L. Housman, Goshen Col chased by sending a check payable to ACMS to Dr. Robert lege. The MAA expects to support another six sites in the Brabenec, Dept. of Mathematics, Wheaton College, Wheaton, summer of 2005. The session is sponsored by the MAA IL 60187. SUMMA (Strengthening Underrepresented Minority Math ematics Achievement) Program. The deadline for propos als is January 31, 2005. More information can be found at Bowling Green, http://www.maa.org/nreup. Session for Chairs: Using the CUPM Curriculum Guide Kentucky 2004 to Guide Curricula and Pedagogy in the 'Right' Di rection, Friday, 9:00 a.m. to 10:20 a.m., organized by Western Kentucky University Daniel P. Maki, Indiana University, and Catherine M. Mur phy, Purdue University Calumet. David M. Bressoud, March 18-19, 2005 Macalester University, and Amy Cohen, Rutgers Univer Friday - Saturday sity, will provide an overview of the Guide and accompa nying resources as well as sharing their experiences in lead Meeting #1 004 ing change. Presentations will be followed by a period for Southeastern Section questions and discussions. Associate secretary: John L. Bryant 1404 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Meetings & Conferences Announcement issue of Notices: January 2005 Partial Differential Equations and Their Applications (Code: Program first available on AMS website: February 3, 2005 SS 12A), Zhongwei Shen and Changyou Wang, University Program issue of electronic Notices: March 2005 of Kentucky. Issue of Abstracts: Volume 26, Issue 2 Representation Theory (Code: SS 6A), Markus Hunziker, University of Georgia. Deadlines For organizers: Expired Semigroups of Operators and Applications (Code: SS 7A), For consideration of contributed papers in Special Sessions: Khristo Boyadzhiev, Ohio Northern University, Lan November 30, 2004 Nguyen, Western Kentucky University, and Quoc-Phong For abstracts: January 25, 2005 Vu, Ohio University. Topology, Convergence, and Order, in Honor of Darrell The scientific information listed below may be dated. For Kent (Code: SS 8A), Gary Richardson, University of Cen the latest information, see www.ams.org/amsmtgs/ tral Florida, and Thomas A. Richmond, Western Kentucky sectional . html. University. Invited Addresses Bennett Chow, University of California, San Diego, Title to Newark, Delaware be announced. University of Delaware Robert McCann, University of Toronto, Title to be an nounced. April2-3, 2005 M. Susan Montgomery, University of Southern California, Saturday - Sunday Title to be announced. James J. Zhang, University of Washington, Title to be an Meeting #1 005 nounced. Eastern Section Associate secretary: Lesley M. Sibner Special Sessions Announcement issue of Notices: February 2005 Advances in the Study of Wavelets and Multiwavelets (Code: Program first available on AMS website: February 17, 2005 SS 5A), Douglas P. Hardin, Vanderbilt University, and Program issue of electronic Notices: April 2005 Bruce Kessler, Western Kentucky University. Issue of Abstracts: Volume 26, Issue 2 Commutative Ring Theory (Code: SS llA), Michael C. Ax Deadlines tell, Wabash College, and Joe Alyn Stickles Jr., University For organizers: Expired of Evansville. For consideration of contributed papers in Special Sessions: Dynamic Equations on Time Scales and Applications (Code: December 14, 2004 SS 3A), Ferhan M. Atici and Daniel C. Biles, Western Ken For abstracts: February 8, 2005 tucky University, and Billur Kaymakcalan, Georgia South ern University. The scientific information listed below may be dated. For Geometric Topology and Group Theory (Code: SS 14A), the latest information, see www.ams.org/amsmtgs/ Jens E. Harlander, Western Kentucky University. sectional . html. Graph Theory (Code: SS 2A), Mustafa Atici, Western Ken Invited Addresses tucky University. Hop{ Algebras and Related Topics (Code: SS lOA), David Xiu Xiong Chen, University of Wisconsin, Title to be an E. Radford, University of Illinois at Chicago, and Bettina nounced. Richmond, Western Kentucky University. Anna Gilbert, AT&T Labs-Research, Title to be announced. Knot Theory and Its Applications (Code: SS 4A), Yuanan Alex Lubotzky, Hebrew University of Jerusalem, Title to Diao, University of North Carolina Charlotte, and Claus be announced. Ernst, Western Kentucky University. Lorenz Schwachhoefer, University of Dortmund, Title to L-Functions (Code: SS 9A), Heather Russell, Nilabh Sanat, be announced. and Dominic Lanphier, Western Kentucky University. Special Sessions Nonlinear Analysis and Applied Mathematics (Code: SS 13A), Robert J. McCann, University of Toronto, and Daniel Arithmetic Groups and Related Topics (Code: SS 9A), Alex P. Spirn, University of Minnesota. Lubotzky, Hebrew University of Jerusalem, and Andrei Numerical Analysis, Approximation, and Computational Rapinchuk, University of Virginia. Complexity: Interdisciplinary Aspects (Code: SS lA), David Asymptotic Behavior of Evolution Equations (Code: SS 4A), Benko, Western Kentucky University, and Steven B. Gaston M. N'Guerekata, Morgan State University, and Damelin, Georgia Southern University. Nguyen Van Minh, James Madison University. DECEMBER 2004 NOTICES OF THE AMS 1405 Meetings & Conferences Designs, Codes, and Geometries (Code: SS 5A), James A. Program issue of electronic Notices: April 2005 Davis, University of Richmond, Keith E. Mellinger, Uni Issue of Abstracts: Volume 26, Issue 3 versity of Mary Washington, and Qing Xiang, University of Delaware. Deadlines Frontiers on Complex Fluid Flows: Analytic and Computa For organizers: Expired tional Methods (Code: SS 7A), L. Pamela Cook and Louis For consideration of contributed papers in Special Sessions: F. Rossi, University of Delaware. December 21, 2004 For abstracts: February 15, 2005 Geometric Analysis (Code: SS 12A), Xiuxiong Chen, Uni versity of Wisconsin, Madison, Pengfei Guan, McMaster Uni The scientific information listed below may be dated. For versity, Zhiqin Lu, University of California Irvine, and Jeff the latest information, see www . ams. o rg/ amsmtgs/ A. Viaclovsky, Massachusetts Institute of Technology. sectional . html. High Dimensional Probability (Code: SS 6A), Wenbo Li, University of Delaware, and Joel Zinn, Texas A&M Uni Invited Addresses versity. Nikolai Ivanov, Michigan State University, Title to be Homotopy Theory (in Honor of Donald M. Davis's and Mar announced. tin Bendersky's 60th Birthdays) (Code: SS lA), Kenneth G. Mattias Jonsson, University of Michigan, Title to be Monks, University of Scranton, and W. Stephen Wilson, announced. Johns Hopkins University. Nicolas Monod, University of Chicago, Title to be Integral and Operator Equations (Code: SS 13A), Charles announced. W. Groetsch, University of Cincinnati, and M. Zuhair Nashed, University of Central Florida. Hee Oh, California Institute of Technology, Title to be announced. Mathematical Biology (Code: SS 8A), David A. Edwards, Uni versity of Delaware. Special Sessions Mathematical Methods for Efficient Simulation of Stochas Classical and Differential Galois Theory (Code: SS 3A), tic Nonlinear Optical Systems (Code: SS 15A), Richard 0. Lourdes Juan and Arne Ledet, Texas Tech University, and Moore, New Jersey Institute of Technology, and Tobin A. Andy R. Magid, Umversity of Oklahoma. Driscoll, University of Delaware. Differential Geometry and Its Applications (Code: SS 2A), Mathematical Methods in Electromagnetic Wave Propaga Josef F. Dorfmeister, Munich University of Technology, tion (Code: SS 3A), Fioralba Cakoni and Peter B. Monk, Uni Magdalena D. Toda, Texas Tech University, and Hongyou versity of Delaware. Wu, Northern Illinois University. Recent Progress in Thin Fluid Flows (Code: SS llA), Richard Discrete Groups, Homogeneous Spaces, Rigidity (Code: SS ]. Braun, University of Delaware. 15A),.Alex Gorodnik, University of Michigan Ann Arbor, Singular Analysis and Spectral Theory of Partial Differen Hee Oh, California Institute of Technology, and Nicolas tial Equations (Code: SS 2A), Juan B. Gil, Pennsylvania State Monod, University of Chicago. University, Altoona, and Gerardo A. Mendoza, Temple Extinction, Periodicity, and Chaos in Population and Epidemic University. Models (Code: SS lOA), Linda J. S. Allen, Texas Tech Uni Spectral and High-Order Discretization Methods for Partial versity, Sophia Ruey-Jen Jang, University of Louisiana at Differential Equations (Code: SS 14A), Tobin A. Driscoll, Lafayette, and Lih-lng W. Roeger, Texas Tech University. University of Delaware. Future Directions in Mathematical Systems and Control Symmetry Methods for Partial Differential Equations (Code: Theory (Code: SS llA), David Gilliam and W. P. Dayawansa, SS lOA), Philip Broadbridge, University of Delaware, and Texas Tech University. Danny Arrigo, University of Central Arkansas. Graph Theory(Code: SS 12A), John C. George, Eastern New Mexico University, and Walter D. Wallis, Southern Illinois University at Carbondale. Lubbock, Texas Homological Algebra and Its Applications (Code: SS 4A), Texas Tech University Alex Martsinkovsky, Northeastern University, and Mara D. Neusel, Texas Tech University. April8-1 0, 2005 Invariants ofLinks and 3-Manifolds (Code: SS 8A), Mieczys Friday - Sunday law Krzysztof Dabkowski, University of Texas at Dallas, Razvan Gelca, Texas Tech University, and Jozef Henryk Meeting #1 006 Przytycki, George Washington University. Central Section Partial Differential Equations and Its Application in Bio Associate secretary: Susan]. Friedlander medical Study (Code: SS 16A), Jay R. Walton, Texas A&M Announcement issue of Notices: February 2005 University, Padmanabhan Seshaiyer and Akif Ibragimov, Program first available on AMS website: February 24, 2005 Texas Tech University. 1406 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Meetings & Conferences Real Algebraic Geometry (Code: SS 6A), Anatoly Korcha Special Sessions gin and David Weinberg, Texas Tech University. Algebraic Geometry and Combinatorics (Code: SS 14A), Recent Advances in Complex Function Theory (Code: SS SA), Alexander Yong and Allen Knutson, University of Cali Brock Williams, Roger W. Barnard, and Kent Pearce, Texas fornia Berkeley. Tech University. Arithmetic Geometry (Code: SS 13A), Adebisi Agboola, Statistical Image Processing and Analysis and Applications University of California Santa Barbara, and Cristian Du (Code: SS 13A), Victor Patrangenaru, Texas Tech Univer rnitru Popescu, University of California San Diego. sity. Automorphisms of Surfaces (Code: SS 4A), Anthony Theory and Application of Stochastic Differential Equa Weaver, Bronx Community College of the City University tions (Code: SS 9A), Edward J, Allen, Texas Tech Univer of New York, and Peter Turbek, Purdue University Calumet. sity, and Armando Arciniega, University of Texas at San Antonio. Complexity of Computation and Algorithms (Code: SS 1 OA), Mark Burgin, University of California Los Angeles. Topology of Continua (Code: SS lA), Wayne Lewis, Texas Tech University. Curvature in Group Theory and Combinatorics (Code: SS llA), Laura M. Anderson, State University of New York at (Code: SS 7A), Brian Raines, Topology ofDynamical Systems Binghamton, Noel Patrick Brady, University of Oklahoma, Baylor University. Robin Forman, Rice University, and Jonathan P. McCam Undergraduate and Graduate Student Research (Code: SS mond, University of California Santa Barbara. Swim, Edward J. Allen, 14A), Ali Khoujmane, Edward W. Dynamical Systems in Neuroscience (Code: SS lA), Eugene and Padmanabhan Seshaiyer, Texas Tech University. M. Izhikevich, The Neurosciences Institute. Function Theory (Code: SS 12A), Mihai Putinar and Stephan Santa Barbara, R. Garcia, University of California Santa Barbara. Geometric Methods in Three Dimensions (Code: SS 6A), Daryl Cooper, David Darren Long, and Martin G. Scharle California mann, University of California Santa Barbara. University of California Santa Barbara Geometry and Physics (Code: SS 8A), Xianzhe Dai, University of California Santa Barbara, and Zhiqin Lu, University of April16-17, 2005 California Irvine. Saturday - Sunday History of Mathematics (Code: SS 2A), Shawnee L. Mc Meeting #1 007 Murran, California State University San Bernardino, and James J. Tattersall, Providence College. Western Section Associate secretary: Michel L. Lapidus Noncommutative Geometry and Algebra (Code: SS SA), Announcement issue of Notices: February 200S Kenneth R. Goodearl, University of California Santa Bar Program first available on AMS website: March 3, 200S bara, J. T. Stafford, University of Michigan, and J. ]. Zhang, Program issue of electronic Notices: April 200S University of Washington. Issue of Abstracts: Volume 26, Issue 3 Recent Advances in Combinatorial Number Theory (Code: SS 3A), Mei-Chu Chang, University of California Riverside, Deadlines and Van Ha Vu, University of California San Diego. For organizers: Expired Representation Theory ofA lgebras (Code: SS 7A), Ed Green, For consideration of contributed papers in Special Sessions: Virginia Polytechnic Institute and State University, Alex December 28, 2004 Martsinkovsky, Northeastern University, Dan Zacharia, 22, 200S For abstracts: February Syracuse University, and Birge K. Huisgen-Zimmermann, Ui:uversity of California Santa Barbara. The scientific information listed below may be dated. For the latest information, see www. ams. o rg/amsmtgs/ Ricci Flow/Riemannian Geometry (Code: SS 9A), Guofang sectional . html. Wei and Rugang Ye, University of California Santa Barbara. Invited Addresses Mei-Chu Chang, University of California Riverside, Title to Mainz, Germany be announced. June 16-19,2005 Mischa Kapovich, University of California Davis, Title to Thursday - Sunday be announced. Mihai Putinar, University of California Santa Barbara, Pos Meeting #1 008 itive Polynomials. ]oint International Meeting with the Deutsche Mathematiker James Sethian, University of California Berkeley, Title to Vereinigung (DMV) and the Oesterreichische Mathematis be announced. che Gesellschaft (OMG) DECEMBER 2004 NOTICES OF THE AMS 1407 Meetings & Conferences Associate secretary: Susan J. Friedlander Functional Analytic and Complex Analytic Methods in Lin Announcement issue of Notices: February 2005 ear Partial Differential Equations, R. Meise, University of Program first available on AMS website: To be announced Dusseldorf, B. A. Taylor, University of Michigan, and Di Program issue of electronic Notices: To be announced etmar Vogt, University of Wuppertal. Issue of Abstracts: To be announced Geometric Analysis, Victor Nistor, Pennsylvania State Uni versity, and Elamr Schrohe, Universitat Hannover. Deadlines Geometric Topology and Group Theory, Cameron MeA. For organizers: To be announced Gordon, The University of Texas at Austin, Cynthia Hog For consideration of contributed papers in Special Sessions: Angeloni, Johann Wolfgang Goethe-Universitat, and Wolf To be announced For abstracts: To be announced gang Metzler, University of Frankfurt. Group Theory, Luise-Charlotte Kappe, Universitat Freiburg, The scientific information listed below may be dated. For Robert Fitzgerald Morse, University of Evansville, and the latest information, see www. ams. org/amsmtgs/ Gerhard Rosenberger, University of Dortmund. sectional . html. Hilbert Functions and Syzygies, Uwe Nagel, University of Kentucky, Irena Peeva, Cornell University, and Tim Romer, Invited Addresses Universitat Osnabruck. Helene Esnault, University of Essen, Title to be announced. History ofMathematics: Mathematics and War, Thomas W. Richard Hamilton, Columbia University, Title to be an Archibald, Acadia University, John H. McCleary, Vassar nounced. College, Moritz Epple, University of Stuttgart, and Norbert Michael J. Hopkins, Massachusetts Institute of Technol Schappacher, Technische Universitat Darmstadt. ogy, Title to be announced. Homotopy Theory, Paul G. Goerss, Northwestern Univer Christian Krattenthaler, University of Lyon-I, Title to be sity, Hans-Werner Henn, Institut de Recherche Mathema announced. tique Avancee, Strasbourg, and Stefan Schwede, Univer sitat Bonn. Frank Natterer, University of Muenster, Title to be an nounced. Hopf Algebras and Quantum Groups, Susan Montgomery, University of Southern California, and Hans-Jurgen Schnei Horng-Tzer Yau, New York University and Stanford Uni der, University of Munich. versity, Title to be announced. Mathematics Education, Gunter Torner, UniversitatDuis Special Sessions burg-Essen, and Alan Schoenfeld, School of Education, Berkeley. Affine Algebraic Geometry, Shreeram Abhyankar, Pur due University, Hubert Flenner, Fakultiit fur Mathematik, Modules and Comodules, Sergio L6pez-Permouth, Ohio and Makar Limanov, Wayne State University. University, and Robert Wisbauer, University of Dusseldorf. Algebraic Combinatorics, Patricia Hersh, University of Multiplicative Arithmetic ofIntegral Domains and Monoids, Michigan, Christian Krattenthaler, University of Lyon-I, and Scott Chapman, Trinity University, San Antonio, Franz Volkmar Welker, Philipps University Marburg. Halter-Koch, University of Graz, and Ulrich Krause, Uni versitat Bremen. Algebraic Cryptography, Dorian Goldfeld, Columbia Uni versity, Martin Kreuzer and Gerhard Rosenberger, Uni Nonlinear Elliptic Boundary Value Problems, Thomas versiti:lt Dortmund, and Vladimir Shpilrain, City College Bartsch, Universitaet Giessen, and Zhi-Qiang Wang, Utah of New York. State University. Algebraic Cycles, Eric Friedlander and Marc Levine, North Nonlinear Waves, Herbert Koch, University of Dortmund, western University, and Fabien Morel, Universite Paris. and Daniel I. Tataru, University of California Berkeley. Algebraic Geometry, Yuri Tschinkel, Georg-August-Uni Ordinary Differential, Difference, and Dynamic Equations, versitat Gottingen, and Brendan E. Hassett, Rice Univer Werner Balser, Universitat Ulm, Martin Bohner, University sity. of Missouri-Rolla, and Donald Lutz, San Diego State Uni versity. Dirac Operators, Clifford Analysis and Applications, Klaus Giirlebeck, University of Weimar, Mircea Martin, Baker Uni Quantum Knot Invariants, Anna Beliakova, Universitat versity, John Ryan, University of Arkansas, and Michael Zurich, and Uwe Kaiser, Boise State University. Shapiro, IPN Mexico. Representations and Cohomology of Groups and Algebras, Discrete Geometry, jacob Eli Goodman, The City College Dave Benson, University of Georgia, and Henning Krause, of New York (CUNY), Emo Welzl, Eidgen Technische Universitat Paderborn. Hochschule, and Gunter M. Ziegler, Technical University Set Theory, joel Hamkins, City University New York, Peter of Berlin. Koepke, Universitiit Bonn, and Benedikt Lowe, Univer Function Spaces and Their Operators, Ernst Albrecht, Uni siteit van Amsterdam. versitat des Saarlandes, Raymond Mortini, Universite de Spectral Analysis of Differential and Difference Operators, Metz, and William Ross, University of Richmond. Evgeni Korotyaev, Humboldt-University Berlin, Boris 1408 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Meetings & Conferences Mityagin, The Ohio State University, and Gerald Teschl, Special Sessions University of Vienna. Geometric Group Theory (Code: SS 1A), Sean Cleary, The Stochastic Analysis on Metric Spaces, Laurent Saloff-Coste, City College of New York, and Melanie I. Stein, Trinity Cornell University, Karl-Theodor Sturm, University of College. Bonn, and Wolfgang Woess, Graz Technical University. The History of Mathematics (Code: SS 2A), Patricia R. Topics in Applied Mathematics and Mechanics: Mathemat Allaire, Queensborough Community College, CUNY, ical Control Theory and Numerical Methods, Peter Benner, Robert E. Bradley, Adelphi University, and Jeff Suzuki, Bard Fakultat fur Mathematik. College. Topics in Applied Mathematics and Mechanics: Mechanics, Friedrich Pfeiffer, Technical University of Munich. Topics in Applied Mathematics and Mechanics: Multiscale Johnson City, Problems, Oscillations in PDEs, and Homogenization, Alexan~ der Mielke, University of Hannover. Tennessee Topics in Applied Mathematics and Mechanics: Numerical East Tennessee State University PDEs, Equations with Inherent Conditions, Rolf Jeltsch, Ei dgen Technische Hochschule, Maria Lukacova, Technical October 1 5-16, 2005 University of Brno, and Mac Hyman, Los Alamos National Saturday - Sunday Laboratory. Topics in Applied Mechanics: Algebraic Approaches to Pre Meeting #1 010 conditioning, Heike Fassbender, Technical University of Southeastern Section Braunschweig, and Andreas Frommer, University of Wup Associate secretary: John L. Bryant pertal. Announcement issue of Notices: August 2005 Topology of Manifolds, Matthias Kreck, University of Hei Program first available on AMS website: September 1, 2005 delberg, and Andrew Ranicki, University of Edinburgh. Program issue of electronic Notices: October 2005 Issue of Abstracts: Volume 26, Issue 4 Deadlines Annandale-on For organizers: March 15, 2005 For consideration of contributed papers in Special Sessions: Hudson, New York june 28, 2005 Bard College For abstracts: August 23 , 2005 October 8-9, 2005 Saturday - Sunday Lincoln, Nebraska Meeting #1 009 University of Nebraska in Lincoln Eastern Section October 21-23,2005 Associate secretary: Lesley M. Sibner Friday - Sunday Announcement issue of Notices: August 2005 Program first available on AMS website: August 25, 2005 Meeting #1 011 Program issue of electronic Notices: October 2005 Central Section Issue of Abstracts: Volume 26, Issue 4 Associate secretary: Susan J. Friedlander Announcement issue of Notices: August 2005 Deadlines Program first available on AMS website: September 8, 2005 For organizers: March 8, 2005 Program issue of electronic Notices: October 2005 For consideration of contributed papers in Special Sessions: Issue of Abstracts: Volume 26, Issue 4 June 21, 2005 For abstracts: August 16, 2005 Deadlines For organizers: March 22, 2005 The scientific information listed below may be dated. For For consideration of contributed papers in Special Sessions: the latest information, see www. ams. o rg/amsmtgs/ July 5, 2005 sect ional.html. For abstracts: August 30, 2005 Invited Addresses The scientific information listed below may be dated. For Persi Diaconis, Stanford University, Title to be announced the latest information, see www. ams. org/ amsmtgs/ (Erdos Memorial Lecture). sectional.html . DECEMBER 2004 NOTICES OF THE AMS 1409 Meetings & Conferences Invited Addresses Howard Masur, University of Illinois at Chicago, Title to Taiwan be announced. December 14-1 8, 2005 Alejandro Uribe, University of Michigan, Title to be Wednesday - Sunday announced. Judy Walker, University of Nebraska, Title to be announced. Meeting #1 013 First joint International Meeting between the AMS and the Xin, University of Texas, Title to be announced. Jack Taiwanese Mathematical Society. Special Sessions Associate secretary: John L. Bryant Announcement issue of Notices: May 2005 Algebraic Geometry (Code: SS lA), Brian Harbourne, Uni Program first available on AMS website: To be announced versity of Nebraska-Lincoln, and Bangere P. Purnaprajna, Program issue of electronic Notices: To be announced University of Kansas. Issue of Abstracts: To be announced Deadlines Eugene, Oregon For organizers: To be announced For consideration of contributed papers in Special Sessions: University of Oregon To be announced For abstracts: To be announced November 12-13,2005 Saturday - Sunday Meeting #1 012 San Antonio, Texas Western Section Henry B. Gonzalez Convention Center Associate secretary: Michel L. Lapidus Announcement issue of Notices: September 2005 January 12-1 5, 2006 Program first available on AMS website: September 29, Thursday - Sunday 2005 joint Mathematics Meetings, including the 112th Annual Program issue of electronic Notices: November 2005 Meeting of the AMS, 89th Annual Meeting of the Mathe Issue of Abstracts: Volume 26, Issue 4 matical Association ofAmer ica, annual meetings of the As sociation for Women in Mathematics (A WM) and the National Deadlines Association of Mathematicians (NAM), the winter meeting For organizers: Aprill2, 2005 of the Association for Symbolic Logic (ASL), with sessions For consideration of contributed papers in Special Sessions: contributed by the Society for Industrial and Applied Math July 26, 2005 ematics (SIAM). For abstracts: September 20, 2005 Associate secretary: John L. Bryant Announcement issue of Notices: October 2005 The scientific information listed below may be dated. For Program first available on AMS website: To be announced the latest information, see www. ams. org/amsmtgs/ Program issue of electronic Notices: January 2006 sectional . html. Issue of Abstracts: To be announced Invited Addresses Deadlines For organizers: Aprill2, 2005 Mattthew Foreman, University of California Irvine, Title For consideration of contributed papers in Special Sessions: to be announced. To be announced Mark Haiman, University of California Berkeley, Title to be For abstracts: To be announced announced. For summaries of papers to MAA organizers: To be an Wilhelm Schlag, California Institute of Technology, Title nounced to be announced. Hart H. Smith, University of Washington, Title to be announced. 1410 NOTICES OF THE AMS VOLUME 51, N UMBER 11 Meetings & Conferences Durham, New Fayetteville, Hampshire Arkansas University of New Hampshire University of Arkansas April22-23, 2006 November 3-4, 2006 Saturday - Sunday Friday - Saturday Eastern Section Southeastern Section Associate secretary: Lesley M. Sibner Associate secretary: John L. Bryant Announcement issue of Notices: To be announced Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Issue of Abstracts: To be announced Deadlines Deadlines For organizers: September 22, 2005 For organizers: April 3, 2006 papers in Special Sessions: For consideration of contributed For consideration of contributed papers in Special Sessions: To be announced To be announced For abstracts: To be announced For abstracts: To be announced San Francisco, New Orleans, California Louisiana San Francisco State University New Orleans Marriott and Sheraton April29-30, 2006 New Orleans Hotel Saturday - Sunday Western Section january 4-7,2007 Associate secretary: Michel L. Lapidus Thursday - Sunday Announcement issue of Notices: To be announced ]oint Mathematics Meetings, including the 113th Annual Program first available on AMS website: To be announced Meeting of the AMS, 90th Annual Meeting of the Mathe Program issue of electronic Notices: To be announced matical Association ofAmerica (MAA), annual meetings of Issue of Abstracts: To be announced the Association for Women in Mathematics (A TtVM) and the National Association of Mathematicians (NAM), and the Deadlines winter meeting of the Association for Symbolic Logic (ASL), For organizers: To be announced with sessions contributed by the Society for Industrial and For consideration of contributed papers in Special Sessions: Applied Mathematics (SIAM). To be announced Associate secretary: Susan]. Friedlander For abstracts: To be announced Announcement issue of Notices: October 2006 Program first available on AMS website: To be announced The scientific information listed below may be dated. For Program issue of electronic Notices: January 2007 ormation, see www. ams. org/amsmtgs/ the latest inf Issue of Abstracts: To be announced section a 1 . html. Deadlines Special Sessions For organizers: April 4, 2006 History of Mathematics (Code: SS lA), Shawnee L. Mc For consideration of contributed papers in Special Sessions: Murran, California State University San Bernardino, and To be announced James J. Tattersall, Providence College. For abstracts: To be announced For summaries of papers to MAA organizers: To be an nounced D ECEMBER 2004 NOTICES OF THE AMS 1411 Meetings & Conferences San Diego, California San Francisco, San Diego Convention Center California January 6-9, 2008 Moscone Center West and the San Fran Sunday - Wednesday cisco Marriott joint Mathematics Meetings, including the 114th Annual Meeting of the AMS, 91st Annual Meeting of the Mathe January 6-9, 201 0 matical Association ofAmerica (MAA), annual meetings of Wednesday - Saturday the Association for Women in Mathematics (AWM) and the joint Mathematics Meetings, including the 116th Annual National Association of Mathematicians (NAM), and the Meeting of the AMS, 93rd Annual Meeting of the Mathe winter meeting of the Association for Symbolic Logic (ASL). matical Association ofAmerica (MAA), annual meetings of Associate secretary: Michel L. Lapidus the Association for Women in Mathematics (A WM) and the Announcement issue of Notices: October 2007 National Association of Mathematicians (NAM), and the Program first available on AMS website: November 1, 2007 winter meeting of the Association for Symbolic Logic (ASL). Program issue of electronic Notices: January 2008 Associate secretary: John L. Bryant Issue of Abstracts: Volume 29, Issue 1 Announcement issue of Notices: October 2009 Program first available on AMS website: November 1, 2009 Deadlines Program issue of electronic Notices: january 2010 For organizers: April 6, 2007 Issue of Abstracts: Volume 31, Issue 1 For consideration of contributed papers in Special Sessions: Deadlines To be announced For organizers: April 5, 2009 For abstracts: To be announced For consideration of contributed papers in Special Sessions: For summaries of papers to MAA organizers: To be an To be announced nounced For abstracts: To be announced For summaries of papers to MAA organizers: To be an nounced Washington, District New Orleans, of Columbia Marriott Wardman Park Hotel and Omni Louisiana Shoreham Hotel New Orleans Marriott and Sheraton New Orleans Hotel January 7-10,2009 Wednesday - Saturday January 5-8,2011 joint Mathematics Meetings, including the 115th Annual Wednesday - Saturday Meeting of the AMS, 92nd Annual Meeting of the Mathe joint Mathematics Meetings, including the 117th Annual matical Association ofAmerica (MAA), annual meetings of Meeting of the AMS, 94th Annual Meeting of the Mathe the Association for Women in Mathematics (A WM) and the matical Association ofAmerica, annual meetings of the As National Association of Mathematicians (NAM), and the sociation for Women in Mathematics (A WM) and the National winter meeting of the Association for Symbolic Logic (ASL). Association ofMathematicians (NAM), and the winter meet Associate secretary: Lesley M. Sibner ing of the Association for Symbolic Logic (ASL). Associate secretary: Susan]. Friedlander Announcement issue of Notices: October 2008 Announcement issue of Notices: October 2010 Program first available on AMS website: November 1, 2008 Program first available onAMS website: November 1, 2010 Program issue of electronic Notices: January 2009 Program issue of electronic Notices: January 2011 Issue of Abstracts: Volume 30, Issue 1 Issue of Abstracts: Volume 32, Issue 1 Deadlines Deadlines For organizers: April 7, 2008 For organizers: April 2, 2010 For consideration of contributed papers in Special Sessions: For consideration of contributed papers in Special Sessions: To be announced To be announced For abstracts: To be announced For abstracts: To be announced For summaries of papers to MAA organizers: To be an For summaries of papers to MAA organizers: To be an nounced nounced 1412 NOTICES OF THE AMS VOLUME 51, NUMBER 11 The 2004 Notices Index Index Section Page Number Index Section Page Number TheAMS 1413 Memorial Articles 1424 Announcements 1414 New Publications Offered by the AMS 1425 Authors of Articles 1416 Officers and Committee Members 1425 Deaths of Members of the Society 1417 Opinion 1425 Education 1418 Opportunities 1425 Feature Articles 1418 Prizes and Awards 1426 Letters to the Editor 1419 The Profession 1428 Mathematicians 1420 Reference and Book List 1428 Mathematics Articles 1423 Reviews 1428 Mathematics History 1424 Surveys 1428 Meetings Information 1424 Tables of Contents 1428 About the Cover AMS-AAAS Mass Media Summer Fellowships, 1075 8,20~ 319,411,495,619,815,883,1023,1194,1347 AMS-AAAS Media Fellow Named, 808 AMS Associate Executive Editor Positions-Applications Invited, 602 '·,·. AMS Book Prize, 450, 568 ...,....,. ·;-::·:. AMS Committee on Meetings and Conferences, 1249 -r + : -+- . t 1,:< AMS Committee on Science Policy, 1246 ~ AMS Email Support for Frequently Asked Questions, 1365 ,. AMS Menger Awards at the 2004 ISEF, 1235 AMS Menger Prizes at the 2004 ISEF, 913 TheAMS AMS Mentoring Workshop, 1304 2000 Mathematics Subject Classification, 60, 275, 454, AMS Officers and Committee Members, 1082 572,992,1290 AMS Participates in Capitol Hill Exhibition, 1076 2003 AMS Election Results, 269 AMS Participates in Celebration of von Neumann's Birth, 2003 AMS Policy Committee Reports, 264 52 2003 Annual Survey of the Mathematical Sciences (First AMS Scholarships for "Math in Moscow", 805 Report), 218 AMS Short Course, 1161 2003 Annual Survey of the Mathematical Sciences (Second AMS Standard Cover Sheet, 58, 273, 452, 570, 990, 1288 Report), 789 Applications Invited for AMS Associate Executive Director, 2003 Annual Survey of the Mathematical Sciences (Third 525 Report), 901 Atlanta Meeting Registration Forms, 1175, 1309, 1431 2004 AMS Election (Nominations by Petition), 271 Biographies of Candidates 2004, 944 2004 AMS Elections-Special Section, 941 Call for Applications: AMS Epsilon Fund, 1074 2004 Frank and Brennie Morgan AMS-MAA-SlAM Prize for Call for Nonlinations for 2004 Frank and Brennie Morgan Outstanding Research in Mathematics by an Under AMS-MAA-SlAM Prize, 451, 569 graduate Student, 451, 569 Call for Nominations for 2005 AMS Book Prize, 450, 568 2004 Notices Index, 1413 Call for Nominations for 2005 B6cherMemorialPrize, LeviL. 2004 Spring Policy Committee Reports, 1246 Conant Prize, Frank Nelson Cole Prize in Number Theory, 2004-2005 AMS Centennial Fellowships Awarded, 660 Ruth Lyttle Satter Prize, Albert Leon Whiteman Memorial 2005 Summer Research Institute-Algebraic Geometry, Prize, 449, 567 1293 Call for Nominations for Leroy P. Steele Prizes, 276, 353 Acknowledgment of Contributions, 5 58 Call for Proposals for the 2006 Joint Summer Research Con American Mathematical Society Centennial Fellowships, 915 ferences, 1115 American Mathematical Society Centennial Fellowships Call for Suggestions for 2004 AMS Election, 270 (Invitation for Applications), 1237 Correction: von Neumann Awards, 444 DECEMBER 2004 NOTICES OF THE AMS 1413 20041ndex Corrections to the 2003 Annual Survey of the Mathemat- Allgower Wins Leibniz Prize, 803 ical Sciences (First Report), 444 Ambrosio Wins Fermat Prize, 234 Deaths of AMS Members, 52, 348, 444, 669, 919, 1366 American Academy of Arts and Sciences Elections, 804 Epsilon Awards for 2004, 553 American Mathematical Society Centennial Fellowships, 915 Ethical Guidelines for the Society, 675 American Mathematical Society Centennial Fellowships Experimental "Current Events" Session at Joint Meetings, (Invitation for Applications), 1237 51 AMS-AAAS Mass Media Summer Fellowships, 1075 Fan and Caldwell Scholarships Awarded, 51, 1241 AMS-AAAS Media Fellow Named, 808 Fan China Exchange Program Names Awardees, 808 AMS Book Prize, 450, 568 General Information Regarding Meetings & Conferences, AMS Menger Awards at the 2004 ISEF, 1235 84 AMS Menger Prizes at the 2004 ISEF, 913 Hawkins Presents Testimony, 668 AMS Mentoring Workshop, 1364 Jane E. Kister Retires from MR, 918 AMS Participates in Capitol Hill Exhibition, 1076 Joint Summer Research Conferences 2005, 1294 AMS Participates in Celebration of von Neumann's Birth, Kevin Clancey Named MR Executive Editor, 807 52 Math in Moscow Scholarships Awarded, 348, 918 AMS Scholarships for "Math in Moscow", 805 Mathematical Sciences Employment Center, 993, 1117 AP Calculus Readers Sought, 441 Mathematical Sciences Employment Center Forms, 998, Asatryan Awarded Emil Artin Junior Prize, 549 1122 Atiyah and Singer Receive 2004 Abel Prize, 649 Meetings and Conferences of the AMS, 85, 289, 373, 479, AWM Awards Presented in Phoenix, 546 591,715,849,1003,1127,1298,1403 AWM Essay Contest, 1075 Membership Forms, 371, 475, 589 AWM Essay Contest Winners Announced, 440, 1360 New Award for Mathematics Departments, 553 AWM Travel Grants for Women, 916 New Publications Offered by the AMS, 65, 280, 363, 462, B. H. Neumann Awards Given, 1235 577,695,836,977,1098,1267,1403 Banchoff Receives NSF Distinguished Teaching Scholar Officers of the Society 2003 and 2004 Updates, 566 Award, 913 (A) Photographic Look at the Joint Meetings, Phoenix, 2004, Biran Awarded Oberwolfach Prize, 660 400 Bjorken and Callan Awarded 2004 Dirac Medals, 1359 Reciprocity Agreements, 1252 Brousseau and Hoyles Receive ICMI Medals, 662 Report of the Executive Director, State of AMS, 2004, 818 Call for Applications: AMS Epsilon Fund, 1074 Report of the Treasurer, 2003, 824 · Call for Nominations for 2005 AMS Book Prize, 400, 568 Report on the April 2004 Council Meeting, 956 Call for Nominations for the 2005 Fermat Prize, 1075 Report on the January 2004 Council Meeting, 565 Call for Nominations for Albert Leon Whiteman Memorial Retirement of Bernard R. McDonald, 668 Prize, 449, 567 Robert G. Bartle (1927-2003), 239 Call for Nominations for AWM Hay and Schafer Awards, Statistics on Women Mathematicians Compiled by the 667 AMS, 1372 Call for Nominations for B6cher Memorial Prize, 449, 567 (A) Summer at Voice of America, 443 Call for Nominations for Clay Research Fellows, 1074 Updated AMSRefs Package Available, 1076 Call for Nominations for CRM-Fields Prize, 441 William Ted Martin (1911-2004), 919 Call for Nominations for Frank and Brennie Morgan AMS MAA-SIAM Prize, 451, 569 Announcements Call for Nominations for Frank Nelson Cole Prize in 2003 Morgan Prize, 438 Number Theory, 449, 567 2004 Award for Distinguished Public Service, 435 Call for Nominations for Information-Based Complexity 2004 Clay Research Fellows Announced, 549 Prize and Young Researcher Award, 237 2004 Conant Prize, 433 Call for Nominations for Leroy P. Steele Prizes, 276, 353 2004 d'Alembert Prize Awarded, 1072 Call for Nominations for Levi L. Conant Prize, 449, 567 Call for Nominations for Frank and Brennie Morgan AMS- Call for Nominations for Ruth Lyttle Satter Prize, 449, 567 MAA-SIAM Prize, 451, 569 Call for Nominations for Sloan Fellowships, 666 2004 Moore Prize, 431 Call for Nominations for Third World Academy of 2004 NSF-CBMS Regional Conferences, 5 51 Sciences Prizes, 1238 2004 Steele Prizes, 421 Call for Nominations for Waterman Award, 1362 2004 Veblen Prize, 426 Call for Proposals for 2005 NSF-CBMS Regional Confer 2004 Wiener Prize, 428 ences, 236 2004-2005 AMS Centennial Fellowships Awarded, 660 Call for Proposals for the 2006 Joint Summer Research AAAS Fellows Elected, 234 Conferences, 1115 AAUW Educational Foundation Fellowships and Grants, Call for Submissions for Sunyer i Balaguer Prize, 806 1238 Chern Receives Shaw Prize, 1067 AlM Five-Year Fellow Announced, 548 Clay Mathematics Institute Liftoff Program, 237 1414 NOTICES OF THE AMS VoLUME 51, NuMBER 11 20041ndex Clay Senior Scholars Program, 666 National Academy of Engineering Elections, 665 CMI Liftoff Program for Summer 2005, 1362 National Academy of Sciences Elections, 664 Collaborations in Mathematical Geosciences, 49 National High School Calculus Student Award, 1356 Cryptology Paper Competitions, 237 NDSEG Fellowships, 1360, 1361 Dawson Awarded CRM-Fields Prize, 440 Nemirovski and Todd Awarded von Neumann Prize, 344 Deadlines and Target Dates at the DMS, 48 New Award for Mathematics Departments, 553 Deligne Receives 2004 Balzan Prize, 13 57 New NSF Funding Opportunities, 441 Demaine Receives MacArthur Fellowship, 44 New NSF Program: Enhancing the Mathematical Sciences Departments Coordinate Job Offer Deadlines, 50 Workforce in the Twenty-First Century, 550 DMS Employment Opportunities, 238 News from AIM, 49 Duquesne Receives Meyer Prize, 548 News from BIRS, 667, 917 EDGE Summer Program, 1361 News from the Clay Mathematics Institute, 441 Engle and Granger Receive Nobel Prize in Economic News from The Fields Institute, 1362 Sciences, 43 News from the IMA, 346, 667, 1363 Enhancing the Mathematical Sciences Workforce in the News from the International Centre for Mathematical Sci- 21st Century, 805, 1074 ences, 442 Epsilon Awards for 2004, 553 News from the MBI, 49 European Mathematical Society Article Competition 2003, News from the Mittag-Leffler Institute, 1362 345 News from PIMS, 551, 917 Experimental "Current Events" Session at Joint Meetings, News from the SAMSI, 49 51 Newton Fellowship Program, 1364 Fan and Caldwell Scholarships Awarded, 51, 1241 NSA Funding Opportunity in Quantum Computing Algo- Fan China Exchange Program Names Awardees, 808 rithms, 1239 Ferran Sunyer i Balaguer Prize Awarded, 802 NSA Grant and Sabbatical Programs, 915, 1239 Friedman Wins 2004 Parzen Prize, 661 NSF CAREER Awards for 2002 and 2003, 46 Fulbright Awards Announced, 664 NSF CAREER Program Guidelines Available, 666 George Ellis Wins 2004 Templeton Prize, 1072 NSF-CBMS Regional Conferences, Summer 2004, 236 Glimm and Witten Receive National Medal of Science, 215 NSF Distinguished International Postdoctoral Research Gromov Receives Nemmers Prize, 787 Fellowships, 916 Guggenheim Fellowships Awarded, 664 NSF Focused Research Groups, 805 Hamilton and Tao Receive Clay Awards, 234 NSF Graduate Fellowships, 916 Holroyd and Benjamini Awarded Rollo Davidson Prize, NSF Graduate Research Fellowships Announced, 663 661 NSF Integrative Graduate Education and Research Train Humboldt Foundation Offers Fellowships, 1074 ing, 550 lAS/Park City Mathematics Institute, 235 NSF International Research Fellow Awards, 916, 1239 ICM 2006 Travel Grants, 1237 NSF Mathematical Sciences Postdoctoral Research Fellow- Intel Science Talent Search Winners Announced, 664 ships, 805 Interdisciplinary Grants in the Mathematical Sciences, 235 NSF Postdoctoral Research Fellowships, 5 50 International Mathematical Olympiad, Athens 2004, 1073 ONR Young Investigator Program, 48 Jane E. Kister Retires from MR, 918 Paul Erdos Award Recipients Announced, 1072 Joint Initiative in Mathematical Biology, 666 Paulos Receives AAAS Award, 548 Joyce Wins Adams Prize, 802 PECASE Awards Announced, 802, 1359 Kevin Clancey Named MR Executive Editor, 807 Pi Mu Epsilon Student Paper Presentation Awards, 1360 Keyfitz Named Director of Fields Institute, 898 Prizes and Elections of the French Academy of Sciences, Kohn Receives 2004 Bergman Prize, 343 344 Kuo Wins Information-Based Complexity Young Researcher Prizes of the Academie des Sciences, 1359 Award, 46 Prizes of the Mathematical Society of Japan, 45, 803 Lindenstrauss and Soundararajan Awarded 2003 Salem Prizes Presented at the European Congress of Mathemati- Prize, 45 cians, 1070 LMS Prizes Awarded, 1072 Project NExT: New Experiences in Teaching, 346 MAA Awards Presented in Phoenix, 544 Putnam Prizes Awarded, 803 MAA Writing Awards Presented, 1234 Research Experiences for Undergraduates, 917 Maria Mitchell Women in Science Award, 551 Research Opportunities for U.S. Graduate Students in Asia, Math in Moscow Scholarships Awarded, 348, 918 1238 Mathe Receives 2004 Prize for Achievement in Information- Rhodes Scholarships Awarded, 344 Based Complexity, 803 Royal Society of Canada Elections, 1073 Mathematical Social and Behavioral Sciences, 442 Royal Society of London Elections, 914 Mathematics Awareness Month: April 2004, 346 Serguei Denissov Awarded Popov Prize, 1071 National Academies Internship Program, 235 Seymour Receives Ostrowski Prize, 900 DECEMBER 2004 NOTICES OF THE AMS 1415 20041ndex SIAM Prizes Awarded, 1234 Harris, Michael, 632 Sloan Fellows Announced, 663 Hirzebruch, Friedrich, 498 Summer Program for Women Undergraduates, 236 Hobbs, Arthur M., 320 Szpiro Receives Media Prize, 803 Hodgson, Bernard R., 639 Third World Academy of Sciences Prizes Awarded, 234 Illusie, Luc, 1060 Training in Biological and Mathematical Sciences, 442 Jackson,Allyn,l94,547,645,651,660, 751,771,776,787, Trjitzinsky Memorial Awards Presented, 47 898,900,919,1038,1064,1196,1241,1355 Twentieth Reunion of Budapest Semesters Program, 12 38 Keyfitz, Barbara Lee, 784 Updated AMSRefs Package Available, 1076 Kirby, Rob, 181 USA Mathematical Olympiad, 804 Kirkman, Ellen E., 218, 789, 901 Vadhan Receives ONR Young Investigator Award, 1235 Kister, Jane E., 240 Veneziano Awarded 2004 Heineman Prize, 661 Knutson, Allen, 35 Visiting Mathematicians, 816 Koblitz, Ann Hibner, 39 Voiculescu Receives NAS Award in Mathematics, 547 Koblitz, Neal, 32 Young Mathematicians Honored in Siemens Westinghouse Kohn, Joseph]., 17 Competition, 345 Kotschick, D., 208 Krantz, Steven G., 896 Krieger, Martin H., 1226 Landsburg, Steven E., 394 Lax, Peter, 1320 Lott, Johnny W., 607 Lubotzky,Alexander, 31 Madison, Bernard, 1317 Magid, Andy, 7, 389, 1181 Authors of Articles Maxwell, James W., 218, 789, 901 Anderson, Michael T., 184 Mazur, Barry, 1214 Applebaum, David, 1336 McCarthy, Timothy, 333 Arthur, James, 498 McDonald, Michael, 741 Aschbacher, Michael, 736 Medina, Herbert A., 772 Bass, Hyman, 639 Morawetz, Cathleen, 1320 Biss, Daniel K., 1217 Mucha, Peter]., 887 Blank, Brian E., 1220 Nirenberg, Louis, 17, 1320 Blum, Lenore, 1024 Oxley, James G., 320 Bombieri, Enrico, 17, 498 Parks, Harold R., 1352 Brown, Anne, 741 Pfender, Florian, 873 Brown, Elizabeth Theta, 417 Porter, Mason A., 887 Callaghan, Thomas, 887 Prasad, Gopal, 498 Casselman, Bill, 392, 884 Ralston, Anthony, 403 Cenkl, Bohous, 17 Rankin, Samuel M., III, 656 Chandrasekharan, Komaravolu, 498 Raussen, Martin, 210 Clark, Claudia A., 443 Reed, Michael C., 338 Cooper, Duane A., 538 Roberts, David Lindsay, 1062 Corti, Alessio, 1350 Rose, Colleen, 218,789,901 Curtis, Philip C., Jr., 1057 Roy, Marie-Fran<;oise, 1231 Devadoss, Satyan L., 620 Saff, E. B., 1186 Delbaen, Freddy, 526 Sarnak, Peter, 762 Devaney, Robert L., 9 Schachermayer, Walter, 526 Dubinsky, Ed, 741 Segal, Dan, 768 Durrett, Rick, 201 Seregin, Gregory, 1320 Ermentrout, G. Bard, 312 Serre, Jean-Pierre, 498 Ewell, Peter, 1317 Sherbert, Donald R., 240 Ewing, John, 309,818 Sinai, Yakov, 412 Garabedian, Paul, 17 Skau, Christian, 210 Garding, Lars, 331 Springer, Tonny A., 498 Goldschmidt, Hubert, 17 Stasheff, Jim, 630 Gordon, Carolyn, 784 Stenger, Cynthia, 741 Griffiths, Phillip A., 17 Teichner, Peter, 894 Friedlander, Susan, 1320 Tits, Jacques, 498 Hardin, D.P., 1186 Toft, Bjarne, 205 1416 NOTICES OF THE AMS VOLUME 51, NUMBER 11 20041ndex Ullman, Daniel, 764 maticians Can Contribute to K-12 Education), 869; Ural'tseva, Nina, 1320 Robert M. Fossum (The Nominating Committee), 1021; van der Geer, Gerard, 493 Peter Ewell and Bernard Madison (Changing Teaching Vishik, Mark, 1320 of Future Teachers), 1317 Waldschmidt, Michel, 1231 Weeks, Jeffrey, 610 Conferences ofthe AMS Weller, Kirk, 741 2005 Summer Research Institute-Algebraic Geometry, Wright, David]., 1332 1293 Wu, H., 529 AMS Short Course, 1161 Ziegler, Gunter M., 414, 873 Call for Proposals for the 2006 Joint Summer Research Con ferences, 1115 Backlog of Mathematics Research journals, 924 Joint Summer Research Conferences in the Mathematical Sciences (2004), 176, 302, 384, 488, 600 Classified Advertisements Joint Summer Research Conferences in the Mathematical 72,284,368,471,583,710,842,984,1106,1274,1384 Sciences (2005), 1294, 1311 Conferences (Other) AAAS Amlual Meeting (2004), Seattle, WA, 176, 302 AAAS Amlual Meeting (2005), Washington, DC, 1429 Fifth Conference on Poisson Geometry, 1311 Corrections Correction: von Neumann Awards, 444 Commentary Correction to Guggenheim Fellowship Competition, 1073 Book Reviews: Reviewed by Allen Knutson (The Mathe Correction to "Has the Women-in-Mathematics Problem matics ofjuggling), 3 5; Reviewed by Arm Hibner Koblitz Been Solved?", 871 (Beyond the Limit: The Dream of Sofya Kovalevskaya), Corrections to the 2003 Amlual Survey of the Mathemat 39; Reviewed by Rick Durrett (The New Science of(Ran ical Sciences (First Report), 444 dom) Networks), 201; Reviewed by Bjarne Toft (Four Corrections to Thesis Titles, 549 Colors Suffice: How the Map Problem Was Solved), 205; Deaths of AMS Members Reviewed by Lars Garding (Abel's Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability), Bartle, R. G., 52 3 31; Reviewed by Timothy McCarthy (Godel's Proof), 3 33; Beard, Jacob T. B., Jr., 919 Reviewed by Elizabeth Theta Brown (A Mathematician's Berger, Agnes, 669 Survival Guide: Graduate School and Early Career De Blok, Willem ]., 669 velopment), 417; Reviewed by H. Wu (Geometry: Our Cul Bolibrukh, A., 348 tural Heritage), 529; Reviewed by Michael Harris (A Carlson, John W., 669 Sometimes Funny Book Supposedly about Infinity-A Chakravarty, Subinoy, 669 Review of Everything and More), 632; Reviewed by Daniel Chinn, William G., 669 Ullman (Count Down), 764; Reviewed by Dan Segal Culbertson, James T., 1366 (Gamma), 768; Reviewed by Steven G. Krantz (A Hand Deeba, Elias, 669 book of Mathematical Discourse), 896; Reviewed by Dekker, ]. C. E., 669 Philip C. Curtis Jr. (Math through the Ages: A Gentle His Dorogovtsev, A. Ya., 669 tory for Teachers and Others), 1057; Reviewed by Brian Elich, Joe, 348 E. Blank (The Constants ofNature and just Six Numbers), Escobar, Jose F., 444 1220; Reviewed by Harold R. Parks (Strange Curves, Evans, Lawrence Stanley, 1366 Counting Rabbits, and Other Mathematical Explorations), Feit, Walter, 1366 1352 Galmarino, Alberto R., 669 Letter from the Editor: Andy Magid (Reflections of a New Goldstein, ]. H., 348 Editor), 7; (Graphics Update), 389; (Mathematics and Goodman, A. W. , 1366 the Public), 1181 Gottschalk, Walter, 669 Letters to the Editor, 8, 182, 310, 390,494, 608, 734, 870, Graves, Robert L., 919 1022, 1182, 1316 Griffin, Ernest L., Jr., 348 Opinion: Rob Kirby (Fleeced?), 181; John Ewing (A Modest Guterman, Martin, 669 Proposal: Copyright and Scholarly Journals), 309; Ger Headley, Velmer, 669 ard van der Geer (We Can Make a Change), 493; Johnny Hillman, Abraham P., 444 W. Lott (Mathematicians and Mathematics Educators Hood, Rodney T., 1366 Must Be Political!), 607; Samuel M. Rankin III (Investing Hotzel, Eckehart, 52 in the Future), 733; Lynn Arthur Steen (How Mathe- Jaeger, Arno, 1362 DECEMBER 2004 NOTICES OF THE AMS 1417 20041ndex Jagadish, M.S., 919 USA Mathematical Olympiad, 804 James, Claiborne M., 669 Kakutani, Shizuo, 1366 Election Information (AMS) Kauffman, Robert M., 669 2004 AMS Elections-Special Section, 941 Khavinson, Semen Y., 348 Biographies of Candidates 2004, 944 Kingston, Paul, 348 Ladyzhenskaya, Olga A., 669, (Memorial article), 1320 Employment Center Leibler, Richard A., 444 Mathematical Sciences Employment Center, 993, 1117 Lindemann, Willi, 348 Mathematical Sciences Employment Center Forms, 998, Lorenz, Dan, 444 1122 Martin, William Ted, 919 Neubauer, Gerhard]., 52 Page, David A., 669 Pedersen, Flemming Damhus, 919 Pedersen, Gert K., 919 Pflumm, Eugene A., 348 Reichaw, Meir, 444 Rich, Nelson, 348 Rosenblum, Marvin, 669 Feature Articles Roy, Nina M., 444 Armand Borel (1923-2003) (James Arthur, Enrico Bombieri, Samur, Jorge D., 348 Komaravolu Chandrasekharan, Friedrich Hirzebruch, Scheffer, Carel L., 669 Gopal Prasad, Jean-Pierre Serre, Tonny A. Springer, Schneider, Joel, 1366 Jacques Tits), 498 Shanahan, John P., 348 (The) Bowl Championship Series: A Mathematical Review Sharma, Ambikeshwar, 1366 (Thomas Callaghan, Peter]. Mucha, Mason A. Porter), 887 Strange, William, 444 Cantor and Sierpinski, Julia and Fatou: Complex Topology Subramanian, R., 669 Meets Complex Dynamics (Robert L. Devaney), 9 Torgerson, Norman Wesley, 669 Combinatorial Equivalence of Real Moduli Spaces (Satyan Voege, Herbert, 669 L. Devadoss), 620 Wauters, Paul, 348 Comme Appele du Neant-As If Summoned from the Void: Welmers, Everett T., 348 The Life of Alexandre Grothendieck, Part I (Allyn Jack Westbrook, Edwin, 348 son), 1038; Part II (Allyn Jackson), 1196 Western, D. W., 52, 348 Computing over the Reals: Where Turing Meets Newton Whitehead, George W., Jr., 669 (Lenore Blum), 1024 Williams, Charles W., 669 Discretizing Manifolds via Minimum Energy Points (D.P. Williams, Dorothy J., 348 Hardin and E. B. Saff), 1186 Williamson, Jack, 444 Donald C. Spencer (1912-2001) (Joseph]. Kohn, Phillip A. Wong, Yung-Chow, 919 Griffiths, Hubert Goldschmidt, Enrico Bombieri, Bohous Yood, Bertram, 669 Cenkl, Paul Garabedian, Louis Nirenberg), 17 Geometrization of 3-Manifolds via the Ricci Flow (Michael Doctoral Degrees Conferred 2002-2003, 246 T. Anderson), 184 Supplementary List, 801 Interview with Joseph Keller (Allyn Jackson), 751 Intimations of Infinity (Kirk Weller, Anne Brown, Ed Du Education binsky, Michael McDonald, Cynthia Stenger), 741 (The) BKPS Letter of 1962: The History of a "New Math" Kissing Numbers, Sphere Packings, and Some Unexpected Episode, 1062 Proofs (Florian Pfender, Gunter M. Ziegler), 873 Doctorate Degrees in Mathematics Earned by Blacks, His Levy Processes-From Probability to Finance and Quantum panics/Latinos, and Native Americans: A Look at the Groups (David Applebaum), 1336 Numbers, 772 Olga Alexandrovna Ladyzhenskaya (1922-2004), 1320 (The) International Commission on Mathematical Instruc (The) Poincare Dodecahedral Space and the Mystery of the tion-What? Why? For Whom?, 639 Missing Fluctuations (Jeffrey Weeks), 610 Mathematician's Group to Provide Advice on Math Stan Quantum Game Theory (Steven E. Landsburg), 394 dards, 1355 Research Mathematicians and Mathematics Education: A Math through the Ages: A Gentle History for Teachers and Critique (Anthony Ralston), 403 Others (A Book Review), 1057 Review of Sync: The Emerging Science of Spontaneous Recommendations for Increasing the Participation and Order(G. Bard Ermentrout), 312 Success of Blacks in Graduate Mathematics Study, 538 RIMS, an Institute for Japan and the World (Allyn Jackson), Research Mathematicians and Mathematics Education: A 194 Critique, 403 1418 NOTICES OF THE AMS VOLUME 51, NUMBER 11 20041ndex (The) Status of the Classification of the Finite Simple Raghunathan, M. S. (Bangalore, India), 85 Groups (Michael Aschbacher), 736 Sanchez-Valenzuela, Adolfo (Houston, TX), 93 Sarnak, Peter (Bangalore, India), 85 Invited Speakers Schapire, Robert (Pittsburgh, PA), 298 Agol, Ian (Evanston, IL), 95 Schlag, Wilhelm (Eugene, OR), 1406 Avramov, Luchezar (Houston, TX), 93 Schonbek, Maria E. (Los Angeles, CA), 92 Balasubramanian, R. (Bangalore, India), 85 Schwachhoefer, Lorenz (Newark, DE), 860 Benkart, Georgia (Atlanta, GA), 719 Seade-Kuri, Jose (Houston, TX), 93 Bertozzi, Andrea L. (Atlanta, GA), 718 Seidel, Paul (Evanston, IL), 95 Billey, Sara C. (Albuquerque, NM), 94 Serfaty, Sylvia (Lawrenceville, NJ), 92 Boneh, Dan (Los Angeles, CA), 92 Sethian, James (Santa Barbara, CA), 724 Bonk, Mario (Athens, OH), 89 Sinha, K. B. (Bangalore, India), 85 Brock, Jeffrey F. (Pittsburgh, PA), 298 Smith, Hart H. (Eugene, OR), 1406 Browder, William (Lawrenceville, NJ), 591 Smith, Paul (Los Angeles, CA), 92 Chang, Der-Chen (Pittsburgh, PA), 298 Stanford, Theodore (Albuquerque, NM), 94 Chang, Mei-Chu (Santa Barbara, CA), 724 Sturmfels, Bernd (Houston, TX), 93; (Atlanta, GA), 718 Charney, Ruth M. (Nashville, TN), 593 Sullivan, Dennis P. (Lawrenceville, NJ), 92 Chen, Xiu Xiong (Newark, DE), 860 Sweldens, Wim F. (Lawrenceville, NJ), 92 Chow, Bennett (Bowling Green, KY), 1301 Thiele, Christopher Martin (Los Angeles, CA), 92 Daubechies, Ingrid (Atlanta, GA), 718 Tracy, Craig A. (Albuquerque, NM), 94 Demaine, Erik D. (Atlanta, GA), 719 Uhlmann, Gunther (Atlanta, GA), 718 Diaconis, Persi W. (Houston, TX), 93; (Annandale-on- Uribe, Alejandro (Lincoln, NE), 862 Hudson, NY), 72 5 Vakil, Ravi D. (Atlanta, GA), 719 Ebenfelt, Peter (Albuquerque, NM), 94 Voevodsky, Vladimir (Bangalore, India), 85 Esnault, Helene (Mainz, Germany), 96 Walker, Judy (Lincoln, NE), 862 Foreman, Matthew (Eugene, OR), 1406 Webb, Glenn F. (Tallahassee, FL), 87 Gamba, Irene M. (Athens, OH), 89 Weikard, Rudi (Nashville, TN), 593 Ghrist, Robert W. (Evanston, IL), 95 Wigderson, Avi (Atlanta, GA), 718 Gilbert, Anna (Newark, DE), 860 Wilson, Robin J (Atlanta, GA), 719 Gitler, Samuel (Houston, TX), 93 Xin, Jack (Lincoln, NE), 862 Gouvea, Fernando Q. (Atlanta, GA), 719 Yau, Horng-Tzer (Mainz, Germany), 96 Grigorchuk, Rostislav I. (Athens, OH), 89 Zaslow, Eric G. (Athens, OH), 89 Haiman, Mark (Eugene, OR), 1406 Zeitouni, Ofer (Pittsburgh, PA), 298 Hamilton, Richard (Mainz, Germany), 96 Zelditch, Steven M. (Atlanta, GA), 718 Hopkins, Michael J (Mainz, Germany), 96 Zhang, Gaoyong (Lawrenceville, NJ), 92 Hunt, FernY. (Tallahassee, FL), 87 Ionel, Eleny (Atlanta, GA), 718 letters to the Editor Ivanov, Nikolai (Lubbock, TX), 723 Babich, Amy (Alternative Freshman Mathematics), 870 Jaco, William H. (Tallahassee, FL), 87 Baker, Patrick (Long Division by Hand), 310 Jonsson, Mattias (Lubbock, TX), 723 Berezin, Alexander A. (Term Copyrights), 608 Kapovich, Mischa (Santa Barbara, CA), 724 Bharali, Gautam (Is Wallace's Chicken Russell's Turkey?), Kleiner, Bruce A. (Atlanta, GA), 718 Krantz, Steven G. (Atlanta, GA), 719 1022 Krattenthaler, Christian (Mainz, Germany), 96 Cowen, Robert (Tutte and Beraha), 609 Lazarsfeld, Robert K. (Atlanta, GA), 718 Drinfeld, Vladimir (Shtuka and Stuka), 8 Lubotzky, Alex (Newark, DE), 860 Drucker, Thomas (Another View of Never at Rest), 495 Mallin, Yuri (Evanston, IL), 95 Escobales, Richard H., Jr. (Paper-and-Pencil Math), 734 Masur, Howard (Lincoln, NE), 862 Gagen, Terry (Australian National Mathematics Summer McCann, Robert (Bowling Green, KY), 1301 School Flourishing), 182 Minsky, Yair (Tallahassee, FL), 87 Gale, David (Underrepresentation), 1318 Monod, Nicolas (Lubbock, TX), 723 Gerstenhaber, Murray (Remembering Max Shiffman), 390 Montgomery, M. Susan (Bowling Green, KY), 1301 Goodman, Jonathan (More Examples of Fuzzy Math), 311 Natterer, Frank (Mainz, Germany), 96 Harris, Michael (Reply to Bharali), 1182 Oh, Hee (Lubbock, TX), 723 Hastrev, Reb (How Mathematics Can Be Political), 1022 Ozsvath, Peter S. (Nashville, TN), 593 Hitchin, Nigel (Alternative Journal Pricing), 871 Papanicolaou, George C. (Bangalore, India), 85 Jackson, Allyn (Shtuka and Stuka), 8 Pevzner, Pavel (Atlanta, GA), 719 Kac, Victor (Work of Morozov, Weisfeiler, and Borel), 735 Popa, Sorin T. (Nashville, TN), 593 Kahane, Joseph (Tutte and Beraha), 609 Putinar, Mihai (Santa Barbara, CA), 724 Kass, Seymour (Revive the Queries Column), 1182 DECEMBER 2004 NOTICES OF THE AMS 1419 20041ndex Landau, Susan (Summer Studies Mathematician Alumnae), Banchoff, Thomas F. (NSF Distinguished Teaching Scholar 182 Award), 913 Lott, Johnny W. (Reply to Hastrev), 1182 Bannai, Kenichi (Take be Junior Prize of the MSJ), 4 5 Marcus, David (Prisoner's Dilemma), 735 Bardos, Claude (French Academy of Sciences Prizes and Mbonu, D. E. (More Recommendations for Minority Math- Elections), 344 ematicians), 1023 Barlow, Richard (2004 MAA Certificate of Meritorious Ser Naimpally, Som (A Theorem of Bartle), 608 vice), 545 Norwood, Rick (Teach More Math K-12), 608 Barthe, Franck (2004 European Congress of Mathematicians Persson, Ulf (Is Research in Mathematics Education Sci- prize), 1070 entific?), 609 Bartle, Robert G. (Memorial), 239 Polster, Burkard (Review of Mathematics of Juggling), 494 Barton, Reid W. (Putnam Prize), 803 Porter, Mason (Postdocs Can't Follow Kirby's Advice), 494 Benjamini, Itai (2004 Rollo Davidson Prize), 661 Proctor, Bob (Homework and Google), 1319 Berestycki, Henri (Grand Prix Sophie Germain), 1359 Ralston, Anthony (Response to Schmid), 310; (Ralston Bernstein, Joseph (National Academy of Sciences Elec- Responds to Escobales), 1022 tions), 664 Roitman, Judy (Geometry Texts for Teachers), 73 5 Besag, Julian (Royal Society of London Elections), 914 Rosa, Domenico (New Math), 311 Betterton, Meredith D. (2004 Sloan Fellow), 663 Rosay, Jean-Pierre (Teaching Loads), 1023 Bezrukavnikov, Roman (2004 Sloan Fellow), 663 Schmid, Wilfried (California Dreaming Reviewer Partisan), Bianchini, Stefano (2004 European Congress of Mathe- 310 maticians prize), 1070 Schremmer, Alain (Textbooks Should Be Cheaper Too), Biran, Paul (2003 Oberwolfach Prize), 660; (2004 Euro- 494 pean Congress of Mathematicians prize), 1070 Stone, H. E. (More on the Prisoner's Dilemma), 1318 Bjorken, James D. (2004 Dirac Medal), 1359 Vassiliev, V. A. (Role of Mathematics, As They Think of It), Borel, Armand (Memorial), 498 870 Boutet de Manvel, Louis (French Academy of Sciences Washburn, Sherwood (Coding Theory and the Genetic Prizes and Elections), 344 Code), 871 Brenner, Michael P. (Guggenheim Fellowship), 664 Weinstein, Alan (Parallelizable Manifolds), 8 Bromberg, Kenneth (2004 Sloan Fellow), 663 Wells, Charles (Review of A Handbook of Mathematical Brousseau, Guy (ICMI Felix Klein Medal), 662 Discourse), 1319 Bruss, F. Thomas (European Mathematical Society Article Wolf, Joseph (Parallelizable Manifolds), 8 Competition 2003), 345 Wu, H. (Wu's Comment on Roitman Letter), 871 Burger, Edward B. (MAA Chauvenet Prize), 1235 Callan, Curtis G. (2004 Dirac Medal), 1359 Cao, Huai-Dong (Guggenheim Fellowship), 664 Capogna, Luca (2002 NSF CAREER Award), 46 Caraiani, Ana (Putnam Prize), 803 Carroll, Gabriel D. (Putnam Prize), 803 Celso de Melo, Wellington (Third World Academy of Sci- ences Prize), 234 Chakraborti, Subha (Fulbright Award), 664 Mathematicians Cheng, Li-Tien (2004 Sloan Fellow), 663 Abramsky, Samson (Royal Society oflondon Elections), 914 Chern, Shiing-Shen (Shaw Prize), 1067 Aczel, Amir D. (Guggenheim Fellowship), 664 Chow, Edmond (2002 PECASE Award), 802 Ahlgren, Scott (2002 NSF CAREER Award), 46 Cohen, Albert (Prix Blaise Pascal du Gamni-Smai), 1359 Ainsworth, Mark (LMS Whitehead Prize), 1072 Colella, Phillip (National Academy of Sciences Elections), Aldous, David (American Academy of Arts and Sciences 664 Elections), 804 Crato, Nuno (European Mathematical Society Article Com- Allgower, Frank (2004 Leibniz Prize), 803 petition 2003), 345 Ambrosio, Luigi (Fermat Prize), 234 Dai, Bo (Fan China Exchange Program), 808 Ariki, Susumu (Autumn Prize of the MSJ), 45 Danielli, Donatella (2003 NSF CAREER Award), 46 Asatryan, Gurgen R. (2004 Emil Artin Junior Prize in Math- Dankowicz, Harry (2003 PECASE Award), 1359 ematics), 549 Daskalopoulos, Panagiota (Guggenheim Fellowship), 664 Atiyah, Michael Francis (2004 Abel Prize), 649 David, Guy (2004 Ferran Sunyer i Balaguer Prize), 802; Atkins, Warren (Paul Erdos Award), 1072 (Prix Servant), 1359 Aubin, Thierry (French Academy of Sciences Prizes and Elec Davis, Stephen H. (National Academy of Sciences Elec- tions), 344 tions), 664 Baik, Jinho (2004-2005 AMS Centennial Fellowship), 660 Dawson, Donald (CRM-Fields Prize), 440 Bal, Guillaume (2003 NSF CAREER Award), 46 Deledicq, Andre (Paul Erdos Award), 1072 Deligne, Pierre (2004 Balzan Prize), 1357 1420 NOTICES OF THE AMS VOLUME 51, NUMBER 11 20041ndex Delman, Charles I. (MAA Carl B. Allendoerfer Award), 1234 Grozdev, Sava (European Mathematical Society Article Delort, Jean-Marc (French Academy of Sciences Prizes and Competition 2003), 345 Elections), 344 Guichard, Megan (NDSEG Fellowship), 1360 Denissov, Serguei (Popov Prize), 1071 Guttman, Anthony J. (B. H. Neumann Award), 1235 Derzhanski, Ivan (European Mathematical Society Article Haiman, Mark (2004 Moore Prize), 431 Competition 2003), 345 Haines, Thomas ]. (2004 Sloan Fellow), 663 Dominici, Diego (SIAM Richard C. DiPrima Prize), 1234 Hamilton, Richard (Clay Award), 234 Dudley, Underwood (2004 MAA Certificate of Meritorious Hand, Paul (NDSEG Fellowship), 1360 Service), 545 Hassett, Brendan (2002 NSF CAREER Award), 46 Dunfield, Nathan M. (2004 Sloan Fellow), 663 Hem, Thomas (2004 MAA Certificate of Meritorious Ser- Dunham, Douglas (MAA Trevor Evans Award), 1234 vice), 545 Duquesne, Thomas (IRMA Prize in Memory of Paul Andre Hesthaven, Jan (2002 NSF CAREER Award), 46 Meyer), 548 Hirachi, Kengo (Geometry Prize of the MSJ), 45 Elkhader, Abderrahmn (Fulbright Award), 664 Holroyd, Ander (2004 Rollo Davidson Prize), 661 Elkies, Noam D. (2004 Conant Prize), 433; (MAA Lester R. Honda, Ko (2003 NSF CAREER Award), 46 Ford Award), 1234 Hayles, Celia (ICMI Hans Freudenthal Medal), 662 Ellis, George F. R. (2004 Templeton Prize), 1072 Hsu, Jason C.-H. (Fulbright Award), 664 Epstein, David B. A. (Royal Society of London Elections), Hurtubise, Jacques (2004 Royal Society of Canada Elec- 914 tions), 1073 Etnyre, John (2003 NSF CAREER Award), 46 Impagliazzo, Russell (Guggenheim Fellowship), 664 Evans, Lawrence C. (2004 Steele Prize), 421 . Inoue, Rei (Takebe Junior Prize of the MSJ), 45 Fauring, Patricia (Paul Erdos Award), 1072 Isaacson, Samuel (NDSEG Fellowship), 1360 Fei, Shao-Ming (Fan China Exchange Program), 808 Itoh, Minoru (Takebe Senior Prize of the MSJ), 4 5 Fienberg, Stephen E. (2004 Royal Society of Canada Elec- Ivanov, Anatoli F. (Fulbright Award), 664 tions), 1073 Izumi, Masaki (Analysis Prize of the MSJ), 45 Fink, John B. (Fulbright Award), 664 Jin, Zhezhen (2002 NSF CAREER Award), 46 Fong, William (NDSEG Fellowship), 1360 Jing, Naihuan N. (Fulbright Award), 664 Frederickson, Greg N. (MAA George P6lya Award), 1234 Joyce, Dominic (2004 Adams Prize), 802 Friedman, Jerome H. (2004 Parzen Prize), 661 Jozsa, Richard (LMS Naylor Prize), 1072 Fujino, Osamu (Takebe Senior Prize of the MSJ), 45 Kadane, Joseph B. (Fulbright Award), 664 Fukuizumi, Reika (Takebe Junior Prize of the MSJ), 45 Kaloshin, Vadim (2004 Sloan Fellow), 663 Fukushima, Masatoshi (Analysis Prize of the MSJ), 45 Kane, Daniel M. (Putnam Prize), 803 Furmaniak, Ralph C. (Putnam Prize), 803 Katok, Anatole (American Academy of Arts and Sciences Gabai, David (2004 Veblen Prize), 426 Elections), 804 Gaboriau, Darnien (French Academy of Sciences Prizes and Katz, Nicholas M. (National Academy of Sciences Elec- Elections), 344 tions), 664 Galperin, Gregory (MAA Carl Allendoerfer Award), 1234 Kawamura, Tomomi (Takebe Junior Prize of the MSJ}, 45 Gambini, Rodolfo (Third World Academy of Sciences Prize), Keller, Joseph (Interview with), 751 234 Kenelly, John W. (2004 MAA Certificate of Meritorious Ser Garity, Dennis]. (Fulbright Award), 664 vice), 545 Garrity, Thomas (2004 MAA Haimo Award), 544 Keyfitz, Barbara Lee (Named Director of Fields Institute), Getz, Jayce (NDSEG Fellowship), 1360 898 Ghomi, Mohammad (2003 NSF CAREER Award), 46 Killip, Rowan (2004 Sloan Fellow), 663 Ghrist, Robert W. (2002 NSF CAREER Award), 46; (2002 Kiselev, Alexander (2002 NSF CAREER Award), 46 PECASE Award), 802 Kisin, Mark (2004 Sloan Fellow), 663 Glimm, James G. (National Medal of Science), 215 Kister, Jane E. (Retires from MR), 918 Glowinski, Roland (SIAM Theodore von Karman Award), Kitchloo, Nitu (2004- 2005 AMS Centennial Fellowship), 1234 660 ' Gneiting, Tilmann (2002 NSF CAREER Award), 46 Kleinbock, Dmitry (2003 NSF CAREER Award), 46 Goldwasser, Shafrira (National Academy of Sciences Elec- Kohn, Joseph J. (2004 Bergman Prize), 343 tions), 664 Kontoyiannis, Ioannis (2004 Sloan Fellow), 663 Griffeath, David (Fan China Exchange Program), 808 Krener, Arthur]. (SIAM W. T. and Idalia Reid Prize), 1234 Grojnowski, Ian (LMS Frohlich Prize), 1072 Kribs Zaleta, Christopher M. (Fulbright Award), 664 Gromov, Mikhael L. (Nemmers Prize), 787 Krylov, Nicolai V. (2004 Steele Prize), 421 Gross, Benedict H. (National Academy of Sciences Elections), Kumagai, Takashi (2004 Spring Prize of the MSJ), 803 664 Kuci, Frances (Information-Based Complexity Young Re- Gross, Leonard (American Academy of Arts and Sciences searcher Award), 46 Elections), 804 Lacey, Michael T. (Guggenheim Fellowship), 664 Grothendieck, Alexandre (Feature Article), 1038, 1196 Ladyzhenskaya, Olga A. (Memorial), 1320 D ECEMBER 2004 NOTICES OF THE AMS 1421 20041ndex Lafforgue, Laurent (French Academy of Sciences Prizes Pan, Jian Zhong, (Fan China Exchange Program), 808 and Elections), 344 Pappas, George G. (2002 PECASE Award), 802 Lebeau, Gilles (French Academy of Sciences Prizes and Parsa, Rahul A. (Fulbright Award), 664 Elections), 344 Pasik-Duncan, Bozenna (2004 AWM Hay Award), 546 Leighton, Frank T. (National Academy of Engineering Elec- Paulos, John Allen (2003 AAAS Award), 548 tions), 665 Penrose, Roger (LMS De Morgan Medal), 1072 Levy, Doran (2002 NSF CAREER Award), 46 Petzold, Linda R. (National Academy of Engineering Elec- Li, Yongqing, (Fan China Exchange Program), 808 tions), 665 Liang, Song (Takebe Junior Prize of the MSJ), 45 Pilla, Ramani (2003 NSF CAREER Award), 46 Ligh, Stephen (2004 MAA Certificate of Meritorious Service), Preiss, David (Royal Society of London Elections), 914 545 Psemeneki, Tiffany (NDSEG Fellowship), 1360 Lin, Fang-Hua (American Academy of Arts and Sciences Range, R. Michael (MAA Lester R. Ford Award), 1234 Elections), 804 Rivest, Ronald L. (National Academy of Sciences Elections), Lin, Yi (2002 NSF CAREER Award), 46 664 Lindenstrauss, Elon (2003 Salem Prize), 45; (2004 European Robertson, Neil (SIAM George P6lya Prize), 1234 Congress of Mathematicians prize), 1070 Rockoff, Maxine L. (AAAS Fellow), 234 Liu, Andrew Chiang-Fung (2004 MAA Raimo Award), 544 Russo, Bernard, (Fan China Exchange Program), 808 Livingston, Charles (MAA Lester R. Ford Award), 1234 Sabatti, Chiara (2003 NSF CAREER Award), 46 Lototsky, Sergey (2003 NSF CAREER Award), 46 Saksena, Nitin (NDSEG Fellowship), 1360 Ludwig, Donald (AAAS Fellow), 234 Seiringer, Robert (2004 Sloan Fellow), 663 Lurie, Jacob (2004 AIM Five-Year Fellowship), 548 Selden, Annie (AAAS Fellow), 234 Lvov, Yuri (2002 NSF CAREER Award), 46 Sendova, Evgenia (European Mathematical Society Article Mair, Bernard A., (Fan China Exchange Program), 808 CompetitiOn 2003), 345 Maitra, Ranjan (2003 NSF CAREER Award), 46 Serfaty, Sylvia (2003 NSF CAREER Award), 46; (2004 Eu- Marrin, Yuri I. (American Academy of Arts and Sciences Elec- ropean Congress of Mathematicians prize), 1070 tions), 804 Serre, Jean-Pierre (Interview), 210 Manolescu, Ciprian (2004 Clay Research Fellow), 549 Sethian, James (2004 Wiener Prize), 428 Mares, Bernard (NDSEG Fellowship), 1360 Seymour, Paul D. (2003 Ostrowski Prize), 900; (SIAM George Markovic, Vladimir (LMS Whitehead Prize), 1072 P6lya Award), 1234 Matchett, Philip (NDSEG Fellowship), 1360 Shapiro, Victor L. (AAAS Fellow), 234 Mathe, Peter (2004 Prize for Achievement in Information- Shima, Akiko (Takebe Senior Prize of the MSJ), 45 Based Complexity), 803 Shipley, Brooke (2002 NSF CAREER Award), 46 Matsumoto, Shigenori (Geometry Prize of the MSJ), 45 Simpson, Jamie (B. H. Neumann Award), 1235 McCague, Hugh (MAA Trevor Evans Award), 1234 Singer, Isadore M. (2004 Abel Prize), 649 McLaughlin, David W. (AAAS Fellow), 234 Smirnov, Stanislav (2004 European Congress of Mathe- McMullen, Curtis T. (2004 Guggenheim Fellowship), 1073 maticians prize), 1070 Milnor, John W. (2004 Steele Prize), 421 Smith, Bryan (NDSEG Fellowship), 1360 Mineyev, Igor (2002 NSF CAREER Award), 46 Smith, Gregory (2002 NSF CAREER Award), 46 Mirzakhani, Maryam (2004 Clay Research Fellow), 549 Smyth, David (NDSEG Fellowship), 1360 Miyajima, Kimio (Analysis Prize of the MSJ), 45 Solna, Knut (2004 Sloan Fellow), 663 Moeglin, Collette (Prix Jaffe), 1359 Sottile, Frank (2002 NSF CAREER Award), 46 Mohammadi, Bijan (Prix Ayme Poirson), 1359 Soundararajan, Karman (2003 Salem Prize), 45 Monasson, Remi (Prix Leconte), 1360 Spears, Kimberly (2004 AWM Schafer Prize), 546 Morawetz, Cathleen Synge (2004 Steele Prize), 421 Spencer, Donald C. (Memorial), 17 Nakos, Anna (B. H. Neumann Award), 1235 Stankova, Zvezdelina (MAA Henry L. Alder Award), 1235 Nayakkankuppam, Madhu (2003 NSF CAREER Award), 46 Stevens, T. Christine (2004 Gung and Hu Award), 544 Nekrassov, Nikita (Prix Jacques Herbrand), 1359 Stewart, G. W. (National Academy of Engineering Elec- Nemirovski, Arkadi (2003 John von Neumann Theory tions), 665 Prize), 344 Stolovitch, Laurent (Prix Paul Doistau-Emile Bluter), 1359 Newell, Alan C. (SIAM John von Neumann Lectureship), 1234 Su, Francis E. (MAA Henry L. Alder Award), 1235 Newman, Charles M. (National Academy of Sciences Elec- Sudakov, Benny (2004 Sloan Fellow), 663 tions), 664 Suri, Manil (Guggenheim Fellowship), 664 Ni, Lei (2004 Sloan Fellow), 663 Szpiro, George (2003 Prix Media), 803 Nicodemi, Olympia (2004 MAA Raimo Award), 544 Tao, Terence (Clay Award), 234 Okounkov, Andrei (2004 European Congress of Mathe- Tapia, Richard A. (2004 Award for Distinguished Public Ser maticians prize), 1070 vice), 435; (SIAM Prize for Distinguished Service to the Oster, George F. (National Academy of Sciences Elections), Profession), 1234 664 Terasoma, Tomohide (2004 Algebra Prize of the MSJ), 803 Pambuccian, Victor V. (Fulbright Award), 664 Thiele, Ruediger (MAA Lester R. Ford Award), 1234 1422 NOTICES OF THE AMS VOLUME 51, NUMBER 11 20041ndex Thomas, Richard (LMS Whitehead Prize), 1072 Zeng, Chongchun (2003 NSF CAREER Award), 46; (2004 Thompson, Russell, (Fan China Exchange Program), 808 Sloan Fellow), 663 Thron, Christopher P. (Fulbright Award), 664 Zilber, Boris (LMS Senior Berwick Prize), 1072 Tian, Gang (American Academy of Arts and Sciences Elec Zuckerman, David (Guggenheim Fellowship), 664 tions), 804 Zuo, Yijun (2002 NSF CAREER Award), 46 Tillmann, Ulrike (LMS Whitehead Prize), 1072 Todd, Michael]. (2003 John von Neumann Theory Prize), 344 Tolsa, Xavier (2004 European Congress of Mathematicians prize), 1070 Tornberg, Anna-Karin (Carl-Erik Froberg Prize), 1071 Trivisa, Konstantina (2003 NSF CAREER Award), 46; (2003 PECASE Award), 1359 Mathematics Tucker, Warwick (2004 European Congress of Mathemati cians prize), 1070 Cantor and Sierpinski, Julia and Fatou: Complex Topology Tutte, William T. (Memorial), 320 Meets Complex Dynamics (Robert L. Devaney), 9 Vakil, Ravi (2003 NSF CAREER Award), 46; (2003 PECASE Combinatorial Equivalence of Real Moduli Spaces, 620 Award), 1359 Comme Appele du Neant -As If Summoned from the Void: Vadhan, Salil P. (ONR Young Investigator Award), 1235 The Life of Alexandre Grothendieck, Part I, 1 038; Part II, Valiant, Paul (NDSEG Award), 1360 1196 Computing over the Reals: Where Turing Meets Newton, Vanden Eijnden, Eric (2003 NSF CAREER Award), 46 1024 Vasy, Andras (2004 Clay Research Fellow), 549 (The) Difficulties of Kissing in Three Dimensions, 884 Veneziano, Gabriele (2004 Heineman Prize), 661 Discretizing Manifolds via Minimum Energy Points, 1186 Venjakob, Otmar (2004 European Congress of Mathe- Double Cusp Group, 1332 maticians prize), 1070 Geometrization of 3-Manifolds via the Ricci Flow (Michael Venkataramani, Shankar (2002 NSF CAREER Award), 46 T. Anderson), 184 Venkatesh, Akshay (2004 Clay Research Fellow), 549 (The) Great Prime Number Record Races, 414 de Verdiere, Yves Colin (American Academy of Arts and Happy 100th, Henri Cartan!, 771 Sciences Elections), 804 Interview with Jean-Pierre Serre, 210 Verschelde, Jan (2002 NSF CAREER Award), 46 Interview with Joseph Keller, 751 Viaclovsky, Jeff (2004 Sloan Fellow), 663 Intimations of Infinity, 741 Viens, Frederi G. (Fulbright Award), 664 Kissing Numbers, Sphere Packings, and Some Unexpected Virag, Balint (2004 Sloan Fellow), 663 Proofs, 873 Viswanath, Divakar (2004 Sloan Fellow), 663 Levy Processes-From Probability to Finance and Quantum Voiculescu, Dan Virgil (2004 NAS Award in Mathematics), Groups, 1336 547 Mathematics Awareness Month 2003, 346 Voisin, Claire (French Academy of Sciences Prizes and Networks, 392 Elections), 344 Oberwolfach Celebrates Its Sixtieth Anniversary,1064 Vu, Van (2003 NSF CAREER Award), 46 Olga Alexandrovna Ladyzhenskaya (1922-2004), 1320 Wallach, Nolan (American Academy of Arts and Sciences (The) Poincare Dodecahedral Space and the Mystery of the Elections), 804 Missing Fluctuations, 610 Werner, Wendelin (French Academy of Sciences Prizes and Quantum Game Theory, 394 Elections), 344 (The) Status of the Classification of the Finite Simple Whyte, Kevin (2004 Sloan Fellow), 663 Groups, 736 Willis, John R. (National Academy of Engineering Elec- (A) Tribute to Boris Weisfeiler (El Ultimo Secreto de Colo tions), 665 nia Dignidad-A Book Review), 32 Witelski, Thomas (2003 NSF CAREER Award), 46 (A) Tribute to Boris Weisfeiler (The Mathematics of Boris Witten, Edward (National Medal of Science), 215 Weisfeiler), 31 Wood, Melanie (2003 Morgan Prize), 438 WHAT IS a Billiard?, 412 Workman, John (NDSEG Award), 1360 WHAT IS an Expander?, 762 Yeats, Karen (2003 Morgan Prize), 438 WHAT IS a Flip?, 1350 Yee, Ae Ja (2004 Sloan Fellow), 663 WHAT IS a Free Lunch?, 526 Yezzi, Anthony (2002 NSF CAREER Award), 46 WHAT IS a Grope?, 894 WHAT IS a Motive?, 1214 Yor, Marc (French Academy of Sciences Prizes and Elec WHAT IS an Operad?, 630 tions), 344 WHAT IS a Quasi-morphism?, 208 Young, Lai-Sang (American Academy of Arts and Sciences WHAT IS a Topos?, 1060 Elections), 804 Why Is Mathematical Biology So Hard?, 338 Zame, William R. (Guggenheim Fellowship), 664 DECEMBER 2004 NOTICES OF THE AMS 1423 20041ndex Mathematics Calendar Evanston, IL, 94, 298, 378, 483, 594, 716, 853, 1005, 1128, 61,277,355,455,573,678,829,957,1094,1263,1373 1298 Pittsburgh, PA, 95, 298, 378,484, 595, 717, 857, 1006, 1129, Mathematics History 1299 Armand Borel (1923-2003), 498 (The) BKPS Letter of 1962: The History of a "New Math" 2005 Meetings Episode, 1062 Atlanta, GA, 95, 299, 379,484, 595, 718, 857, 1008, 1130, Comme Appele duNeant- As If Summoned from the Void: 1300, 1399 The Life of Alexandre Grothendieck, Part I, 1038; Part II, Bowling Green, KY, 95,299, 379,484, 595, 723, 859, 1010, 1196 1154, 1301, 1404 Donald C. Spencer (1912-2001), 17 Newark,DE,96,299,379,485, 596,723,859,1010,1155, Math through the Ages: A Gentle History for Teachers and 1301, 1405 Others (A Book Review), 1057 Lubbock,TX,96,299,380,485,596, 723,860,1011,1155, Oberwolfach Celebrates Its Sixtieth Anniversary, 1064 1302, 1406 Olga Alexandrovna Ladyzhenskaya (1922-2004), 1320 Santa Barbara, CA, 96, 299, 380, 485, 596, 724, 860, 1011, Robert G. Bartle (1927-2003), 239 1156, 1303, 1407 William T. Tutte (1917-2002), 320 Mainz, Germany, 96, 300, 380, 485, 596, 724, 861, 1011, 1156, 1303, 1407 Annandale-on-Hudson, NY, 597, 725, 861, 1012, 1157, 1305, 1409 Johnson City, TN, 96, 300, 381, 486, 597, 725, 862, 1012, 1157, 1305, 1409 Lincoln, NE, 97, 300, 381,486, 597, 725, 862, 1013, 1157, 1305, 1409 Meeting Announcements, Presenters of Papers, Eugene, OR, 725,862,1013,1158,1305,1410 and Programs Taiwan, 862, 1013, 1158, 1306, 1410 Albuquerque, NM (announcement), 851 Athens, OH (announcement), 89 2006 Meetings Atlanta, GA (announcement and timetable), 1130, 1164 San Antonio, TX, 97, 300, 381, 486, 597, 726, 862, 1013, Evanston, IL (announcement), 853 1158, 1306, 1410 Houston, TX (announcement), 295 Durham, NH, 1158, 1306, 1411 Lawrenceville, NJ (announcement), 292 San Francisco, CA, 863, 1013, 1159, 1306, 1411 Los Angeles, CA (announcement), 290 Fayetteville, AR, 1306, 1411 Nashville, TN (announcement), 849 Phoenix, AZ (presenters and program), 99 2007 Meetings Pittsburgh, PA (announcement), 1006 New Orleans, LA, 97, 301, 381, 486, 598, 726, 863, 1014, Tallahassee, FL (announcement), 87 1159, 1307, 1411 Meetings and Conferences 2008 Meetings 85,289,373,479,591,715,849,1003,1127,1298,1403 General Information Regarding Meetings & Conferences of San Diego, CA, 97, 301, 381,487, 598, 726,863, 1014, 1159, the AMS, 84 1307, 1412 Meetings and Conferences Table of Contents, 176, 302, 384, 488,600,728,864,1016,1174,1311,1430 2009 Meetings Washington, DC, 98, 301, 382, 487, 598, 726, 863, 1014, 2003 Meeting 1159, 1307, 1412 Bangalore, India, 85 2010 Meetings 2004 Meetings San Francisco, CA, 1160, 1307, 1412 Phoenix, AZ, 86 Tallahassee, FL, 87, 289, 373 2011 Meetings Athens, OH, 89, 290, 373, 479 New Orleans, LA, 1160, 1308, 1412 Los Angeles, CA, 91, 290, 374, 480 Lawrenceville, NJ, 92, 292, 375, 480, 591 Memorial Articles Houston, TX, 93, 295, 376, 481, 592, Armand Borel (1923-2003) (James Arthur, Enrico Bombieri, Nashville, TN, 94,297,377,482, 593,715,849, 1003, 1127 Komaravolu Chandrasekharan, Friedrich Hirzebruch, Albuquerque,NM,94,297, 377,482,593,716,851,1004, Go pal Prasad, Jean-Pierre Serre, Tonny A. Springer, and 1128 Jacques Tits), 498 1424 NOTICES OF THE AMS VOLUME 51, NUMBER 11 20041ndex Donald C. Spencer (1912-2001) (Joseph]. Kohn, Phillip A. Call for Nominations for Frank Nelson Cole Prize in Num Griffiths, Hubert Goldschmidt, Emico Bombieri, Bohous ber Theory, 449, 567 Cenkl, Paul Garabedian, Louis Nirenberg), 17 Call for Nominations for Information-Based Complexity Olga Alexandrovna Ladyzhenskaya (1922-2004) (Susan Prize and Young Researcher Award, 237 Friedlander, Peter Lax, Cathleen Morawetz, Louis Niren Call for Nominations for Levi L. Conant Prize, 449, 567 berg, Gregory Seregin, Nina Ural'tseva, and Mark Vishik), Call for Nominations for Ruth Lyttle Satter Prize, 449, 567 1320 Call for Nominations for Sloan Fellowships, 666 Robert G. Bartle (1927-2003), 239 Call for Nominations for Third World Academy of Sci William T. Tutte (1917-2002) (Arthur M. Hobbs and James ences, 1238 G. Oxley), 320 Call for Nominations for Waterman Award, 1362 William Ted Martin (1911-2004) (Allyn Jackson), 919 Call for Proposals for 2005 NSF-CBMS Regional Confer ences, 236 New Publications Offered by the AMS Call for Proposals for 2006 Joint Summer Research Con- 65,280,363,462,577,695,836,977,1098,1267,1380 ferences, 1115 Call for Submissions for Sunyer i Balaguer Prize, 806 Clay Mathematics Institute Liftoff Program, 237 Clay Senior Scholars Program, 666 CMI Liftoff Program for Summer 2005, 1362 Collaborations in Mathematical Geosciences, 49 Cryptology Paper Competitions, 237 Deadlines and Target Dates at the DMS, 48 Departments Coordinate Job Offer Deadlines, 50 Officers ofthe Society DMS Employment Opportunities, 238 566, 1082 EDGE Summer Program, 1361 Enhancing the Mathematical Sciences Workforce in the Opinion 21st Century, 805, 1074 Letter from the Editor, 7, 389, 1181 Humboldt Foundation Offers Fellowships, 1074 Letters to the Editor, 8, 182, 310, 390,494, 608, 734, 870, lAS/Park City Mathematics Institute, 235 1022, 1182, 1318 ICM 2006Travel Grants, 1237 Opinion, 181,309,493,607,733,869,1021,1317 Interdisciplinary Grants in the Mathematical Sciences, 235 Joint Initiative in Mathematical Biology, 666 Opportunities Maria Mitchell Women in Science Award, 551 2004 NSF-CBMS Regional Conferences, 551 Math in Moscow Scholarships Awarded, 918 AAUW Educational Foundation Fellowships and Grants, Mathematical Social and Behavioral Sciences, 442 1238 National Academies Internship Program, 235 American Mathematical Society Centennial Fellowships, NDSEG Fellowships, 1361 915, 1237 New NSF Funding Opportunities, 441 AMS-AAAS Mass Media Summer Fellowships, 1075 New NSF Program: Enhancing the Mathematical Sciences AMS Book Prize, 450 Workforce in the Twenty-First Century, 550 AMS Mentoring Workshop, 1364 News from AIM, 49 AMS Scholarships for "Math in Moscow", 805 News from BIRS, 667, 917 AP Calculus Readers Sought, 441 News from the Clay Mathematics Institute, 441 AWM Essay Contest, 1075 News from The Fields Institute, 1362 AWM Travel Grants for Women, 916 News from the IMA, 346, 667, 1363 Call for Applications: AMS Epsilon Fund, 1074 News from the International Centre for Mathematical Sci- Call for Nominations for 2004 Frank and Brennie Morgan ences, 442 AMS-MAA-SIAM Prize, 451, 569 News from the MBI, 49 Call for Nominations for 2005 Bocher Memorial Prize, News from the Mittag-Leffler Institute, 1362 Frank Nelson Cole Prize in Number Theory, Levi L. News from PIMS, 551, 917 Conant Prize, Ruth Lyttle Satter Prize, and Albert Leon News from the SAMSI, 49 Whiteman Memorial Prize, 449, 567 Newton Fellowship Program, 1364 Call for Nominations for the 2005 Fermat Prize, 1075 NSA Funding Opportunity in Quantum Computing Algo- Call for Nominations for Albert Leon Whiteman Memorial rithms, 1239 Prize, 449, 567 NSA Grant and Sabbatical Programs, 915, 1239 Call for Nominations for AWM Hay and Schafer Awards, NSF CAREER Program Guidelines Available, 666 667 NSF-CBMS Regional Conferences, Summer 2004, 236 Call for Nominations for B6cher Memorial Prize, 449, 567 NSF Distinguished International Postdoctoral Research Call for Nominations for Clay Research Fellows, 1074 Fellowships, 916 Call for Nominations for CRM-Fields Prize, 441 NSF Focused Research Groups, 805 DECEMBER 2004 NOTICES OF THE AMS 1425 20041ndex NSF Graduate Fellowships, 916 2004 AWM Schafer Prize (Kimberly Spears), 546 NSF Integrative Graduate Education and Research Train 2004 Balzan Prize (Pierre Deligne), 13 57 ing, 550 2004 Bergman Prize (Joseph]. Kohn), 343 NSF International Research Fellow Awards, 916, 1239 2004 Clay Research Fellows (Ciprian Manolescu, Maryam NSF Mathematical Sciences Postdoctoral Research Fellow- Mirzakhani, Andras Vasy, Akshay Venkatesh), 549 ships, 805 2004 Conant Prize (Noam D. Elkies), 433 NSF Postdoctoral Research Fellowships, 550 2004 d'Alembert Prize, 1072 ONR Young Investigator Program, 48 2004 Dirac Medals Games D. Bjorken, Curtis G. Callan), 1359 Project NExT: New Experiences in Teaching, 346 2004 Emil Artin Junior Prize (Gurgen R. Asatryan), 549 Research Experiences for Undergraduates, 917 2004 European Congress of Mathematicians Prizes (Franck Research Opportunities for U.S. Graduate Students in Asia, Barthe, Stefano Bianchini, Paul Biran, Elon Lindenstrauss, 1238 Andrei Okounkov, Sylvia Serfaty, Stanislav Smirnov, Stipends for Study and Travel, 928 Xavier Tolsa, Warwick Tucker, Otmar Venjakob), 1070 Summer Program for Women Undergraduates, 236 2004 Ferran Sunyer i Balaguer Prize (Guy David), 802 Training in Biological and Mathematical Sciences, 442 2004 Heineman Prize (Gabriele Veneziano), 661 Twentieth Reunion of Budapest Semesters Program, 1238 2004 IRMA Prize (Thomas Duquesne), 548 2004 Leibniz Prize (Frank Allgower), 803 2004 London Mathematical Society Prizes (De Morgan Medal-Roger Penrose; Senior Berwick Prize-Boris Zil ber; Naylor Prize-Richard Jozsa; Frohlich Prize-Ian Grojnowski; Whitehead Prizes-Mark Ainsworth, Vladimir Markovic, Richard Thomas, Ulrike Tillmann), 1072 2004 MAA Certificates of Meritorious Service (Richard Bar Prizes and Awards low, Underwood Dudley, Thomas Hem, John W. Kenelly, 2002 PECASE Awards (George G. Pappas, Robert W. Ghrist, Stephen Ligh), 545 Edmond Chow), 802 2004 MAA Gung and Hu Award (T. Christine Stevens), 544 2002 and 2003 NSF Career Awards (Scott Ahlgren, Guil 2004 MAA Haimo Award (Thomas Garrity, Andrew Chiang laume Bal, Luca Capogna, Donatella Danielli, John Et Fung Liu, Olympia Nicodemi), 544 nyre, Mohammad Ghomi, Robert Ghrist, Tilmann Gneit 2004 Moore Prize (Mark Haiman), 431 ing, Brendan Hassett, Jan Hesthaven, Ko Honda, Zhezhen 2004 NAS Award in Mathematics (Dan Virgil Voiculescu), Jin, Alexander Kiselev, Dmitry Kleinbock, Doron Levy, 547 Yi Lin, Sergey Lototsky, Yuri Lvov, Ranjan Maitra, Igor 2004 Parzen Prize (Jerome H. Friedman), 661 Mineyev, Madhu Nayakkankuppam, Ramani Pilla, Chiara 2004 Paul Erdos Award (Warren Atkins, Andre Deledicq, Sabatti, Sylvia Serfaty, Brooke Shipley, Gregory Smith, Patricia Fauring), 1072 Frank Sottile, Konstantina Trivisa, Ravi Vakil, Eric Van 2004 Prize for Achievement in Information-Based Com den Eijnden, Shankar Venkataramani, Jan Verschelde, plexity (Peter Mathe), 803 Van Vu, Thomas Witelski, Anthony Yezzi, Chongchun 2004 Rollo Davidson Prize (Ander Holroyd, Itai Benjamini), Zeng, Yijun Zuo), 46 661 2003 AAAS Award (John Allen Paulos), 548 2004 Sloan Fellows (Meredith D. Betterton, Roman 2003 AWM Essay Contest (Esther Feldblum, Jessica John, Bezrukavnikov, Kenneth Bromberg, Li-Tien Cheng, Sergei Shubin), 1360 Nathan M. Dunfield, Thomas]. Haines, Vadim Kaloshin, 2003 International Commission on Mathematical Instruc Rowan Killip, Mark Kisin, Ioannis Kontoyiannis, Lei Ni, tion Medals (Felix Klein Medal-Guy Brousseau; Hans Robert Seiringer, Knut Solna, Benny Sudakov, Jeff Via · Freudenthal Medal-Celia Hayles), 662 clovsky, Balint Virag, Divakar Viswanath, Kevin Whyte, 2003 Morgan Prize (Melanie Wood, Karen Yeats), 438 Ae ]a Yee, Chongchun Zeng), 663 2003 Oberwolfach Prize (Paul Biran), 660 2004 Steele Prizes (John W. Milnor, Lawrence C. Evans, Nico- 2003 Ostrowski Prize (Paul D. Seymour), 900 2003 PECASE Awards (Konstantina Trivisa, Ravi Vakil, lai V. Krylov, Cathleen Synge Morawetz), 421 Harry Dankowicz), 1359 2004 Veblen Prize (David Gabai), 426 2003 Prix Media (George Szpiro), 803 2004 Wiener Prize (James Sethian), 428 2003 Salem Prize (Elon Lindenstrauss and Kannan 2004~2005 AMS Centennial Fellowships (Jinho Baik, Nitu Soundararajan), 45 Kitchloo), 660 2004 Abel Prize (Michael Francis Atiyah and Isadore M. AAAS Fellows (Donald Ludwig, David W. Mclaughlin, Max Singer), 649 ine L. Rockoff, Annie Selden, Victor L. Shapiro), 234 2004 Adams Prize (Dominic Joyce), 802 American Academy of Arts and Sciences (David Aldous, 2004 AIM Five-Year Fellowship (Jacob Lurie), 548 Leonard Gross, Anatole Katok, Fang-Hua Lin, Yuri I. 2004 Award for Distinguished Public Service (Richard Marrin, Gang Tian, Nolan Wallach, Lai-Sang Young, Yves Tapia), 435 Colin de Verdiere), 804 2004 AWM Hay Award (Bozenna Pasik-Duncan), 546 AMS Menger Awards at the 2004 ISEF, 1235 1426 NOTICES OF THE AMS VOLUME 51, NUMBER 11 20041ndex AMS Menger Prizes at the 2004 ISEF, 913 ett, John Workman; (ONR) Megan Guichard, Bernard AWM Essay Contest Winners, 440, 1360 Mares, David Smyth), 1360 B. H. Neumann Awards (Anthony]. Guttman, Anna Nakos, Nobel Prize in Economic Sciences (Robert F. Engle, Clive Jamie Simpson), 1235 W. ]. Granger), 43 Carl-Erik Froberg Prize (Anna-Karin Tornberg), 1071 NSF Distinguished Teaching Scholar Award (Thomas F. Clay Awards (Richard Hamilton, Terence Tao), 234 Banchoff), 913 CRM-Fields Prize (Donald Dawson), 440 NSF Graduate Research Fellowships Announced, 663 Epsilon Awards for 2004, 553 ONR Young Investigator Award (Salil P. Vadhan), 1235 European Mathematical Society Article Competition 2003 Pi Mu Epsilon Student Paper Presentation Awards (Nuno Crato, F. Thomas Bruss, Sava Grozdev, Ivan (Stephanie Barille, Jeremy Hamilton, Colleen Hughes, Derzhanski, Evgenia Sendova), 345 Theodore Stadnik, Ryan Sternberg, Alyssa Wood), 1360 Fan and Caldwell Scholarships Awarded, 51, 1241 Popov Prize (Serguei Denissov), 1071 Fan China Exchange Program Awardees (Russell Thomp Prizes of the Academie des Sciences (Grand Prix Sophie Ger son, Yongqing Li, David Griffeath, Jian Zhong Pan, main: Henri Berestycki; Prix Jaffe: Colette Moeglin; Prix Bernard A. Mair, Shao-Ming Fei, Bernard Russo, Eo Dai), Paul Doistau-Emile Bluter: Laurent Stolovitch; Prix Ser 808 vant: Guy David; Prix Ayme Poirson: Bijan Mohammadi; Fermat Prize (Luigi Ambrosio), 234 Prix Blaise Pascal du Gamni-Smai: Albert Cohen; Prix French Academy of Sciences Prizes and Elections (Claire Jacques Herb rand: Nikita Nekrassov; Prix Leconte: Remi Voisin, Louis Boutet de Monvel, Wendelin Werner, Claude Monasson), 1359 Bardos, Gilles Lebeau, Damien Gaboriau, Jean-Marc De Prizes of the Mathematical Society of Japan (2004 Spring lort, Thierry Aubin, Laurent Lafforgue, Marc Yor), 344 Prize-Takashi Kumagai; Algebra Prize-Tomohide Tera Fulbright Awards (Subha Chakraborti, AbderrahmnElkhader, soma), 803 John B. Fink, Dennis]. Garity, Jason C.-H. Hsu, Anatoli F. Prizes of the Mathematical Society of Japan (Autumn Ivanov, Naihuan N. Jing, Joseph B. Kadane, Christopher Prize-Susumu Ariki; Geometry Prize-Kengo Hirachi, M. Kribs-Zaleta, Victor V. Pambuccian, Rahul A. Parsa, Shigenori Matsumoto; Analysis Prize-Masaki Izumi, Christopher P. Thron, Frederi G. Viens), 664 Masatoshi Fukushima, Kimio Miyajima; Takebe Senior Guggenheim Fellowships (Amir D. Aczel, Michael P. Bren Prize-Osamu Fujino, Akiko Shima, Minoru Itoh; Take be ner, Huai-Dong Cao, Panagiota Daskalopoulos, Russell Junior Prize-Song Liang, Reika Fukuizumi, Rei Inoue, · Impagliazzo, Michael T. Lacey, Manil Suri, William R. Tomomi Kawamura, Kenichi Bannai), 45 Zame, David Zuckerman), 664 Putnam Prizes (Reid W. Barton, Ana Caraiani, Gabriel D. Car Information-Based Complexity Young Researcher Award roll, Ralph C. Furmaniak, Daniel M. Kane), 803 (Frances Kuo), 46 Rhodes Scholarships Awarded (Olivia Rissland, Delavane International Mathematical Olympiad, Athens 2004, 1073 Diaz, Robin M. Rotman, Allison Gilmore, Decker Walker, MAA Carl B. Allendoerfer Award (Charles I. Delman, Gregory Galperin), 1234 Lara B. Anderson), 344 MAA Chauvenet Prize for Expository Writing (Edward B. Royal Society of Canada Elections (Stephen E. Fienberg, Burger), 1235 Jacques Hurtubise), 1073 MAA George P6lya Award (Greg N. Frederickson), 1234 Royal Society of London Elections (Samson Abramsky, Ju MAA Henry L. Alder Award for Distinguished Teaching lian Besag, David B. A. Epstein, David Priess), 914 (Francis E. Su, Zvezdelina Stankova), 1235 Shaw Prize (Shiing-Shen Chern), 1067 MAA Lester R. Ford Award (Noam Elkies, Charles Liv SIAM George P6lya Prize (Neil Robertson, Paul Seymour), ingston, R. Michael Range, Ruediger Thiele), 1234 1234 MAA Trevor Evans Award (Douglas Dunham, Hugh SIAM John von Neumann Lectureship (Alan C. Newell), McCague), 1234 1234 MacArthur Fellowship (Erik Demaine), 44 SIAM Prize for Distinguished Service to the Profession National Academy of Engineering Elections (Frank T. (Richard A. Tapia), 1234 Leighton, Linda R. Petzold, G. W. Stewart, John R. Willis), SIAM Richard C. DiPrima Prize (Diego Dominici), 1234 665 SIAM Theodore von Karman Prize (Roland Glowinski), National Academy of Sciences Elections (Joseph Bernstein, 1234 Phillip Colella, Stephen H. Davis, Shafrira Goldwasser, SIAM W. T. and Idalia Reid Prize (Arthur]. Krener), 1234 Benedict H. Gross, Nicholas M. Katz, Charles M. New Siemens Westinghouse Competition (Linda Westrick, Araceli man, George F. Oster, Ronald L. Rivest), 664 Fernandez, Yiduo "David" Wang, Hannah Chung), 345 National High School Calculus Student Award (Ryan Templeton Prize (George F. R. Ellis), 1072 Williams), 1360 Third World Academy of Sciences Prizes (Wellington Celso National Medal of Science (James G. Glimm, Edward Wit de Melo, Rodolfo Gambini), 234 ten), 215 Trjitzinsky Memorial Awards (Thida S. Aye, Andrew Richard NDSEG Fellowships (AFOSR) Samuel Isaacson, Tiffany Tackmann, Maria Chris tin Llewellyn, Rahbar Virk, Sarah Psemeneki, Nitin Saksena, Bryan Smith, Paul Valiant; Deiwert, Angela Martinho, Timothy P. Lewis, Bishal (ARO) William Fong, Jayce Getz, Paul Hand, Philip Match- Thapa), 47 DECEMBER 2004 NOTICES OF THE AMS 1427 20041ndex von Neumann Prize (Arkadi Nemirovski, Michael]. Todd), Four Colors Suffice: How the Map Problem Was Solved (Re 344 viewed by Bjarne Toft), 205 Gamma (Reviewed by Dan Segal), 768 The Profession Geometry: Our Cultural Heritage (Reviewed by H. Wu), 2003 Annual Survey of the Mathematical Sciences (First Re 529 port), 218 Gddel's Proof(Reviewed by Timothy McCarthy), 333 2003 Annual Survey of the Mathematical Sciences (Second (A) Handbook of Mathematical Discourse (Reviewed by Report), 789 Steven G. Krantz), 896 2003 Annual Survey of the Mathematical Sciences (Third Math through the Ages: A Gentle History for Teachers and Report), 901 Others (Reviewed by Philip C. Curtis Jr.), 1057 Backlog of Mathematics Research Journals, 924 (A) Mathematician's Survival Guide: Graduate School and Communicating with Congress: An Interview with James Early Career Development (Reviewed by Elizabeth Theta H. Turner Jr., 645 Brown), 417 Doctoral Degrees Conferred 2002-2003, 246 (The) Mathematics ofjuggling (Reviewed by Allen Knutson), Doctoral Degrees Conferred 2002-2003, Supplementary 35 List, 801 (The) New Science of (Random) Networks (Reviewed by Doctorate Degrees in Mathematics Earned by Blacks, His Rick Durrett), 201 panics/Latinos, and Native Americans: A Look at the Review of Sync: The Emerging Science of Spontaneous Numbers, 772 Order(G. Bard Ermentrout), 312 (The) Elephant in the Internet, 1217 (A) Sometimes Funny Book Supposedly about Infinity-A Experimental "Current Events" Session at the Joint Meet Review of Everything and More (Reviewed by Michael ings, 51 Harris), 632 Has Math Funding Hit the Deficit Wall?: NSF Fiscal Year Strange Curves, Counting Rabbits, and Other Mathemati 2005 Budget Request, 651 cal Explorations (Reviewed by Harold R. Parks), 1352 Has the Women-in-Mathematics Problem Been Solved?, 776 Stipends for Study and Travel, 928 Mathematical Sciences in the FY 2005 Budget, 656 Mathematics and the Public, 1181 Surveys Recommendations for Increasing the Participation and 2003 Annual Survey of the Mathematical Sciences (First Re Success of Blacks in Graduate Mathematics Study, 538 port), 218 Research Mathematicians and Mathematics Education: A 2003 Annual Survey of the Mathematical Sciences (Second Critique, 403 Report), 789 RIMS, an Institute for Japan and the World, 194 2003 Annual Survey of the Mathematical Sciences (Third Societe Mathematique de France, 1231 Report), 901 Some of What Mathematicians Do, 1226 Doctoral Degrees Conferred 2002-2003, 246 Statistics on Women Mathematicians Compiled by the AMS, 1372 Table of Contents Women in Academia: Are We Asking the Right Questions?, 5, 179,307,387,491,605,731,867,1019,1179,1315 784 Visiting Mathematicians, 816 WHAT IS ... WHAT IS a Billiard? (Yakov Sinai), 412 WHAT IS an Expander? (Peter Sarnak), 762 WHAT IS a Flip? (Alessio Corti), 1350 WHAT IS a Free Lunch? (Freddy Delbaen and Walter Schachermayer), 526 WHAT IS a Grope? (Peter Teichner), 894 Reference and Book List WHAT IS a Motive? (Barry Mazur), 1214 53,241,349,445,554,670,809,920,1077,1242,1367 WHAT IS an Operad? (Jim Stasheff), 630 WHAT IS a Quasi-morphism? (D. Kotschick), 208 Reviews WHAT IS a Topos? (Luc Illusie), 1060 Abel's Proof: An Essay on the Sources and Meaning of Math ematical Unsolvability (Reviewed by Lars Garding), 331 Beyond the Limit: The Dream of Sofya Kovalevskaya (Re viewed by Ann Hibner Koblitz), 39 (The) Constants ofNature and Just Six Numbers (Reviewed by Brian E. Blank), 1220 Count Down (Reviewed by Daniel Ullman), 764 1428 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Cosponsored Conferences AAAS Meeting to Offer Strong Mathematics Program The 2005 Annual Meeting of the American Association for the generous contributions of AMS for travel support and the Advancement of Science, February 17-21, in Washing SlAM for support of media awareness.) In presenting math ton, DC, will feature many outstanding expository talks by ematics-related themes to the AAAS Program Committee, prominent mathematicians. These include the following I have found the committee to be genuinely interested in three-hour symposia (and organizers) sponsored by Sec offering symposia on mathematical topics of current in tion A (Mathematics) of the AAAS: terest. Thus, Section A's committee seeks organizers and speakers who can present substantial new material in an • Mathematical Oncology: Bridging the Scientific Divide accessible manner to a large scientific audience. Toward (Kristin Swanson, University of Washington) this end, I invite you to attend our Section A Committee • Understanding the Interaction of Noise in Complex Sys business meeting 7:45 p.m.-10:45 p.m. Friday, February 18, tems (Rachel Kruske, University of British Columbia) 2005, at the Marriott Wardman park Hotel (room to be de • Mapping the Human Brain from Infancy to Old Age termined). I invite you also to send me, and encourage your (Paul Thompson, UCLA School of Medicine) colleagues to send me, symposia proposals for future • Finding and Keeping Graduate Students in the Mathe AAAS annual meetings. matical Sciences (Amy Cohen, Rutgers University) -Warren Page, secretary of Section A of the AAAS Other symposia that will be of interest to the mathemati [email protected] cal community include: Mathematics and Human Infectious Disease Something from Nothing? Scientific Inference and Missing Data Complex Adaptive Systems: Advances in Theory and Practice Mathematics and Biology 2010: Linking Undergraduate Disciplines Einstein in Historical and Philosophical Perspective Astrotomogaphy Continuing to Learn from TIMSS and Now Also from PISA The above symposia are only a few of the 150 or so AAAS program offerings in the physical, life, social, and biological sciences. For further details about the 2005 AAAS program, see the October 8, 2004, issue of Science. AAAS annual meetings are the showcases of American science, and they encourage participation by mathemati cians and mathematics educators. (AAAS acknowledges DECEMBER 2004 NOTICES OF THE AMS 1429 Meetings and Conferences of the AMS Associate Secretaries ofthe AMS Western Section: MichelL. Lapidus, Department of Math Eastern Section: Lesley M. Sibner, Department of Mathe ematics, University of California, Sproul Hall, Riverside, CA matics, Polytechnic University, Brooklyn, NY 11201-2990; 92521-0135; e-mail: l api dus@math. ucr. edu; telephone: 909- e-mail: lsi bne r@duke. poly. edu; telephone: 718-260-3 505. 787-3113. Southeastern Section: John L. Bryant, Department of Math Central Section: Susan J. Friedlander, Department of Math ematics, Florida State University, Tallahassee, FL 32306-4510; ematics, University of Illinois at Chicago, 851 S. Morgan (MIC e-mail: bryant@math. fsu. edu; telephone: 850-644-5805. 249), Chicago, lL 60607-7045; e-mail: susan@math. nwu. edu; tele phone: 312-996-3041. The Meetings and Conferences section of the Notices 2008 gives information on all AMS meetings and conferences January 6-9 San Diego, California p. 1412 approved by press time for this issue. Please refer to the page Annual Meeting numbers cited in the table of contents on this page for more 2009 detailed information on each event. Invited Speakers and January 7-10 Washington, DC p. 1412 Special Sessions are listed as soon as they are approved by Annual Meeting the cognizant program committee; the codes listed are needed 2010 for electronic abstract submission. For some meetings the list January 6-9 San Franciso, California p. 1412 may be incomplete. Information in this issue may be dated. Annual Meeting Up-to-date meeting and conference information can be 2011 found at www. ams. orglmeeti ngsl. January 5-8 New Orleans, Louisiana p. 1412 Annual Meeting Meetings: 2005 Important Information regarding AMS Meetings January 5-8 Atlanta, Georgia p. 1403 Potential organizers, speakers, and hosts should refer to Annual Meeting page 84 in the January 2004 issue of the Notices for general March 18-19 Bowling Green, Kentucky p. 1404 information regarding participation in AMS meetings and April2-3 Newark, Delaware p. 1405 conferences. April8-10 Lubbock, Texas p. 1406 Abstracts April16-17 Santa Barbara, California p. 1407 Several options are available for speakers submitting June 16-19 Mainz, Germany p. 1407 abstracts, including an easy-to-use interactive Web form. No October 8-9 Annandale-on- Hudson, knowledge of 0f£X is necessary to submit an electronic form, New York p. 1409 although those who use 0f£X may submit abstracts with October 15-16 Johnson City, Tennessee p. 1409 such coding, and all math displays and similarily coded ma October 21-22 Lincoln, Nebraska p. 1409 terial (such as accent marks in text) must be typeset in LA:f£X. November 12-13 Eugene, Oregon p. 1410 To see descriptions of the forms available, visit http: I I December 14-18 Taiwan p. 1410 www. ams. orglabstractsli nstructi ons. html, or send mail to abs-submi t@ams. org, typing help as the subject line; de 2006 scriptions and instructions on how to get the template of your January 12-15 San Antonio, Texas p. 1410 choice will be e-mailed to you. Annual Meeting Completed email abstracts should be sent to abs-submi t@ April 22-23 Durham, New Hampshire p. 1411 ams. org, typing submission as the subject line. Questions about April29-30 San Francisco, California p. 1411 abstracts may be sent to abs-i nfo@ams. or g. Paper abstract forms may be sent to Meetings & Confer November 3-4 Fayetteville, Arkansas p. 1411 ences Department, AMS, P.O. Box 6887, Providence, RI 02940. There is a $20 processing fee for each paper abstract. There 2007 is no charge for electronic abstracts. Note that all abstract dead January 4-7 New Orleans, Louisiana p. 1411 lines are strictly enforced. Annual Meeting Conferences: (see http: I lwww. ams. o rglmeeti ngsl for the most up-to-date information on these conferences.) June 5-July 21, 2005: Joint Summer Research Conferences in the Mathematical Sciences, Snowbird, Utah (see November 2004 Notices, page 1294). July 25-August 12, 2005: Summer Research Institute on Algebraic Geometry, Seattle, Washington (see November 2004 Notices, page 1293). Co-sponsored conference: June 2006: Fifth Conference on Poisson Geometry, Tokyo, Japan (watch http: I ltmugs. math. metro-u. ac. jplgeneral. html for future information). 1430 NOTICES OF THE AMS VOLUME 51, NUMBER 11 Joint Mathematics joint Meetings Advance Registration/Housing Form Meetings Name (please write name as you would like it to appear on your badge) ATLANTA, GEORGIA January 5 - 8, 2005 Mailing Address------ Membership v- all that apply. 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A A / / _ r e and 174 136 184 156 11 119 10 beds t N N o $99 Quad Quad $ $ $ $ $ $ $ the _ 2 y sui il listed. ype check t n o am f ____ not Date s l l th _ i room through 9 9 A w/cot w 26 / _ 109 11 please hote Exp. 164 detai 199 1 10 N $ $ $ $ $ $164 $204 $136 $ r w/cot) Triple a (queen _ fo made date. King at vately . ri er be t _ _ __ p requested a l _ _ a directly w/cot the A A A A A A A must / / / / / _ / / _ at 119 109 N N N N N N N/A N els reservation, $ $ Triple staying _ reservations beds ______ a guarantee hot _ Date Date be 2 with hotels circling _ the own by will ng _ ll card eservation room r or my ca _ a a and making double / to ollowi _ sleeper) f Departure area are left 36 Departure Departure credit h not he 1 109 beds t of make s $99 $99 with making $164 $199 $126 $164 $204 $ $ Triple the a 2 __ the urged tax. at to to (Double n i be are _ or on l King l ______ are an l Time 109 p plan live wi or $ sales mn _ I I I I you __ lu o o o o If form) and co _ 14% 6 __ of a Reservations the 144 11 144 beds $99 _ $99 $89 $ $179 $ $184 $116 to Participants 2 _ Date _ __ Double in t . , _ _ _ c. t the rate listed. e reverse , e t. Number i to l subjec Date Date 3 __ es 6 $ __ ---- t e l on 2, bed _ 144 11 144 184 116 ra are _ - $99 cred $89 $ $179 1 $ $ $ Card Signature 1, Double __ Arrival Arrival Reservations rates __ ting comparab rd ri accessib _ a w _ All 6 $ ca is payment at 144 116 144 184 11 convention _ by $99 $99 $99 $99 $99 $99 $89 $ $179 $ $ $ $ ------appropriate __ Single to that rate. ----- - the _ credit hotel __ - ve i my (add room _ receive __ eference higher r Hotel ith _ to p rece a --- _ w e of _ to to - unranked _ ik l eeping l old check Rooms - or s H Rooms a by __ order __ o MMSB n would i -- _ _ changed anked r Regular the a and require - be Regular __ ------ hotels - at deposit that _ - club may ____ rank through _ room Hotel _ ADA night a form) -- _ Meetings (co-hqtrs) hotels ------ Peachtree only of l (co-hqtrs) _ the are: are: please - r ve the . the First Downtown by - front Le at made Downtown assigned ents, frequent-travel Marquis with needs Atlanta Occupant Occupant be numbe Inn (see be nm Level otel Atlanta My defined ill h Arrival can . w Joint card Atlanta a as Requests: directly assig Club Student Concierge Student Inn Marriott Room Room of of ______ Regency es you Inn and Western , iti enclosed requirements: made Time Hyatt Best Atlanta Holiday AmeriSuites Days Other Other accurate challenged chain Housing member disabil reservations requests: e of of r a Deposit available and 0 hotel er have am suite ensu e choice I I Other , Order Guarantee Th long Reservations er of To o Date Name 0 o Name physically Atlanta Special ADVERTISERS' Society for Industrial and Applied Mathematics FORUM <{~l~DEo'' AMS AMERICAN MATHEMATICAL SOCIETY www.siam.org/membershiplindmem.htm Pacific Institute for the Mathematical Sciences Promoting the Mathematical Sciences in the Pacific Northwest. www.ams.org/bookstore Web: http://www.pims.math.ca Email: [email protected] The American S tatistical Association Founded in 1839, the ASA is the nation's leading professional association for statistics and statisticiam. 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Springer ...... cover 4 NEW AND NOTEWORTHY GALl LEO COMBINATORIAL MARTINGALE GALl LEI COMMUTATIVE ALGEBRA METHODS IN When the World EZRA MILLER, University of Minnesota, Minneapolis and BERND STURMFELS, University of California at FINANCIAL Stood Still Berkeley ATLE NAESS, Ski, Norway MODELLING This book provides an introduction to SECOND EDITION "I, Cali! eo, son of the late combinatorial commutative algebra with MAREK MUSIELA, BNP Vincenzio Galilei, particular emphasis on combinatorial Paribas, London, UK and Florentine, aged seventy techniques for multigraded polynomial rings, MAREK RUTKOWSKI, years ... kneeling before Warsaw University of semi group algebras, and determined rings. 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