ISSN 0002-9920

of the American Mathematical Society February 2006 Volume 53, Number 2

Math Circles and Olympiads MSRI Asks: Is the U.S. Coming of Age? page 200

A System of Axioms of Set Theory for the Rationalists page 206

Durham Meeting page 299

San Francisco Meeting page 302

ICM Madrid 2006 (see page 213) > To mak• an antmat•d tub• plot Animated Tube Plot 1 Type an expression in one or :;)~~~G~~~t;~~i~~~~~~~~~~~~~:rtwo ' 2 Wrth the insertion point in the 3 Open the Plot Properties dialog the same variables Tl'le next animation shows • knot Plot 30 Animated + Tube

Scientific Word

... version 5.5

Scientific Word"' offers the same features as Scientific WorkPlace, without the computer algebra system. Editors INTERNATIONAL Morris Weisfeld Editor-in-Chief Enrico Arbarello MATHEMATICS Joseph Bernstein Enrico Bombieri Richard E. Borcherds Alexei Borodin RESEARCH PAPERS Jean Bourgain Marc Burger James W. Cogdell http://www.hindawi.com/journals/imrp/ Tobias Colding Corrado De Concini IMRP provides very fast publication of lengthy research articles of high current interest in Percy Deift all areas of mathematics. All articles are fully refereed and are judged by their contribution Robbert Dijkgraaf to the advancement of the state of the science of mathematics. Issues are published as S. K. Donaldson frequently as necessary. Each issue will contain only one article. IMRP is expected to publish 400± pages in 2006. Yakov Eliashberg Edward Frenkel Articles of at least 50 pages are welcome and all articles are refereed and judged for Emmanuel Hebey correctness, interest, originality, depth, and applicability. Submissions are made by e-mail to Dennis Hejhal [email protected]. An abstract for each article should be included. A copy may also Helmut Hofer be sent to an editor. Only an acknowledgment from the editorial office officially establishes Gerhard Huisken the date of receipt. Submissions not prepared using TeX should be typed or printed on one Yasutaka Ihara side of the page, be double-spaced (including references), and have ample margins. Check Michio Jimbo contact information for submission by fax or post. When articles are accepted, production Kurt Johansson begins immediately; authors should be available to assist the editorial staff. Masaki Kashiwara Please note that it is a condition of submission of a paper that the author(s) permit editing Kiran S. Kedlaya the paper for language correctness, readability, and compliance with the IMRP mathematical Carlos Kenig style. Sergiu Klainerman Illustrations can be in color. There are no page charges. Each author shall receive 100 Toshiyuki Kobayashi complimentary reprints with covers. Maxim Kontsevich Igor Krichever Recently Published Articles Shigeo Kusuoka Gilles Lebeau • Degasperis-Procesi Peakons and the Discrete Cubic String, Joachim Lohkamp Hans Lundmark and Jacek Szmigielski John Lott • Mckay's Observation and Vertex Operator Algebras Generated by Tvvo Conformal Vectors Nikolai Makarov of Central Charge 1/2, Ching Hung Lam, Hiromichi Yamada, and Hiroshi Yamauchi Yu. I. Manin • Graded Multiplicities in the Macdonald Kernel. Part I, John R. Stembridge Barry Mazur Haynes Miller • Bost-Connes-Marcolli Systems for Shimura Varieties. Part I. Definitions and Formal Shinichi Mochizuki Analytic Properties, Eugene Ha and Frederic Paugam Fabien Morel • The Ci-Approach to Approximate Inverse Scattering at Fixed Eric Opdam Energy in Three Dimensions, R . G. Novikov Michael Rapoport • The Blowup Behavior of the Biharmonic Map Heat Flow N. Yu. Reshetikhin in Four Dimensions, Roger Moser Igor Rodnianski Peter Sarnak Subscription Information Freydoon Shahidi Stanislav Smirnov Subscription E-mail: [email protected] Michael Struwe Institutional subscription rates for 2006 (400± pages) are $195.00 for online only, $214.50 G. Tian for print only, and $234.00 for both online and print editions. Subscribers to the online John Toth only edition or to the print and online editions of the journal in 2006 will get perpetual Takeshi Tsuji access to volumes 2005-2006 (i.e., permanent online access to volumes 2005-2006 even if the David Vogan subscription is canceled in the future). Dan-Virgil Voiculescu All orders should be accompanied by payment and sent to Hindawi Publishing Corporation, Andrei Zelevinsky 410 Park Avenue, 15th Floor, #287 pmb, New York, NY 10022, USA. Maciej Zworski

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ToRies in the Theory of Vortices in Bose-Einstein Introduction to Plane Alg:ebraic Function Fields Condensates Algebraic Curves GABRIEL DANIEL VILLA SALVADOR, C/NVESTAV del lPN, AMANDINE AFTALION, CNRS, Laboratoire Jacques-Louis ERNST KUNZ, University of Regensburg, Germany MexicOCity, Mexico Lions, Paris, France RICHARD G. BELSHOFF, Southwest Missouri State University, Springfield, MO (Translator) Algebraic function fields of one variable are used in One of the key issues related to superfluidity is the This work treats an introduction to commutat several areas of mathematics: complex analysis, existence of vortices. In very recent experiments on ive ring theory and algebraic plane curves, algebraic geometry, and number theory. This text Bose- Einstein condensates, vortices have been requiring of the student only a basic knowledge of algebra, applies an arithmetic-algebraic viewpoint to the study of observed in various conditions. This monograph is with all of the algebraic facts collected into severa function fields as part of the algebraic theory of dedicated to the mathematical modeling of these l appendices that can be easily referre numbbrs. The author does not ignore the geometric and phenomena. The mathematical tools employed are d to, as needed. Kunz's proven conception of teaching topics analytic aspects of function fields, but focuses on an in­ energy estimates, Gamma convergence, and in commutative algebra together with their applications to algebra depth examination from a number-theoretic perspec­ homogenization techniques. The mathematical analysis ic geometry makes this book tive. The exposition explains both the similarities and is made in the framework of the Gross- Pitaevskii significantly different from others on plane algebraic curves. fundamental differences between function fields and energy. Results are presented and open problems number fi elds, including many examples to motivate related to recent experiments are explained. From a review of the German edition: "The reader unde~standing and further study. The only prerequisites is invited to learn some topics from commutative ring are abasic knowledge of field theory, complex analysis, 2006/APPROX. 160 PP., 2S ILLUS./HARDCOVER theory by mainly studying their illustrations and and some commutative algebra. ISBN 0-8176-4392-3/$79.95 (TENT.) applications in plane curve theory. ... The whole text is a PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS real masterpiece of clarity, rigor, comprehension, The book can serve as a text for a graduate course in AND THEIR APPLICATIONS methodical skill, algebraic and geometric motivation .. number theory or an advanced graduate topics course. highly enlightening, motivating and entertaining at the Alternatively, chapters 1-4 can serve as the base of an same time. .. One simply cannot do better in writing introductory undergraduate course for mathematics Conformal Groups in Geometry such a textbook. " - ZENTRALBLATT MATH majors, while chapters 5-10 can support a second and Spin Structures course for advanced undergraduates. Researchers 2005/293 PP., 52 ILLUS./SOFTCOVER PIERRE ANGLES, Universite Paul Saba tier, Toulouse, France interested in number theory, fi eld theory, and their ISBN 0-81 76-4381-8/$59.95 interJctions will also find the work an excellent Conformal groups play a key role in geometry and spin reference. structures. This book provides a self-contained Compactifications of overview of this important area of mathematical physics, 2006/APPROX. 685 PP., 20 ILLUS./HARDCOVER beginning with its origins in the works of Cartan and Symmetric and Locally ISBN 0-8176-4480-6/$69.95 (TENT.) Chevalley and progressing to recent research in spinors Symmetric Spaces and conformal geometry. All the major aspects of the A. BOREL; LIZHEN JI, University of Michigan, field are introduced, followed by detailed descriptions Ann Arbor, Ml and definitions. Rich in exercises- accompanied by full Noncompact symmetric and locally symmetric spaces Vortices in the Magnetic proofs and hints,--the book will provide further naturally appear in many mathematical theories, directions for study and research. including analysis (representation theory, nonabelian Ginzburg-Landau Model harmonic analysis), number theory (automorphic ETIENNE SANDIER, Universite Paris-12 Val-de-Marne, 2006/APPROX. 320 PP., 40 ILLUS./HARDCOVER forms), algebraic geometry (modulae) and algebraic Creteil, France; SYLVIA SERFATY, CMLA, Ecole Normale ISBN 0-8176-3512-2/$89.95 (TENT.) topology (cohomology of discrete groups). ln most Superieure de Cachan, France PROGRESS IN MATHEMATICAL PHYSICS applications it is necessary to form an appropriate The Ginzburg-Landau (G- L) functional has become an compactification of the space. The literature dealing important phenomenological model since its Introduction to Complex with such compactifications is vast. The main purpose of confirmation both theoretically and experimentally. It Analysis in Several Variables this book is to introduce uniform constructions of most describes the phase transition occurring in certain of the known compactifications with emphasis on their VOLKER SCHEIDEMANN, Marburg, Germany metals from a normal conducting state to a geometric and topological structures. superconducting state. This text describes the critical This book is an introduction to complex analysis in seve­ 2006/496 PP./HARDCOVER points of the G- L functional of superconductivity in two ral variables, focusing on special topics rather than trying ISBN 0-8176-3247-6/$79.95 dimensions in terms of vortices, introducing tools for to encompass a comprehensive treatment of the sub­ MATHEMATICS: THEORY & APP LICATIONS analyzing certain complex situations. The material ject. Many cross references to other areas of mathema­ presented requires basic knowledge of Sobolev spaces tics, such as functional analysis or algebra, are pointed Modern Differential Geometry and linear elliptic theory. The book is aimed at out in order to broaden the view and understanding of mathematicians, physicists, and graduate students the chosen topics. Containing many examples and suppor­ in Gauge Theories interested in this very active field of research. ting exercises, the book is primarily aimed at students Yang-Mills Fields, Volume II starting to work in the field of complex analysis in several ANASTASI OS MALLIOS, University of Athens 2006/APPROX. 250 PP./HARDCOVER variables and instructors preparing university courses. Panepistimioupolis, Athens, Greece ISBN 0-8176-4316-8/$69.95 (TENT.) PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS 2005/180 PP./SOFTCOVER 2006/APPROX. 304 PP./SOFTCOVER AND THEIR APPLI CATION S ISBN 3-7643-7490-X/$34.95 ISBN 0-8176-4379-6/$119.00 (TENT.)

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Feature Articles 200 Math Circles and Olympiads MSRI Asks: Is the U.S. Coming of Age? ]ames Tanton Math circles are extracurricular school organizations of students and mentor teachers that explore mathematics. The author reports on several different models of such organizations, and on a recent conference about them.

206 A System of Axioms of Set Theory for the Rationalists ]an Mycielski The author proposes and discusses a system of axioms for set theory based on his principle that logic and set theory constitute a framework for describing reality consistent with evolving human natural perception.

Communications Commentary

218 In High Gear: Spanish Mathematics 197 Opinion: Welcome to Madrid for Looks to the Future-and to ICM2006: The Spanish Mathematics ICM2006 Fiesta Allyn jackson Manuel de Leon 223 InterviewwithPeterD.Lax 1 98 Letters to the Editor Martin Raussen and Christian Skau 21 5 PopCo-A Book Review 2 30 2 00 5 Annual Survey of the Reviewed by Alex Kasman Mathematical Sciences (First Report) Ellen E. Kirkman, ]ames W. Maxwell, and Colleen Rose Notices Departments Mathematics People ...... 246 Colmez and Le Gall Awarded Fermat Prize, AAAS Fellows EDITOR: Andy Magid Elected, NSF Graduate Fellowships Awarded. ASSOCIATE EDITORS: Susanne C. Brenner, Bill Casselman (Graphics Editor), Mathematics Opportunities ...... 248 Robert]. Daverman, Nathaniel Dean, Ri ck Durrett, NSF-CBMS Regional Conferences, 2006; Call for Proposals for Susan Friedlander, Robion Kirby, Steven G. Krantz, 2007 NSF-CBMS Regional Conferences; National Academies Elliott H. Lieb, Mark Saul, Karen E. Smith, Audrey Terras, Lisa Traynor Research Associateship Programs, National Academies SENIOR WRITER and DEPUTY EDITOR: Graduate Fellowship Program, ONR Young Investigator Allyn jackson Pr ogram, Clay Mathematics Institute 2006 Summer School. MANAGING EDITOR: Sandra Frost Inside the AMS ...... 251 CONTRIBUTING WRITER: Elaine Kehoe AMS Congr essional Briefing: How Mathematics Helps Predict PRODUCTION ASSISTANT: Muriel Toupin Storm Su rges, AMS Email Suppor t for Fr equently Asked PRODUCTION: Kyle Antonevich, Stephen Moye, Questions, Deaths of AMS Members. Erin Murphy, Lori Nero, Arlene O'Sean, Karen Ouellette, Donna Salter, Deborah Smith, Peter Sykes Reference and Book List ...... 254 ADVERTISING SALES: Anne Newcomb Doctoral Degrees Conferred (2004-2005) ...... 258 SUBSCRIPTION INFORMATION: Subscription prices for Volume 53 (2006) are US$430 list; US$344 institu­ tional member; US$258 individual member. (The sub­ Mathematics Calendar ...... 284 scription price for members is included in the annual dues.) A late charge of 10% of the subscription price New Publications Offered by the AMS ...... 288 will be imposed upon orders received from nonmem­ bers after January 1 of the subscription year. Add for postage: Surface delivery outside the United States Classified Advertisements ...... 294 and lndia- US$20; in lndia- US$40; expedited delivery to destinations in North America- US$35; elsewhere­ General Information Regarding Meetings & US$87. Subscriptions and orders for AMS publications Conferences of the AMS ...... 296 should be addressed to the American Mathematical Society, P.O . Box 845904, Boston, MA 02284-5904 USA. All orders must be prepaid. Meetings & Conferences of the AMS ...... 297 ADVERTISING: Notices publishes situations wanted and classified advertising, and display advertising for Meetings and Conferences Table of Contents ...... 311 publishers and academic or scientific organizations. Advertising material or questions may be faxed to 401-331-3842 (indicate " Notices advertising" on fax cover sheet). SUBMISSIONS: Articles and letters may be sent to the editor by email at noti ces@mat h. ou. edu, by fax at 405-325-5765, or by postal mail at Department of Mathematics, 601 Elm, PHSC 423, University of Okla­ homa, Norman, OK 73019-0001. Email is preferred. Correspondence with the managing editor may be sent to noti ces@ams . o rg. For more information, see the section "Reference and Book List". From the NOTICES ON THE AMS WEBSITE: Most of this publi­ cation is available electronicall y through the AMS web­ AMS Secretary site, the Society's resource for delivering electronic products and services. Use the URL htt p : I / www . ams . o rg/ noti ces/ to access the Notices on the website. 2005 Election Results ...... 278

]Notices of the American Mathematica l Society (I SSN 0002· 9920) is published monthlyexceptbimonthJyinjune/ July by Call for Suggestions for 2006 AMS Elections ...... 279 the American Mathemati cal Society at 201 Charles Street, Prov· idence, R1 02 904·2294 USA, GST No. 12189 2046 RT* *** . Pe­ Nomination Petition for 2006 Election ...... 280 riodicals postage paid at Providence, Rl , and additional mail­ ing offices. POSTMASTER: Send address change notices to Notices o{theAmerican Mathematica l Society, P.O. Box 6248, Call for Nominations for AMS Exemplary Program Prize ..... 282 Providence, Rl 02 940-6248 USA. ! Publication here of the So­ ciety's street address and the other information in brackets above is a technical requirement of the U.S. Postal Service. Tel: Call for Nominations for leroy P. Steele Prizes ...... 283 401-455·4000, email: noti ces@ams. org. © Copyright 2006 by the Ameri can Mathematical Society. All rights reserved. Printed in the Uni ted States of America.The paper used in this journal is acid-free and fall s within the gu ideli nes 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 policies of the Ameri can Mathematical Society. Opinion

during the first third of the twentieth century, Spanish sci­ Welcome to Madrid for ence, and mathematics in particular, experienced a period of development known as the Edad de Plata, or "Age of Sil­ ICM2006: The Spanish ver", of which the Junta de Ampliaci6n de Estudios, or Council for the Extension of Studies, formed the corner­ stone. Spanish progress in science is also very recent, but Mathematical Fiesta in the case of mathematics it has been nothing short of The International Congress of Mathematicians will be held spectacular. If we consider that in 1980 the contribution for the first time in Madrid, Spain, August 22-30, 2006. of Spanish mathematicians accounted for a mere 0.3 per­ The Spanish mathematics community is delighted to be cent of all articles and papers published in lSI (Institute hosting this event and wishes to extend its warmest wel­ of Scientific Information) journals and compare this with come to mathematicians from all over the world. It will be the figure for the five-year period 2000-2004, which rose without doubt not only the most important mathematical to 4.83 percent, we have an idea of the progress achieved event ever held in Spain but probably the greatest in any in Spanish mathematical research. scientific discipline in this country. The ICM2006 in Madrid Furthermore, the complex social organization of Span­ follows the International Congress on Mathematical Edu­ ish mathematics is a highly articulated structure. The pi­ cation held in Seville in 1996 and the Third European Con­ oneering mathematical body in this field is the Royal Span­ gress of Mathematics held in Barcelona in 2000. Although the venue for the ICM2006 will be Madrid, the ish Mathematical Society, whose founding in 1911 Spanish Mathematical Committee regards it as a collective culminated a process started in 1903. In 1931 the Catalan project embracing the whole country, a fact that is borne Society for Physics, Chemistry, and Mathematics was out in the following two ways: the broad cross-section of founded within the Institute of Catalan Studies; the Cata­ members making up the Organizing Committee and the lan Mathematical Society, as an independent body, was cre­ financial support provided by all the mathematics de­ ated in 1986. More recently, other societies have appeared partments in Spanish universities. on the scene, such as the Society of Statistics and Opera­ The preparations for the congress have received in­ tions Research (1961), the Spanish Society of the History valuable support, not only from the city of Madrid, but also of Techniques and Sciences (197 4), the Spanish Federation from government bodies at the regional and national lev­ of Teachers of Mathematics (1989), the Spanish Society of els. From the very beginning of our candidacy, the head Applied Mathematics (1991), and the Spanish Society for of state, His Majesty D. Juan Carlos I, king of Spain, gave Research in Mathematical Education (1996). They all par­ his backing to the event, and the Organizing Committee ticipate in the Spanish Mathematical Committee (CeMAT, has requested the honor of his presence at the opening cer­ http: I lwww. ce-mat. org), which represents Spain in the emony as well as at the award presentations of the Fields, International Mathematical Union (IMU) and whose struc­ Nevanlinna, and Gauss Medals. Furthermore, the commit­ ture is based on that of the IMU itself, providing a point tee has received vital funding from the community of of encounter for secondary and university education as well Madrid, from the Madrid City Council, and from the Min­ as for research. Some 8,500 mathematicians are repre­ isteries of Education and Foreign Affairs. sented in CeMAT. Given Spain's geopolitical location, the Organizing Com­ The venue for the Madrid ICM is the Palacio Municipal mittee has outlined three main axes for the ICM2006: the de Congresos, a spectacular marble building designed by European axis, symbolized by the holding of the General the Spanish architect Ricardo Bofill, an example of the mod­ Assembly, which will take place prior to the ICM, in the ern, open Spain that has been forged since the transition city of Santiago de Compos tela, renowned for the Road to to democratic rule. Organized around the congress will be Santiago or Pilgrim's Way, an artery of European science over fifty satellite conferences, the highest number in the and culture in the Middle Ages; the Latin American axis, history of the ICM, many of them held in different parts an integral part of Spanish history and culture; and the of Spain and constitutfug an example of the experience and Mediterranean axis, celebrating the Spain of the "three cultures", a universal example of tolerance and cohabita­ organizing ability of Spanish mathematicians. These tion. In support of this structure, the Organizing Committee achievements make us feel highly optimistic about the at­ aims to make many more grants available to both young tendance at the ICM itself. and senior mathematicians corning from these last two We cordially invite you to visit our website at areas. http: I lwww. i cm2006. org, which contains up-to-date in­ Mathematics in Spain has a relatively short history, and formation about the congress. if we look for mathematicians born in our country in the Middle Ages, we find names of Spanish Arabs and Jews. - Manuel de Le6n, President The need for naval pilots, architects, and engineers led King Spanish Committee of Mathematics Philip II to found the Madrid Academy of Mathematics in Chairman, Local Organizing Committee of ICM2006 1572. Unfortunately, the venture was short-lived, but [email protected]

FEBRUARY 2006 NOTICES OF THE AMS 197 a priori dichotomy and does not de­ students. Thus our policy should help Letters to the Editor pend on the uses one finds for a math­ them buy significantly cheaper (i.e., ematical theory after it has been devel­ used) copies of textbooks. As soon as we oped, so I don't agree that the area to realize this, we can see that the solution Winter Meeting Sites which a problem or a result belongs is simple: allow the students to use pre­ Years ago the AMS had its January meet­ can't be predicted in advance. (And, of vious editions of the textbook, not nec­ ing in Chicago, and the participants ex­ course, I certainly don't agree with some essarily the latest one, with the obvious perienced a couple of days with maxi­ people that one area is in any way su­ caveat that we are discussing here the mum temperatures below zero; all. perior to the other.) typical "new edition" that offers no sig­ interest in meeting again in Chicago nificant advantage over the previous during January vanished. Since then we -jacob E. Goodman one. In the case of a fundamentally new have had extreme winter experiences in City College edition, we may decide to require it, or, St. Louis and Cincinnati, and ice and City University of New York alternatively, we may decide to consider cold in Washington. A number of meet­ [email protected] an entirely new text, since a radically dif­ ings in warmer climates have followed, ferent edition may not suit our course but it seems the lessons of the past have (Received November 4, 2005) anymore. In a way, we are then falling not been learned, as the AMS will meet back on the UCLA policy. in Washington in 2009 and Boston in Another Textbook Policy 2012. Prepare for the worst again. The big advantage of this approach We have the following reply to the let­ is that we need no cooperation from ter titled "A Textbook Editions Policy" - ]on Alperin the publishers or other math depart­ that originally appeared in the Sept. ments. As long as used copies of old edi­ University of Chicago 2005 Notices of the AMS, Vol. 52, No.8, [email protected] tions are available, students can buy p. 830: those cheaply even if (or especially if) a We see some problems with the new (Received October 19, 2005) new edition comes out. The only disad­ textbook editions policy adopted by the vantage is that instructors can't assume UCLA math department (as appeared in that every student has the same edition the Sept. 2005 Notices, Vol. 52, No. 8, Pure and Applied of the textbook; thus assignments have p. 830), in which they automatically to be given explicitly instead of by prob­ Regarding the Letter from the Editor, search for a replacement text whenever lem number only. This minor incon­ November 2005 ("Graduate Students a new edition of a textbook appears be­ venience is a small price to pay for the and Applications"): At Brown we have a yond the third unless it is pedagogically immediate gain by the students. More­ Division of Applied Mathematics and a justified. over, some gain can be realized by mathematics department, physically The stated goal, with which we agree, adopting the policy even for just one separated by about a block's distance is to reduce the number of editions of but fortunately not so distantly sepa­ textbooks and increase the shelf life of course! Thus each of us can adopt this rated in our associations. People at each edition. The current practice serves policy without waiting for department Brown outside the two sections would no purpose other than enriching pub­ discussions and approval. usually ask me, "Are you in the applied lishers at the expense of students. Yet To get the most benefits, it is neces­ math department or the pure math de­ the suggested policy is likely to cause sary that the department officially partment?" and I decided to reply, "No, the department to search for new text­ adopts a variant of this policy so book­ I'm in the unmodified math depart­ books much more frequently for all stores will buy back used textbooks of ment." courses. For every new textbook, in­ the old editions. In the meantime, stu­ structors have to make substantial dents can use the Internet to find used -jonathan Lubin changes in the course outlines, and stu­ copies if our syllabi clearly state which Professor of Mathematics, Emeritus dents will be unable to buy used copies editions of the text are acceptable. Brown University of the new text on campus, since they If adopted by most departments, will [email protected] are unlikely to be available. Moreover, this policy decrease the frequency of the policy is unlikely to achieve its goals new editions coming out? Our guess is (Received October 24, 2005) in the long run. Even if most depart­ yes, but it really doesn't matter. The im­ ments adopt it, the net effect might sim­ portant goal is achieved anyway. ply be a regular reshuffling of the text­ Pure and Applied Ma1thematics books used by various math depart­ -Serge Kruk Regarding the brief discussion of "pure': ments, thus actually increasing the num­ Oakland University vs. "applied" mathematics in the No­ ber of new textbooks students have to Rochester, MI vember Notices (Letter from the Editor): buy. Since the publishers' main interest [email protected] I've always thought that "applied is in the overall number of new text­ mathematics" simply meant mathe­ books sold, they might embrace this -Laszlo Liptak matics motivated by questions in other, policy and produce new editions even Oakland University nonmathematical, fields, whereas "pure more frequently. Rochester, MI mathematics" meant questions moti­ What should we do instead? It seems [email protected] vated mainly by mathematical consid­ to us that the important goal should be erations. This is, on the face of it, an to ease the financial burden on our (Received October 24, 2005)

198 NOTICES OF THE AMS VOLUME 53, NUMBER 2 N CHINA EXCHANGE PROGRAM

Grants to support collaborations between Chinese and U.S./Canadian researchers are made possible through the generosity of Ky and Yu-Fen Fan.

The Fan China Exchange Program is intended to send eminent mathematicians from the U.S. and Canada to make a positive impact on the mathematical research community in China and to bring Chinese scientists in the early stages of their research to the U.S. and Canada to help further their careers. The program encourages host institutions to provide some type of additional support for the travel or living expenses of the visitor and to ensure a suitable length of stay.

Applications received before March 15 will be considered for the following academic year.

For more information on the Fan China Exchange Program and application process see www.ams.org/employment/chinaexchange.html or contact the AMS Membership and Programs Department by telephone at 800-321- 4267, ext. 4170 (U.S. and Canada), or 401-455-4170 (worldwide), or by email at [email protected]. Math Circles and Olympiads MSRIAsks: Is the U.S. Coming of Age? ]ames Tanton

he list of outreach programs aimed at point of discussion. What route- alternative to providing rich mathematical experiences math competitions and math camps- do circles T for middle- and high-school students is provide for the discovery of young talent? Is the growing. Programs such as the Berkeley use of the word "talent" appropriate? Can circles Math Circle [6], the San Jose Math Circle contribute to the general secondary curriculum? Are [8], and the Boston Math Circle [7] are thriving; a math circles self-sustaining? What makes them plethora of summer math camps exist across the work? Hugo Rossi comments: nation; and student participation in regional, na­ I am convinced that the idea of math cir­ tional, and international mathematics competi­ has come of age in the U.S., and it tions is significant. Clearly there is some important cles can become a movement which devel­ issue being addressed by these programs. It's ex­ ops fast so as to be something like what citing and intriguing, even if the "it" cannot be eas­ exists in Eastern Europe. The people at ily articulated. our conference are the resource for this On December 16-18, 2004, the Mathematical development; we have to make that re­ Sciences Research Institute (MSRI) took the bold source widely available. step to bring together over one hundred dedicated folk, all with strong interests in these programs and MSRI recognizes that the time is right to draw all clearly committed to the larger goal of sharing upon the collective experiences of our colleagues­ the joy of pure mathematics. Organized by Hugo here and abroad-and examine the opportunities Rossi, Deputy Director of MSRI; Tatiana Shubin of that lie before us. I am personally intrigued by the San Jose State University, CA; Zvezdelina Stankova broader challenge of possibly incorporating math of Mills College, CA; and Paul Zeitz of the Univer­ circle ideals into the fixed secondary curriculum. sity of San Francisco, the Conference on Math Cir­ (i have had the pleasure of working with Bob and cles and Olympiads united educators and re­ Ellen Kaplan of the Boston Math Circle for a num­ searchers from the pre-college and college worlds, ber of years before leaving the college world to brought focus to the questions of "what are we tackle life as a high-school teacher.) I have no real doing?" and "where are we going?," and offered con­ answers, but I was delighted to learn from this crete steps towards fostering discussion and shar­ conference that I am far from alone in exploring ing resources. From it, MSRI plans to establish a per­ issues like these. Serious discussion about the "it" manent national educator/researcher network. that math circles and other extracurricular activi­ "One of the central purposes of this conference was ties provide is now under way. to bring these communities together to begin an The Math Circle Experience interaction," writes Hugo Rossi. And it seems that the math circle concept provided a key intersection Extracurricular circles in a variety of subjects began in Hungary in the 1800s, all with the goal of pro­ ]ames Tanton is professor of mathematics at St. Mark's viding young students opportunities to pursue per­ Institute of Mathematics. His email address is sonal interests to the fullest. Today they are con­ [email protected]. sidered a standard part of the Eastern-European

200 NOTICES OF THE AMS VOLUME 53, NUMBER 2 student experience, and participation in them is re­ to conduct original research [5]. The Boston Math garded as just as natural as participation in sports Circle works hard to remove any sense of compe­ activities is viewed in the U.S. Although there is no tition and completely disregards labels of "tal­ set protocol to a math circle experience, all circles ented" and "gifted". It relies solely on the "intel­ have the same goal of sharing the intellectual ap­ lectual seduction of attractive questions," as Ellen peal and beauty of mathematics with as large an puts it, to engage and excite. The role of an in­ audience as possible. They engage faculty from structor is not to teach, but to guide, nudge, offer both secondary and post-secondary institutions in suggestions, and, more often than not, to step out their operation and successfully welcome students of the way. of all backgrounds to the mathematical experi­ The Berkeley Math Circle, founded in 1998 and ence. Circles now exist in many countries, includ­ run by Zvezdelina Stankova, works with over 50 San ing the U.S. (see also [1], for instance), and follow Francisco Bay Area middle- and high-school stu­ multiple styles and approaches. Given the success dents. It openly recognizes that there are many dif­ of the Eastern European model it is natural to ask ferent routes for the enjoyment of mathematics and then whether some version(s) of the math circle ex­ actively works to offer a variety of experiences. perience could be incorporated into the U.S. cultural Meetings tend to vary in style, organization, and norm. Could even more be accomplished? Tatiana topic from week to week, and competition and Shubin notes: competition preparation play an important role in the circle experience. (The Berkeley circle has had unique situa­ We're in a wonderful and tremendous success helping students prepare for the widest source tion ... where we have national and international competitions.) Stankova from all over of practices and traditions also recognizes that great joy and beauty can be the world to draw upon. And there exist found in advanced mathematics and may preface and TV ... If new tools, like the Internet a session with a lecture on a sophisticated topic. be aired on real circle meetings could For example, the following is a Berkeley Math Cir­ TV, lots of people would see how kids cle favorite: interact with it- and it might make a profound impact on the public's per­ Four planar circles are pair-wise exter­ ception of our beloved discipline. nally tangent. Three of the circles are also tangent to a line L. If the radius of imagine the impact! As a beginning step, Indeed, the fourth circle is one unit, what is the participants at the conference were treated to two distance of its center from L? demonstration classes- one from each of the Boston and Berkeley Math Circle programs- and Participants tackle this problem after attending it was clear each time that indeed something re­ a lecture on circle inversion. The power and beauty markable was taking place. of this advanced topic is made astoundingly clear when one discovers that this problem has a Two U.S. Models tractable, unique solution based on a single appli­ The Boston Math Circle was founded by Bob and cation of the Pythagorean Theorem! During the Ellen Kaplan and Tomas Guillermo in 1994 and cur­ MSRI demonstration, Stankova led young partici­ rently has over 120 participants. In this circle, the pants through a series of interactive challenges on lecture format is completely set aside and mathe­ the principles of Eulerian circuits and on winning matics is discovered and developed through ex­ strategies in some innovative checker-move games. ploration, intellectual play, and the give-and-take of One thing was clear from the demonstrations: conversation (see [4]). The questions discussed are both programs have hit upon ways not only to ex­ attractive and mathematically rich and offer mul­ cite young students with mathematics, but also to tiple pathways for exploration, generalization, and help young folk develop the tenacity to tackle sus­ variation. Students Work on the same fundamental tained challenges via consistent- andjoyful- hard question and the ideas generated from it for ten con­ work. In each circle the creative and organic math­ secutive weeks. As examples, young students, K- 3, ematical process is clearly laid bare and students have explored the vague question "Are there num­ are placed in command of their own learning. What bers between numbers?" to discover, by the end of an accomplishment! Rick Umiker of St. Mark's the semester, the density and the countability of the School, an independent high school in Southbor­ rationals. Middle schoolers, in exploring the issue ough, MA, comments: "Math circles demonstrate of whether or not a power of two ever begins with very good teaching ... Are they rediscovering the a seven, created their own versions of logarithms, power of small classes and an intimate environ­ developed basic results in ergodic theory, and ment?" Is it precisely the personal, intimate nature proved density results on infinite sets. Slightly older of the experience that leads to a circle's success? students have found their own means to compute Is it perhaps the human experience that is being ii, to prove the fundamental theorem of algebra, and laid bare?

FEBRUARY 2006 NOTICES OF THE AMS 201 On this issue Shubin writes "Circles might be asset and advantage as she now embarks on a path harmful if taught without caution and discretion, of original inquiry. or without life and spark. And I don't know what Joe Gallian of the University of Minnesota, Du­ is worse . ... As every delicate, subtle and complex luth, recent second vice president of the Mathe­ organism, they [circles] require very specific and matical Association of America, remarked that in diligent care in order to thrive." Stankova com­ his observation students who had participated in ments: and were good at competitions are generally doing better in Research Experiences for Undergraduate [Math circle] sessions must be master­ programs than the typical participant. Inna Za­ fully designed so as to do an array of kharevich, a winner of the USA and the Bay Area things: invite the students, intrigue Mathematical Olympiads, and now at Harvard Uni­ them, engage them, teach them, chal­ versity, also added that students do not feel bad lenge them, and leave them with more if they lose a competition. She stated that the gen­ questions to think about than when eral attitude is one of struggling against problems they entered the session. The format rather than competing against colleagues and that of the session is less relevant, as long everyone appreciates and admires a good solution as the above goals are achieved. How can even if it is not one's own. a session leader keep the students' at­ The primary role of competitions is often per­ tention on harder or more intricate con­ ceived as a means for identifying and culling bright cepts: that's what distinguishes a truly potential in mathematics and consequently as fun­ gifted teacher. damentally elitist. Is it possible to turn this per­ One could naively say that it is not difficult to ception around and foster, articulate, and com­ start a circle: simply gather a few young students municate instead the sentiments expressed by the and add a handful of exciting problems. The young scholars? Rossi comments: amount of organization and finance needed is min­ Just look at what's going on and ob­ imal. But Paul Zeitz expresses concern that it all serve that competition is an essential seems to ultimately rely on personality-and over­ motivator for some people, and irrele­ loaded schedules. "[These] programs work because vant or even detrimental to others. Is it of one or two people with incredible charisma mak­ bad to have problems drive education ing sacrifices. There is no evidence of a program and good to drive education with con­ that is truly self-sustaining." Is the only feasible tent? Or the other way around? ... Both math circle model a local one, run by the passion approaches work well, especially to­ and dedication of an energetic individual or two? gether. It seems to be the only model that currently exists in the U.S. Is this the one we should encourage and Some suggested at the conference that high-school support? And if so, how do we find math circle lead­ teachers might not know what the ultimate mission ers with just the right touch? How do we cultivate of the competition experience is for their students, and support them? And can we share resources? nor know how to prepare students for them. Can we help? Individuals, such as Richard Rusczyk, with his The Role of Competitions site http: I jwww. a rtofp rob l em solving. com, are Melanie Wood, a graduate student at Princeton and attempting to do so. How can we support and aid former Putnam fellow and International Mathe­ such attempts? And what about those for whom the matical Olympiad (IMO) silver medalist, expressed culture of competitions might be deemed "detri­ an alarming concern at the conference. She said she mental"? Are we adequately conveying multiple de­ felt a negative bias from the research community finitions of success in mathematics? Are we clear for having succeeded so well in the competition ourselves about the image we wish to promote? world. "Some people reason that since problem solving isn't 'real math', then students who did The Typical Secondary Curriculum: Do We well in competitions must not be good at research Have Something to Offer? and, in particular, decide those students don't have Many secondary-school teachers feel that the na­ the patience it takes to do research." Melanie ex­ ture of the teenage mind is different from the mind pressed a sentiment that her IMO colleagues also of a young adult in college, requiring special at­ present at the conference supported, that the com­ tention and care and special approaches when it petition route brought her great joy and success comes to education in mathematics. They are, of in mathematical exploration, that she was exposed course, right, and the U.S. secondary educational to and learned a considerable bulk of new mathe­ system has, over the decades, homed in on a by and matics outside the typical school curriculum, and large successful, and certainly valuable, approach that she developed thinking skills and maturity of to mathematics education. The question is not, mind that can only be described as an incredible what is wrong with how mathematics is taught in

202 NoTICEs oF THE AMS VOLUME 53, NUMBER 2 the secondary scene, but what more can we offer? aim to provide good psychological impact-it feels The existence of extracurricular mathematics pro­ good to young students to be right, and it feels good grams is not a statement of dissatisfaction, only the to have success quickly. Problems in textbooks are recognition that there is certainly room and op­ often carefully designed to offer hand-holds, pats portunity for discussion and connection between on the back, and indicators of success. (If, for ex­ the pre-college and college worlds. ample, you find yourself working with the famil­ "We need math circles for teachers," comments iar quantity sin(30°) chances are you must be on Umiker, "so that they will value that kind of free­ the right path.) dom for their students. [We need to see] the things But one could note that research mathemati­ that can be done around the edges. Not all of us cians and students taking competitions often look are aware of what can be done." for the same indicators of success. Complicated A typical example that comes to mind is the in­ problems are usually attacked in very small steps, troduction of the trigonometric functions in the and in studying them one is always looking for fa­ ninth-grade curriculum. It comes at a time when miliarity and connection to techniques previously many-but certainly not all-young teenagers are practiced. If progress on a problem is leading to a starting to learn not to memorize formulae. Yet certain sense of elegance, or if a formula obtained many texts first introduce the subject as a list of possesses symmetry of some kind, then one tends three (perhaps six) ratios to be committed to mem­ to feel good and feel confident about the path one ory ("SOHCAHTOA"). is following. (A key difference here, of course, is A math circle-type approach (as I have done that success is usually not garnered quickly. Nor with young students in a math circle) would be to are solution manuals available.) introduce "circle-ometry" and define the sine and Is it possible to view the experience offered cosine (properly!) as the "height" and "overness" through the typical mathematics text as intimately functions of a point rotating about the simplest cir­ connected to the research mathematical experi­ cle possible in mathematics, the unit circle centered ence? Is this too radical a point of view? Is there a about the origin. Just to play with (and cement?) way to highlight a connection between the typical the ideas, one can then explore "square-ometry" and school curriculum and the creative research expe­ look at, and graph, the squine and cosquine func­ rience? Is this what math circles, math camps, and tions, as my young students dubbed them, de­ math competitions are ultimately trying to offer? scribed by a point moving about a square with ver­ I was personally confronted with this issue some tices (±1, ±1). What do these graphs look like? months ago when I came to theorem 5.15 of my Could this also be done in typical ninth-grade class­ class's geometry text: The midpoint of the hy­ rooms? It would be interesting to find out. "There­ potenuse of a right triangle is equidistant from the search community," adds Umiker, "should note three vertices of the triangle. One could, of course, that we need people who can challenge us to ex­ present this as a known result to be proved and fol­ plore mathematics beyond a prescribed end." low up the discussion with a variety of practice Of course, secondary educators are faced with problems to be completed. I decided to turn mat­ the absolute necessity to cover a fixed bulk of con­ ters around and offered instead a mystery: tent. (The pressure I personally experience in the secondary world is far greater than anything I ever felt teaching at the college level.) Math circles do not have to contend with this. Nor do secondary teachers have the luxury of working with a self­ selected group of math-excited students. But these are not insurmountable issues. Tatiana Shubin is delighted to say that she is having some success in her college calculus classes moving away from center stage, and I, in my ninth-grade and AP cal­ Place two tacks in a wall. Insert a sheet culus teaching, have not at all given up my math of paper between them at some angle circle tendencies. Multiple approaches can suc­ and mark where the corner of the paper cessfully work together. The issue is to explore lies. Move the paper to a different angle how to communicate ideas, share resources be­ between the tacks and again mark the tween educators of all levels, and find the forum location of the corner. Repeat multiple to discuss observations and results. times. What curve is produced? Another issue to consider is the role of high­ school textbooks. They are designed to be intellec­ In the lively discussion that ensued students tually safe and are usually written so as to provide discovered theorem 5.15 for themselves, proved it, the young scholar structure, processes composed and then began to wonder about other mysteries: of small steps, routine, and rote practice. They also What if the corner of the paper is not a ninety fEBRUARY 2006 NOTICES OF THE AMS 203 degree angle: do we still obtain the arc of a circle? For me, discovering that I am not alone in this Is the converse true: Given a circle first, does this pursuit was a great comfort. Establishing connec­ mean that all angles from the diameter are ninety tions between like-minded educators is proving to degrees in measure? (Note that the answer to this be immensely fruitful and rewarding. Discussions latter question provides a nifty means for finding about the issues raised carry on through email and the diameter of a given circle using nothing more local discussions, and ideas and approaches are ac­ than the corner of a piece of paper.) tively being explored. I am delighted that this was I was particularly delighted that the first of a series of conferences on the topic of one of my students took Math Circles and Olympiads that MSRI intends to hold of these problems offer. The number of attendees surely will grow. and managed to prove, Fundamental questions remained unanswered. completely in his own Some participants wonder, for example, whether way, that all points the math circle model is destined to remain local­ subtending the same ized and extracurricular. Others are trying to in­ angle from a fixed corporate math circle ideals directly into the class­ chord do indeed room experience. Work is under way to create a trace the arc of a cir­ general website, supported by MSRI, offering ad­ cle-a remarkable vice, plans, and resource materials as a means to achievement. I wit­ r each out to those who may be interested in ex­ nessed the math circle ploring these ideas. We should consider how to help experience come alive teachers pursue this work. Would the formation of within my classroom. a special interest group on math circles and com­ It was apparent at the con­ petitions through the mathematics professional ference that many extracurricular societies be of help? activities- math circle topics, competition prob­ Mary Fay-Zenk, mathematics resource teacher for lems-favor graph theory, combinatorics, and num­ the Cupertino Union School District, CA, having ex­ ber theory as sources of content. (Admittedly, perienced great pedagogical success with the use ' geometry too.) These topics are immediately ac­ of math competitions as motivators, suggested the cessible and offer multiple routes of exploration idea of starting a math circle for middle- and high­ and discovery. Surprisingly, none of these topics school teachers. A number of people are picking appear in any depth in the typical secondary cur­ up on this idea. Matthias Beck of San Francisco State riculum, if at all. Is it worth asking why? Are there University and Paul Zeitz of the University of San ways to make all topics- pre-calculus? algebra 11?­ Francisco, for instance, with the support of MSRI equally appealing and accessible, and to present and funded by the McKesson Foundation, are start­ them with multiple paths of discovery and explo­ ing a new math circle for young students in the Bay ration? Is this appropriate? How much of this is con­ Area, accompanied with math-circle type courses tent-dependent? How much is dependent on indi­ for their teachers. St. Mark's Institute of Mathe­ vidual teacher style? How do we connect with and matics in Southborough, MA, in collaboration with support teachers who may already be asking these the Northeastern University School of Education, questions and experimenting? Is this the wrong began a similar program for teachers. Not only will track? programs like these disseminate the ideas and principles of math circle teaching, they will also help What Can We Do to Support Educators on establish a network of support and communication. All Levels? MSRI is organizing a number of special work­ Elevating mathematics through education is a noble shops to explore and address directly some of the pursuit. The work being done by those organizing questions raised at its December 2004 conference. and running math competitions, math camps, and For example, the "Mathematical Knowledge lfor math circles is often unrecognized by their sup­ Teaching" workshop, May 25-28, 2005•, brought porting institutions and is done as an overload to together K-12 educators, educational researchers, their professional activities. Secondary-school mathematicians, and policy makers to examine teachers have demands placed upon them above what is known about the knowledge needed for and well beyond the requirements of simply teach­ teaching mathematics. ing mathematics, often leading to fragmented and Is this enough to get the big ideas "out there"? ridiculously lengthy work days. There is often very Perhaps the only route for success along these little freedom of mind (and freedom of practice) to lines is to consistently offer forums for discussion pause, reflect, and experiment. Yet the determi- and to rely on local dissemination of ideas. (Such . nation and passion of a growing number of edu­ a route certainly works for the Boston Math Circle, cators to look for and provide more is astounding. for instance. Relying solely on word-of-mouth, the What can be done to offer support? program is consistently over 120 students strong.)

204 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Some programs are reluctant to write down any form of "curriculum" to share, not because of are­ luctance to disseminate ideas-far from it- but rather because the very nature of creative explo­ ration is organic and nonlinear and cannot be pre­ scribed. On the other hand, one can argue that it TENURE TRACK FACULTY is certainly better to have something written to share, even if it ends up not being used as in­ FINANCIAL MATHEMATICS tended. (And thankfully the Kaplans have decided MATHEMATICAL SCIENCES on this too. Their book, Out of the Labyrinth: Math­ The Worcester Polyrechnic Institute (WPI) Deparrmenr of Mathematical Sciences invites ematics Set Free will be released by Oxford Uni­ applications for a facu lty position to begin in rhe faU of 2006 at rhe assistant professor level. versity Press later this year.) I have to say that An earned Ph.D. or equivalent degree is required. Preference wi ll be given co cand idates whose main research interest is in financial mathematics or closely related areas of stochastic processes, Dmitri Fomin, Sergey Genkin, and Ilia Itenberg's stochastic analysis, or the numerical solution of stochastic systems. Successful candidates must book Mathematical Circles (Russian Experience) demonstrate strong research potential and evidence of qual ity reaching and will be expected to contribute to the department's research activi ci es and ro irs innovative, project-based educational (AMS, Providence, 1996) significantly guided my programs, in particular to rhe graduate program in financial mathematics. own ideas about how to conduct a math circle. WPI is a private and highly selective technological un iversity with an enrollment of2700 under­ (For the more structured experience, one may con­ graduates and about 1100 full - and parHime graduate students. Worcester, New England's third sult [7] for a collation of over seven years' worth largest city, offers ready access to the diverse economic, cultural and recreational resources of rhe region. of Berkeley Math Circle lecture notes and [3] for an The Mathematical Sciences Department has 24 renuredlrenure-track faculty and supporrs BS, impressive collection of guest lectures given at the MS, and PhD programs in applied and computational mathematics and applied statistics. For Bay Area Mathematical Adventures series, a pro­ additional information, see http://www.wpi.edu/+math. gram intimately connected with the San Francisco Qualified applicants should send a derailed curriculum vitae, a brief statement of specific reaching and research objectives, and rhree leners of recommendation, at least one of which Bay Area math circles.) addresses teaching potential, ro: Math Search Committee, Mathematical Sciences Maybe the key is to articulate and clarify the no­ Department, WPI, 100 Institute Road, Worcester, MA 01609-2280, USA. tion that mathematics is ultimately a creative Applicancs will be considered on a co ntinuing basis until all positions are fill ed. Review of human endeavor, and maybe we should strive to applications will start December I, 2005. To enrich education through diversity, WPI is an affirmative action, equal opportunity employe1: offer means for it to be experienced as such by NO PHONE CALLS PLEASE. teacher and student alike. Can we communicate (teach?) educators of all levels not to fear pursu­ ing, or at least exploring, the creative process- to let go of the perception of needing to be the mas­ ter of the subject at all times? Can we encourage folks to trust the mathematical experience even if one cannot identify where a class is heading with it at a particular moment (day? week?)? Can we en­ courage educators to be comfortable and confi­ VISITING FACULTY dent with the process even if time is running out, there is a common exam next week, and the Dean STATISTICS & APPLIED MATH POSITIONS of Faculty wants evidence of demonstrable suc­ MATHEMATICAL SCIENCES cess? Should we? The Worcester Polytechnic lnstirure (WPI) Department of Mathematical Sciences invites applications for several Yisi ri ng Msistam Professorship positions to begin in rhe fall of 2006, in rhe areas compatible with the References research interests in rhe department. An earned PhD or equivalent degree is required. Successful candidates must demonstrate strong research potential and evidence of quality reaching, and will be expected to con­ [1] R. CAVALIERJ and D. HARTENSTINE, Math circle: An outreach tribute to the department's research activities and to irs innovative, project-based educational programs. Appointments will be made for one or two years, contingent on satisfactory performance. The reaching load program at the University of Utah, FOCUS, 25(1) (2005), will be either five seven-week undergraduate courses or four of these plus one semester-long graduate course. 6-8. The Department has strong research programs in applied mathematics and applied statistics: [2] D. HAYES and T. SHUBIN, Eds., Mathematical Adventures APPUED MATHEMATICS: Preferred research imeresrs are partial dilferemial equations with applications for Students and Amateurs, Mathematical Association in continuum mechanics and composite materials, computational modeling and simulation, mathematical biology, financial mathematics, numerical analysis, oprimizarion, control theory, applied probabi li cy, and of America, Washington DC, 2004. discrete mathematics. [3] R. KAPLAN, The math circle, Notices of the American STATISTICS: Ap plicants are especially encouraged in the areas of biostatistics, experi mental design, Bayesian Mathematical Society, 42(9) (1995), 976-978. m~rhods , Monte Carlo methods, data mining methods, sample suiVe}' methods, suiVival analysis and rime se nes. [4] S. KENNEDY, The math circle, Math Horizons, April WPI is a private and highly selective technological university with an en rollment of2700 undergraduates and (2003), 9-10, 27-28. about 11 00 full- and parr-rime graduate srudems. Worcester, New England's third largest city, offers ready [5]]. TANTO N, Young students approach integer triangles, access ro the diverse economic, cultural and recrearional resources of rhe region. The Mathematical Sciences Department has 22 tenured/tenure-track facu lty and supports BS, MS, and PhD programs in applied and FOCUS, 22(5) (2002), 4-6. computational mathematics and applied statistics. Interactions wirh industry, business and government are [6] The Berkeley Math Circle: http: I lmathci rcl e. facilitated by rhe Center for Industrial Mathematics and Statistics. For additional information, see berkeley.edu. http://www.wpi.edultmath. Qualified applicants should send a derailed curriculum vitae, a brief statement of specific reaching and research [7] The Boston Math Circle: http: I lwww . themathci rc l e. objectives, and three letters of recommenda ti on at least one of which addresses reaching potential, to Math org. Search Committee, Mathematical Sciences Department, WPI, 100 Institute Road, Worcester, MA [8] The San Jose Math Circle: http: I lwww. mathci rc l es. 01609-2280, USA. or g. Applicants will be considered on a continuing basis beginning December 1, 2005 until all positions are filled. To enrich education through diversit;\ WPI is tin tljfinnative fiction, equt1/ opportunity employe1:

fEBRUARY 2006 NOTICES OF THE AMS 205 A System of Axioms of Set Theory for the Rationalists ]anMycielski

Introduction We cannot take here the time and space to criticize This paper proposes and discusses a list of ax­ them, but we believe that the evidence in favor of ioms for set theory based on the principle: Accept our opinion is overwhelming.] (Note: In this article, as much regularity or specificity as possible with­ I will use parentheses to indicate additional infor­ out weakening the theory. mation that is necessary but outside the main flow The philosophy of mathematics has little or no of ideas, square brackets for additions that are influence upon 99% of mathematics. But there is more remote from the main flow, and curly braces that 1% where it matters, namely the choice of ax­ for digressions.) ioms of set theory, and this is the theme of this Thus we accept a view which is intermediate be­ paper. tween (a) and (b) and which says that not only ap­ There are two extreme ontologies of mathe­ plications but (in a great measure) human nature matics: (a) Platonism, which tells us that pure math­ itself defines and causes pure mathematics. The ematics is a description of an ideal structure that ideal actually infinite sets of the Platonists are re­ exists independently of humanity, and (b) Formal­ placed by physical phenomena in human brains, ism, which says that pure mathematics is just a that is, thoughts of things like boxes whose con­ game with symbols. (Both views acknowledge the tent is not fully imagined (see [H1 ]). The meaning seminal role of applications, e.g., both agree that of quantifiers is explained as follows (see [SK] and Greek geometry is an abstract approximate de­ [H2 ]): If we claim in pure mathematics that scription of the physical space-time.) We think that 'v'x3ycp(x, y), where x andy range over a universe neither (a) nor (b) is convincing; (a) assumes too U, we assert only that we have a mental operation much, it violates Ockham's principle entia non sunt such that given any a in U we can imagine a b in multiplicanda praeter necessitatem, and (b) ignores U satisfying cp(a, b). Hence the infinite sets and uni­ that logic and set theory constitute a framework and verses of pure mathematics are not actually but only a tool for describing reality which was given to us potentially infinite. (For a fuller explanation see re­ by natural evolution. We believe the latter since peo­ mark 3 at the end of this paper.) Thus pure math­ ple of all cultures agree that mathematical argu­ ematics is a finite human construction in a state ments are convincing, and those who study the of growth dealing with imaginary objects. It makes rules of logic and the axioms of set theory (ZFC with no sense to call it true or false since truth can ap­ urelements allowed) think that they are evident. pear only in applications (this does not contradict [Some postmodernists try to refute this observa­ the fact that tion by quoting various psychological experiments. there exists a mathematical theory of the relation of truth). And yet logic and set theory ]an Mycielski is professor emeritus in the Department of are not arbitrary since human intelligence is made Mathematics at the University of Colorado in Boulder. His to describe reality in this framework (i.e., to clas­ email address is jmyci e l @euclid. col or ado. edu. sify using sets, sets of sets. etc.).

206 NOTICES OF THE AMS VOLUME 53, NUMBER 2 {Although we have explained pure mathemat­ This axiom defines the concept of a set in terms ics without introducing actual infinity, it seems of the membership relation E. Since x and y are that actual infinity does exist in physical reality, e.g., unrestricted variables, (1) also precludes the exis­ the space-time continuum appears to be infinite (see tence of objects that are not sets. This may appear e.g., [P]). But some objects or structures of mathe­ too restrictive since in real life we imagine many matics are purely imaginary, for example, a well­ objects which we do not treat as sets. Therefore in ordering of the real line, while others have poten­ some older books the universe of set theory is di­ tial interpretations as physical objects or processes, vided into sets and non-sets (called urelements), and and we call them real. In mathematical practice in the Axiom of Extensionality the range of x and many real objects are constructed or explained by y is restricted to sets; see e.g., [KM] and [Su]. How­ means of imaginary ones. This is the natural way ever, experience has shown that in mathematics ure­ to do mathematics, such are the necessities of lements are not essential (they can be constructed human intelligence. Constructivism, which tries to in terms of sets and a modification of the relation avoid imaginary objects, is unwieldy, but the dis­ E). Therefore, in view of its simplifying role, we ac­ tinction between imaginary and real objects is in­ cept the Axiom of Extensionality. teresting, see [DM] and [Ms].} The Axiom of Union: Although the concept of truth does not apply to pure mathematics, we can ask does such and such (2) Vx3yVz[z E y ~~ 3s[z E s & sEx]]. a set-theoretic proposition P constitute a natural law Of course we often need to construct a set y in of thought? Of course if the answer is yes we ac­ terms of a set x in the above way. Thus we accept cept P as an axiom. If it is no, but P is consistent with the natural laws, then we are free to accept the Axioms of Union. (We write y = U(x) .) or to reject P. After Godel and Cohen it is known The Axiom of the Powerset: that many simple set-theoretic propositions Pare (3) Vx3yVz[z E y ~~ Vs[z E s ~sEx]]. in that last category. And yet some of them can be desirable axioms if they have any of the following Once again, we often need to construct y in terms properties: (1) They simplify set theory, inducing of x in the above way. Thus we accept the Axiom regularities without excluding any interesting ob­ of the Powerset. (We write y = P(x) .) jects. (2) They strengthen set theory and enrich its The Axiom of Replacement: universe with interesting objects. For these reasons it is rational to add new ax­ Vii[Vxy3z[

(1) Vxy[V z[z EX ~~ z E y] ~ X= y]. (5) Vx[x =f 0 ~ 3y[y Ex & Vs[s E y ~ s $. x]]]. fEBRUARY 2006 NOTICES OF THE AMS 207 The only role of this axiom is to simplify the uni­ Vx3cx[x E Vex], verse of sets. It precludes the existence of infinite and we write sets {a1, a2, ... } such that a1 3 a2 3 a3, .. .. In­ deed if x was such a set it would violate (5). It also (*) V= U Vex. precludes sets a such that a E a. Indeed, for such e< EOrd an a, the set x = {a} would violate (5). Of course Thus V denotes the universe of all sets. Unlike the any urelements would also violate (5). Set theories Vex's, Vis not a set, and hence ( *) is not a formal without the axiom of regularity have been consid­ definition in the language of set theory. ered, but they do not appear to lead to any suffi­ Now we form the models (Vex, E), and we denote ciently interesting mathematics. Therefore, in view by D ex the set of elements of Vex which can be de­ of its simplifying role, we accept the Axiom of Reg­ fined by unary formulas in the model (Vex, E ). Then ularity. OD is a class informally defined as follows: However, we will introduce below an axiom (7) OD = U Dcx. which implies (5); thus (5) is superfluous in ST, but e< EOrd it will appear in some later remarks. Again OD is not a set. But our seventh axiom, V = The Axiom of Infinity: OD, can be formally expressed as follows:

(6) 3x[x =f 0 & Vy[y EX~ y U {y} E xj], (7) Vx:Jcx[x E Dcx]. where y u {y} = U {y, {y}} . This axiom is essential Notice that each Dcx is finite or countable. Still the for the construction of infinite sets, for example, union U~ < cx Dcx builds up relentlessly, so we never of the set N of positive integers. The former axioms need in mathematics any set that has to be outside (1)-(5) of set theory constitute a system defini­ of OD. [Of course we could assume that there exist tionally equivalent to Peano's Arithmetic (PA), and such sets, but heretofore this assumption has not this system is not strong enough to develop math­ led to any interesting mathematics.] ematics in a natural way. For example, (6) is nec­ We mention three consequences of V = OD: (a) essary for the development of analysis. it implies the Axiom of Choice, and moreover it [A very artificial finitistic way of doing set the­ yields a certain binary formula cp(x, y) that well or­ ory is possible. It is based on the Completeness The­ ders all of V; (b) it implies the Axiom of Regular­ orem of Gbdel. Namely, we can develop mathe­ ity (5); (c) the set theory S based on the axioms matics within the theory PA + Con(S), where PAis (1)-(7) has the elegant property that the definable Peano's Arithmetic and Con(S) expresses in the elements of any model M of S constitute an ele­ language of PA (by means of Gbdel numbers) the mentary submodel of M. Peano's arithmetic also has consistency of a set theory S. In this theory we can this property, but the traditional system of axioms define a model of S. But this is not natural since it ZFC does not have it. I believe that, in view of these is only a translation of the idea of S into the lan­ consequences and for sake of definiteness, it is ra­ guage of PA.] tional to accept V = OD. The Axiom V = OD: Of course this may be a temporary situation. For From now on we depart from the beaten track example, some interesting theory involving real numbers since V = OD and the remaining axioms have not that are not in OD could arise in the fu­ yet been accepted by other set theorists. To explain ture. But we have no reason to predict that such a this axiom, recall first that the class of ordinal thing will happen. numbers Ord is defined to be the smallest class [It appears natural to add a refinement (?<') of of sets that contains 0 and that is closed under (7), which, in the presence of (5), implies (7): unions of its subsets and closed under the func­ (71') Vex c; D ~ , tion x ...... x u {x}. (One shows that £X E Ord if and U I only if V xy[x c; y c; £X~ x E y E cx].) The former ~ < IV"' axioms (1)-(6) yield a proof that each ordinal £X is where IVex I is the ordinal of the least well-order­ well-ordered by the relation E. As usual, E re­ ing of Vex. But I do not know any interesting con­ stricted to ordinals is denoted by < , and w denotes sequences of (7 1'). Every set x has the structure of the least infinite ordinal. For every ordinal £X, we a tree (Tr(x), E ), where define £X + 1 = £X u {£X} . Then we define recursively Tr(x) = {x} u x u U(x) u U(U(x)) u ... the sets Vex (cx E Ord): Perhaps one can postulate some more detailed re­ Vex= U P(V~). lation between the definitions of definable sets ~ < C< and their trees?]

Thus Vo = 0 , V1 = {0 }, V2 = {0 , {0 }}, ... , Vcx+l = The Axiom GCH: P(Vcx), .... The former axioms (1)-(6) yield the The cardinal number of a set a, in symbols Ia I , is theorem: the smallest ordinal number which has a bijection

208 NOTICES OF THE AMS VOLUME 53, NUMBER 2 to a. Thus the least infinite cardinal number is w, then IAI ~ 2~'< 0 . McKenzie and Shelah proved with­ also denoted No. The next one is denoted w1 or N1, out using CH that No < IAI < 2~'< 0 is impossible. etc. For every cardinal number 0< we define According to the idea expressed earlier, the proof 20( = IP(O<) I and 01+ =(the least cardinal larger than should yield a stronger theorem T* which remains 01). The Axiom GCH is: nontrivial even if we assume the theorem of Tay­ lor and CH. I do not know such a theorem. For every infinite cardinal 0< Another example of this situation is the fol­ (8) we have 20( = 01+ . lowing. A well known conjecture of R. L. Vaught says This axiom greatly simplifies the theory of infi­ that if Tis a countable theory, then the number 0< nite cardinal numbers, and it adds many interest­ of isomorphism types of countable models ofT can­ ing theorems to the combinatorics of infinite sets. not satisfy No < 0< < 2~'< 0 • Morley [Mol has shown a These well known advantages are so significant little less, namely that N 1 < 01 < 2No is impossible. that it is rational to accept GCH as an axiom of set Again I think that a stronger conjucture and a the­ theory. (Even CH, that is 2~'< 0 = N1, has many inter­ orem that do not follow immediately from CH esting consequences.) should exist. Set theorists often say that probably GCH re­ The above ideas should not be construed as a stricts too much the sets PP(O<). But one can also criticism of a branch of foundations called Reverse surmise the opposite. Indeed 20( > 01+ precludes the Mathematics. In this branch one proves theorems existence of any subset of P(O<) which codes a func­ of the form T ~ A, where Tis some interesting the­ tion{: P(O<) ~ P(O<) such that whenever x, y E P(O<) orem and A is an axiom (of course A is not assumed and x =f. y, then f(x) and f(y) code different well­ in the proof ofT ~ A). Some examples of such the­ orderings of 01. Since, as we explained in the first orems are.the following. Tarski's theorem: (For all section, PP(O<) is only potentially infinite, we are infinite sets X there exists a bijection of X to X x X) free to accept GCH. [It is often said that the Axiom ~ (Axiom of Choice). Or Sierpiliski's theorem: (The of Choice (AC) and CH have consequences that space JR 3 with a Cartesian coordinate system contradict probabilistic intuition that is based on X, Y, Z, is a union of three sets A, B, and C such that physical experience. However, a closer look shows every linear section of A parallel to X is finite, that those paradoxical consequences do not per­ every linear section of B parallel to Y is finite, and tain to any mathematical objects that have a po­ every linear section of C parallel to Z is finite) ~ tential for direct physical interpretations (for a de­ CH. There are many interesting theorems of Reverse tailed discussion see [DM] and [Ms ]). On the other Mathematics, but some critics do not care for such hand AC and GCH have similar organizing or sim­ results. [Tarski told me the following story. He plifying roles, which motivate their presence in ST. tried to publish his theorem (stated above) in the (As mentioned earlier AC is a consequence of V = Comptes Rendus Acad. Sci. Paris but Frechet and OD.)] Lebesgue refused to present it. Frechet wrote that The acceptance of GCH leads us to the follow­ an implication between two well known proposi­ ing considerations. If we have a nontrivial proof of tions is not a new result. Lebesgue wrote that an a theorem T which does not use GCH, such that T implication between two false propositions is of no becomes trivial if GCH is assumed, then that proof interest. And Tarski said that after this misadven­ ought to give a stronger theorem T* that is still ture he never tried to publish in the Comptes Ren­ nontrivial even in the presence of GCH. I will give dus.] two examples where I do not know the correct The Axiom SH: statement of T*. The first is a theorem of R. McKenzie and If A is a linearly ordered set such that S. Shelah [MS]. To state it we need the following con­ every set of disjoint open intervals of A cepts. An algebra A of countable type is a system (9) is countable then A has a countable (A, f1, f2, ... ) , where A is a nonempty set and each subset which intersects every non-empty fn is a function of finitely many variables running open interval of A. over A and with values in A. Let I be an infinite This axiom, called Suslin's Hypothesis, has been system of equations written in terms of the fn 's and extensively studied (see [Ku]). Once again, we do any (possibly infinite) number of unknowns. A is not meet in mathematics any linear orders violat­ said to be equationally compact if every L has the ing (9). So we accept (9) since it simplifies set the­ property that if all its finite subsystems can be ory in a natural way. solved in A then the entire system L can be also solved in A. And, A will be called folded if for It may be of some interest to recall a statement every proper homomorphic image B of A there ex­ equivalent to (9) (see e.g., [Ku]). By a tree we mean ists a finite system I which can be solved in B but a partially ordered set T such that the set of pre­ not in A. It was known (W. Taylor [T]), that if A is decessors of any element ofT is fully well-ordered. of countable type, equationally compact, and folded A subset of T is called a chain if and only if it is fEBRUARY 2006 NOTICES OF THE AMS 209 well-ordered; it is called an antichain if no two of let a set X<::::: {0, l}w be given. Player I chooses Eo, its elements are comparable. Then (9) can be ex­ then player II chooses EI. then again I chooses E2, pressed equivalently as follows: and II chooses E3, etc. The set X and the sequence (Eo, ... , En - l) are known to the player choosing En. (9') If every chain and every antichain I wins if the sequence (Eo, El, .. . ) belongs to X and of a tree T is countable then T is countable. II wins otherwise. (Perhaps the simplifying nature of (9') is more The Axiom of Determinacy AD is the statement salient than that of (9). SH or (9') may suggest sim­ for every X one of the players has a winning strat­ ilar axioms for higher cardinal numbers.) egy. It is easy to prove using the Axiom of Choice AD ADL(IR) The Axiom ADL(IR): that is false. But the Axiom [which was suggested in [M5S] and in [M4] footnote (1 )] is the To explain this axiom we need the following con­ following restriction of AD: cepts. For every set A, we form the relational struc­ ture (A, E}, where E is restricted to A. Then a set (10) AD is true provided X E L(JR). X <::::: A is called A -constructible if there exists a for­ This axiom has many interesting consequences. mula of set theory cp(x, y) and a finite string a of Assuming ADL(IR) the class L(JR) becomes the nat­ elements of A such that ural universe of sets for mathematical analysis in X E X -- (cp(x, a) is true in (A, E)). Polish spaces. Indeed, AD implies that: all un­ Let C(A) denote the set of A -constructible subsets countable sets of reals have perfect subsets, all sets of A. ofreals are Lebesgue-measurable, and all have the Then we define property of Baire (see [M2 ]). Also the theory of pro­ jective sets gets a very regular form (see e.g., [M]). L()( = U C(L£) Therefore it is rational to accept the axiom £< !X ADL(IR). and The Axiom SC: L= U L()(. To explain this axiom we need the following con­ !X EOrd cepts. For every infinite cardinal Oi, a Hausdorff We define also space S is called Oi-compact if every covering of S with open sets has a subcovering with less than Oi Lo(JR) = Vw+lr sets. (Thus w-compact means compact in the usual and, for all Oi > 0, sense.) A cardinal Oi is called strongly compact if every topological Cartesian product of any number LdlR) = U C(L£(1R)), of ()(-compact spaces is ()(-compact. By the Ty­ £<()( chonoff product theorem, w is a strongly com­ pact cardinal. (There exist other definitions of and finally strongly compact cardinals. They were introduced L(JR) = U L()((JR). in [KT] and the above definition was shown in [MI].) !X EOrd The axiom SC is the following:

(The notation L(JR) derives from the existence of For every cardinal K there exists a natural bijections from V w+ 1 to the set lR of real (11) strongly compact cardinal larger thanK. numbers.) The structures (L, E) and (L(JR), E) are It is natural to replace the product topology in of special interest. The first satisfies all the axioms the definition of a strongly compact cardinal Oi by (1)-(8) (but not (9)), and the second satisfies (1)-(6). a larger topology whose basis is the set of all cylin­ In fact (L(JR ), E} is the smallest structure which ders over products of less than Oi open sets. But contains lR and all the ordinal numbers and which the corresponding concept of strong compactness satisfies (1)-(6). is equivalent to the former. Although L(JR) is minimal in the above sense it Thus SC postulates the existence of many car­ is large enough for mathematical analysis. For ex­ dinal numbers similar to w. One can prove many ample, it contains not only all the real numbers but large cardinal properties of Oi-compact cardinals, also the projective sets of all ranks < WI, and pre­ for example they are strongly inaccessible and sumably all sets that are of true significance for even measurable (see [D] and [Ka]). analysis over Polish spaces. On the other hand, it The axiom SC is also interesting for other rea­ does not contain sets that appear pathological in sons. One of them is a theorem of R. M. Solovay [So], a probabilistic sense. But these claims depend on which says that all cardinals Oi, which are larger than the axiom ADL(IR) which we will explain presently. the least uncountable strongly compact cardinal Consider the following infinite binary game of and are singular and strong limit1 , satisfy 2()( = Oi+. perfect information. Let {0, 1} w be the set of all in­ finite sequences (Eo, EI. .. . ) where En E {0, 1}, and 1 oc is strong limit if K < oc- 2K < oc.

210 NOTICES OF THE AMS VOLUME 53, NUMBER 2 {Again we believe that the proof in [So] should of supercompact cardinals or any cardinals suffi­ yield a property of e< stronger than 2()( = e<+, which cient for that proof (see [NI, Nz ]), are so compli­ does not become obvious under the assumption of cated that the claim that ST is consistent is more GCH.} convincing to me than the claim that these very To state an interesting consequence of SC let us strong theories are consistent.] generalize the infinite game defined in the previ­ ous section. We replace the set {0, 1} by an arbi­ Additional Remarks trary set P, and the set X by any X c; pw. (Thus the Let ZFC denote (as usual) the system of axioms players I and II choose their En in P.) Let N be a (1)-(6) plus the Axiom of Choice. Let me reiterate countable set, and consider the product topology the motivation of ST. As we mentioned in the In­ in pw x Nw, where both P and N are given the dis­ troduction, ZFC is natural in the sense that almost crete topology. A set X c; pw is called analytic if every mathematician who reads its axioms feels that it is a projection of a closed subset of pw x Nw. It he accepts them. However, as explained in our dis­ is a consequence of SC that if X is analytic then the cussion of axioms (1) and (5), ZFC departs from the game is determined, i.e., one of the players has a natural way of thinking by accepting some simpli­ winning strategy. (In fact a large cardinal axiom sig­ fications which eliminate certain sets that are not nificantly weaker than SC suffices to prove this the­ important for mathematics (urelements and sets orem, viz. (3K > IPI) [K ~ (WI)~w], see [Mz]. This that are not well founded). So it is natural to fol­ result for P = w is due to D. A. Martin; in [Mz] his low this path and accept the other axioms of ST that proof is generalized to all sets P.) simplify the theory, namely V = OD, GCH, SH, and Large cardinal axioms much stronger than SC ADL(IR). (Of course SC enriches rather than simpli­ have been proposed and studied. Some of them fies.) imply the axiom ADL(IR) (this is a difficult theorem This suggests the question why these well known of Martin, Steel, and Woodin, see [NIL [Nz] and propositions are not yet generally accepted by [Ka]), but I stated SC rather than those stronger ax­ most set theorists. I see three reasons: (a) the tra­ ioms since the latter are more complicated and, as dition of treating them as open problems; (b) the far as I know, unlike SC, they are not suggested by thought that they oversimplify set theory; (c) the any properties of w. belief of Platonists that they could be false. In the next three sections I will argue contra (a), (b), and Conclusion (c). This concludes my definition of a set theory ST 1. Ad (a). Of course (a) should be dismissed which I believe to be reasonable, that is, as strong since it is known that none of the axioms (7)-(11) and simple as possible and unrestricted by any is a consequence of the other ones. Platonic beliefs. Thus 2. Ad (b). If we agree that ST does not appear to impose any bounds on the consistency strength of ST = [ZF + (V = OD) + GCH + SH + ADL(IR) + SC], its possible extensions, then the fear that it over­ where, as usual, ZF denotes the system (1)-(6). But, simplifies set theory has no motivation. Thus I feel as explained in the introduction, ST is an attempt that (b) is not true (at least at the present time). at a good synthesis of the current state of mathe­ However, alternative theories were proposed re­ matics. It will have to be strengthened or modified cently in [WI, Wz]. These theories yield certain de­ if mathematics calls for more sets. scriptions of the model However, much of the current work in set the­ (P(WI), WI,+,·, E), ory consists of difficult and ingenious proofs in theories weaker than ST (see e.g., [Ka], [KL], and [S]), where + and · are ordinal addition and multipli­ and of constructions of very artificial models that cation restricted to countable ordinals, and they yield independence and consistency results. Of happen to disprove the Continuum Hypothesis; course this is interesting to the specialists, but I they prove 21'< 0 = Nz. This looks odd, and it is abig think that it is difficult to justify such work to complication of the theory of cardinal numbers or mathematicians at large. Indeed they can object We of the combinatorics of infinite sets. Moreover, all are not very interested in methodology; if you have uncountable subsets of WI (and of JR ) are imagi­ the freedom to assume strong and simplifying ax­ nary objects without the potential for any direct ioms why don't you assume them? physical interpretations (see [DM] and [Ms ]). Hence Recently W. H. Woodin and others have pro­ any additions to ZFC describing these objects can posed set theories that are inconsistent with ST, but be motivated only by human preference. There­ I think that the motivation of ST is better (see re­ fore the only objective criteria which can guide mark 2 below). our choice among these theories are precisely the [It is known that in very strong set theories, e.g., simplicity of the axioms and the regularity of their ZFC + (there exists a supercompact cardinal), one consequences. Are the theories proposed in [WI, can prove that ST is consistent. But the definitions Wz] so attractive from this point of view that we fEBRUARY 2006 NoTICES oF THE AMS 211 should give up GCH? {In the presence of V = OD we have a definable [Some philosophers have tried to dismiss the well-ordering of the universe, and then the opera­ concept of simplicity of a theory, claiming that it torE can be also defined: Er:p,y(x) is the least 15'1- is vague or language-dependent or irrelevant. Yet tuple such that Mathematical Logic (H) cp(x, y) ~ cp(x, Er:p,y(x)) (]. Barwise, ed.), North -Holland, 1991, pp. 783-815. [MS] R. McKENZIE and S. SHELAH, The cardinals of simple essentially due to Hilbert [Hz]. Granted this axiom, models for universal theories, Proc. Symp. Pure Math., quantifiers can be defined as abbreviations vol XXV, Proceedings of the Tarski Symposium, Amer. Math. Soc., Providence, RI, 1974, pp. 53- 74. :Jycp(x, y) = cp(x, Er:p,y (x)) [Mol M. MoRLEY, The number of countable models,]. Sym­ bolic Logic 35 (1970), 14- 18. and !M1l]. MYcrELSKJ, Two remarks on Tychonoff's Product The­ Vycp(x, y ) = cp(x, E~r:p,y(x)). orem, Bull. Acad. Polan. Sci., Series Math. Astr. Phys. 12 (1964), 439-441. Then the usual rules of logic concerning quantifiers (Mz] __, Games with perfect information, Handbook can be derived from (H). Also using these formu­ of Game Theory with Economic Applications (R.]. Au­ las and working from inside out, variables (and mann and S. Hart, eds.), North- Holland, 1992, pp. 41- 69. quantifiers) can be eliminated from every sentence; [M3] __, Axioms which imp ly G CH, Fund. Math. 176 and (H) can be viewed as an axiom-schema or a rule, (2003), 193- 207. where x andy are arbitrary strings of names of con­ !Mil __, On the axiom of determinateness, Fund. Math. stants. 53 (1964), 205- 224.

212 N OTICES OF THE AMS VOLUME 53, N UMBER 2 About the Cover [Ms] __, Pure mathematics and physical reality, to ap­ pear in Fundamental and Applied Mathematics (Fun­ ICM Madrid 2006 damentalnaya i prikladnaya matematika) 11(5), 2005. As Manuel de Leon and Allyn Jackson explain elsewhere [M5 S]]. MYCIELSKI and H. STEINHAUS, A mathematical axiom in this issue, the next International Congress of Mathemati­ contradicting the axiom of choice, Bull. Acad. Polan. cians will be held in the summer of 2006 in Madrid. As many Sci., Series Math. Astr. Phys. 10 (1962), 1-3. mathematicians already know, a number of extremely hand­ [N1lL NEEMAN, Optimal proofs of determinacy, Bull. Sym­ some posters have been distributed to advertise the event. bolic Logic 1 (1995), 327-339. The image on this issue's cover, which shows the cupola of [Nz] _ _ , Optimal proofs of determinacy (II), ]. Math. Logic 2 (2002), 227-258. the Sala de las dos Hermanas in the Alhambra, is taken from [P] R. PENROSE, The Road to Reality, A. A. Knopf, New York, one of them. Two of the posters are shown in the article by 2005. Allyn Jackson, and the other two are reproduced below. The [S] S. SHELAH, Logical dreams, Bull. Amer. Math. Soc. 40 verses by Ibn Zarnrak, mentioned in a caption in Jackson's (2003), 203-228. article, are just visible on the cover. One of the posters below [Sk] T. SKOLEM, Logico-combinatorial investigations in the exhibits a view of the Colegio de las Teresianas, designed by satisfiability or provability of mathematical proposi­ the Barcelonian architect Gaudi, and the other the cupola of tions (1920), in From Frege to G6del, A Source Book in the imperial Escorial Palace just outside Madrid. The graph­ Mathematical Logic, 1879-1931, (].van Heijenoort, ics designer for all of the posters associated with the ICM ed.), Harvard Univ. Press, Cambridge, 1976, pp. 2006 was Maria Casassas of Barcelona. The photographer was 252-263. Marc Llimargas, who specializes in architectural photogra­ [So] R. M. SoLOVAY, Strongly compact cardinals and the GCH, Proc. Symp. Pure Math., vol X\Y, Proceedings of phy. In particular, he did the photography for a recent book the Tarski Symposium, Amer. Math. Soc., Providence, on Gaudi. Rl, 1974, pp. 365-372. The geometric nature of Islamic design, incorporating [Su] P. SUPPES, Axiomatic Set Theory, Dover Publ. Inc., New complex symmetries, has been well-explored from a math­ York, 1972. ematical point of view. A fairly sophisticated discussion, re­ [T] W. TAYLOR, Some constructions of compact algebras, ferring specifically to the Alhambra, can be found in the book Annals of Math. Logic 3 (1971), 395-436. Classical Tessellations and Three-manifolds by Jose Maria [W1l W. H. WOODIN, The Continuum Hypothesis, Notices Montesinos. One good introduction to the Alhambra, with a Amer. Math. Soc. 48 (2001), Part I, 567-576; Part II, short discussion of the mathematics in context, is the book 681-690; correction to Part II, ibidem 49 (2002), 46. The Alhambra by Oleg Grabar. A mathematical treatise much [Wz] W. H. WooDIN, Set theory after Russell: The journey back to Eden, One Hundred Years of Russell's Paradox, respected by nonmathematicians is the University of Zurich (G. Link, ed.), de Gruyter, Amsterdam, New York, 2004, Ph.D. thesis of Edith Muller, Gruppentheoretische und Struk­ pp. 29-47. turanalytische Untersuchungen der Maurischen Ornamente aus der Alhambra in Granada. Our thanks to Manuel de Leon for his help in obtaining the images we used. - Bill Casselman, Graphics Editor ([email protected])

FEBRUARY 2006 NOTICES OF THE AMS 213 NIH DIRECTOR'S

PIONEER A·W·A· R· D '\' Book Review

PopCo Reviewed by AlexKasman

PopCo all of her spare time Scarlett Thomas attempting to prove Harvest Books, 2005 the Riemann Hy­ 512 pages, US$14.00 pothesis. Her grand­ ISBN015603137X father, Peter Butler, who was not allowed The novel PopCo by Scarlett Thomas is many dif­ to help Britain with ferent things at once. It is a psychological study of the war effort due to the social pressures on a teenage girl in a new his early antiwar school. It presents a sort of "conspiracy theory" activism, writes a about the manipulation of consumers by advertisers column on mathe­ and manufacturers (and a "counter-conspiracy" by matical puzzles for an underground movement). It parodies the events a science magazine. at a corporate retreat, where workers are forced to (At one point the participate in morale building exercises. It also book mentions Mar­ tells an adventurous story of pirates and the mod­ tin Gardner and his ern rediscovery of long hidden treasure. Surpris­ column in Scientific ingly, PopCo is also a particularly good example of American, calling it "mathematical fiction". an "American version" of Butler's "Mind Mangle" The protagonist in this book is Alice Butler, a column.) However, because he was not allowed to young British woman working as an inventor of work at Bletchley Park, Peter Butler still feels that he has something to prove to the world. So, Alice's products for introverted teenager~ at the multi­ national toy corporation, PopCo. Her product line grandfather spends his time trying to decode fa­ includes toys involving code-breaking, spying, and mous mysterious documents like the Voynich Man­ uscript and the Stevenson/Heath manuscript. puzzle-solving. In fact, Alice has a very good back­ While the Voynich manuscript is a real document ground for this sort of job because of her grand­ whose original purpose remains unknown (see, for parents. After her mother died and her father left instance, mathematician John Baez's page on it at she was raised by her grandparents who were both http://math.ucr.edu/home/baez/voynich. rp.athematicians. Her grandmother, who was a code­ html ), the Stevenson/Heath manuscript is sup­ breaker at Bletchley Park during World War II, spent posedly known to be the key to a pirate's hidden treasure and was invented for this book. When Alex Kasman is associate professor of mathematics at the C:ollege .of Charleston. His email address is Alice was still very young, Peter Butler broke the [email protected]. code of the Stevenson/Heath ·manuscript and

fEBRUARY 2006 NOTICES OF THE AMS 215 discovered the location of the treasure. However, antisocial, as unfeeling, etc.) are all avoided here. for reasons both personal and environmental, he And her ability to fit mathematical ideas into a decides not to retrieve it or tell anyone else where story without the result seeming forced is quite it is. (It was this decision that prompted her father amazing. In the world of PopCo, sophisticated to leave.) Instead, he encodes a secret message in mathematics can arise in a casual conversation a locket that he gives to young Alice which will serve and not seem at all out of place. Of course, I am a as proof that he was indeed the first to break the mathematician, and so I might not be reacting to code and discover the location of the treasure. the mathematics the way a non-mathematically in­ The locket has in it the expression clined reader might. However, that I could com­ "2 .14488156Ex48" and the Hebrew letter "aleph" fortably read through Alice's frequent discussions with a subscript zero, Georg Cantor's notation for of homeopathy testifies to Thomas' literary skill. the cardinality of a countably infinite set. Alice Because of my own skeptical inclinations, I would learns the mathematical significance of the aleph not normally choose to read about someone trying early on in her childhood, entertaining her grand­ to decide which homeopathic remedy one should parents by answering questions such as "How many take when one "feels like glass". Though reading biscuits would you like, Alice?" with "Aleph-null, this book has not changed my mind about home­ please". However, the significance of the other clue opathy, it has given me a better understanding of on the necklace eludes her and becomes the main those who feel differently. And I would like to focus of her own hunt for the pirate's treasure. think that the same might be true of readers who Mathematics is everywhere in Alice's world, not would not normally want to read about someone only in those portions connected to her mathe­ discussing math. matical grandparents. In those scenes that take Thomas also comes very close to avoiding one place when she is in school, mathematics gets men­ of the other pitfalls of mathematical fiction. Often tioned frequently. In part, this is because she has authors have such a poor understanding of the an interest in mathematics, but most of the focus mathematical objects they choose to include in is on her sexist teacher who refuses to allow girls their fiction that the result is unreadable by math­ to excel in his math class. Later, a speaker at the ematicians. Although her writing is not entirely PopCo retreat talks to the workers about networks mathematically correct, Scarlett Thomas does ba­ and asks if anyone there has heard of Paul Erdos. sically understand the main ideas and conveys Alice is able to say that she has-her grandmother them well. For instance, without getting into any had an Erdos number of 2-but she is not alone. details about modular arithmetic, she really gets A coworker who has aleph-one (the next "size" of across the significance of public key encryption in infinity) tattooed on his hand demonstrates de­ the form of an analogy about locked boxes. Since tailed familiarity with Erdos and also with net­ Alice has been factoring numbers in an attempt to works. And, when the workers are divided into help her grandfather with the Voynich manuscript, teams for a sailing competition, Alice is elected as she appreciates the difficulty presented by factor­ her boat's navigator because of her mathematical ing very large numbers, which also helps the reader skills. Clearly, mathematics is something one needs appreciate modern number theoretic methods in to know about in the fictional world of PopCo. cryptography. Thomas also does an excellent job The list of mathematical topics discussed in discussing Godel's method for encoding mathe­ the book, some addressed in depth and others just matical expressions as numbers. However, she casually, is quite broad. Among them are: Cantor's becomes a bit confused in her explanation of the transfinite cardinals, prime numbers, public key proof of his incompleteness theorem, leaving encryption, the Monty Hall problem, the Riemann out the key point of its meta-mathematical recur­ Hypothesis, Pythagoras' numerical analysis of pleas­ siveness. In her version, Gbdel writes logical ing musical tones, Go del's incompleteness theorem, statements only about arithmetic properties (she the Continuum Hypothesis, logical paradoxes, Con­ suggests that "If 1 + 1 = 2 then 1 + 1 = 3" is akin to way's "Game of Life", and the Fibonacci sequence. the key step in the proof), and so she seems to The novel even includes as an appendix a table of conclude that mathematics is inconsistent. Fortu­ the first 1,000 prime numbers and relates anecdotes nately, this is not true or we might all be out of a about mathematicians such as Turing, Erdos, and job! If she had explained that it was also possible Hardy. to encode statements about whether something Thomas' ability to include mathematics in her was provable, she could have more correctly used fiction is impressive on several counts. She avoids "This statement cannot be proved" as her simpli­ two of the most common problems of mathemat­ fied example of Gbdel's key step, since the ability ical fiction: awkwardly including technical prose to make such a statement in arithmetic terms that seems out of place, and relying too heavily on leads either to the conclusion that arithmetic is stereotypes. The common stereotypes of mathe­ inconsistent (because proving this statement maticians in fiction (as male, as schizophrenic, as would contradict the statement itself) or that it is

216 NOTICES OF THE AMS VOLUME 53, NUMBER 2 incomplete (since if it could not be proved then this would be an example of a true but unprovable statement). Her poetic description of the Riemann Department of Hypothesis also borders on being mathematically Mathematics incorrect, and one of the substitution ciphers in the book had two letters accidentally interchanged. Revised announcement. The Department However, I do not want to dwell too much on these of Mathematics anticipates two vacancies. The successful candidate will teach all small problems when the book is so successful levels of undergraduate mathematics and appealing otherwise. courses, as well as participate in research. Of course, whether one likes a novel or not is Candidates with expertise in Actuarial largely a matter of taste. PopCo has a subversive Sciences will be given special and lively style that appealed to me. One aspect of consideration. my personal taste in fiction is that I like to see an Founded in 1919, AUC 's campus is ending in which all of the mysteries and dilemmas currently located in Cairo, Egypt, but will be moving to a new, state-of-the-art are resolved, especially if it is able to achieve that campus in New Cairo beginning Fall "Aha!" feeling that one gets after solving a difficult Semester, 2007 (see the New Campus problem or proving a mathematical result. Others website at www.aucegypt.edu/ncd/ may prefer an ambiguous ending, such as the New%20Campus.html). AUC's degree programs are accredited by the ending of David Auburn's play Proof, which leaves Commission on Higher Education of the everything to the audience's imagination. An end­ Middle States Association of Colleges and ing that is conclusive and satisfying is very diffi­ Schools. For more information see our cult to achieve, and PopCo succeeds here as well. website at www.aucegypt.edu. One- two­ In the end, there is a resolution ("Aha!") that ties or three-year appointments subject to mutual agreement will begin September together all of the loose threads. Mathematically 2006. Renewal of an appointment inclined readers may also appreciate the self­ depends upon institutional needs and/or referential implications towards the end of the the appointee's performance. The normal book, when Alice begins talking about how she teaching load is three courses per semester and English is the language of would like to write a book about her experiences. instruction. Salary and rank are according PopCo is an entertaining and satisfying novel to scale based on qualifications and that embeds real mathematical ideas into a story professional experience. For expatriates, about toys, trends, and fashions. That this im­ benefits include housing, annual round­ trip air travel for appointee and qualifying probable sounding combination is so successful dependents, plus schooling for the may explain why Scarlett Thomas was the winner equivalent of up to two children at Cairo of a 2002 style award from Elle magazine. American College. In view of AUC's protocol agreement with the Egyptian For more information, visit Scarlett Thomas' Government, which requires specific proportions of Egyptian, U.S., and third­ homepage at http: I lwww. bookgi r 7. org (where country citizen faculty, at this time you can find two very mathematical chapters that preference will be given to qualified were cut from the book) and http:llmath. cafe. applicants who are U.S. citizens. edulkasmaniMATHFICTI where you can read more APPLICATION INSTRUCTIONS: E­ about PopCo and other works of mathematical mail a letter of intent specifying fiction. Position # MATH-1/2 with a current C.V. to [email protected] and arrange to have three letters of recommendation mailed to: Dr. Earl (Tim) Sullivan, Provost @ American University in Cairo 420 Fifth Avenue, Fl. 3 New York, N.Y. 10018-2729 For full consideration, candidates must also complete the Personnel Information Form provided at http://forms.aucegypt.edu/ provost/pif3.html. Applications accepted until position is filled; review of candidates will begin immediately. The American University in Cairo is an equal opportunity employer.

fEBRUARY 2006 NOTICES OF THE AMS 217 In High Gear: Spanish Mathematics Looks to the Future and to ICM2006 Allyn jackson

The International Congress of Mathematicians will be held in Madrid, Spain, August 22-30, 2006. The Second Announcement of the Congress appeared in the December 2005 issue of the Notices, pages 1407-1432, and contains information about the scientific program, the social program, registration, and accommodations. Updated information may be found on the ICM2006 website, http: I /www. i cm2006. org.

Today, mathematics in Spain is in high gear. Many a mathematics research laboratory was established Spanish mathematicians are working at the top in­ in Madrid in 1915. But the laboratory disappeared ternational echelons of research, speaking at im­ during the Spanish Civil War, and the RSME began portant conferences, and publishing papers in the a slow decline that was reversed only with its re­ best journals. But this high level of mathematical founding in 1997. activity is a relatively recent phenomenon in Spain. During much of the twentieth century, when Even as Spanish mathematicians applaud the many other countries were building up the infra­ growth in their field, they see challenges ahead structure and traditions that support research, and know that sustaining the newfound momen­ Spain was under the dictatorship of Francisco tum will take plenty of effort. Their successful bid Franco, which lasted from the 1930s until Franco's to bring the International Congress of Mathemati­ death in 1975 and kept Spain rather isolated from cians (ICM) to Madrid in August 2006 is emblem­ atic of their efforts to highlight Spanish mathe­ research at the international level. The Franco matics and keep it thriving. regime did make some efforts to support research within Spain and in particular founded the CSIC, Scientifically, A Developing Country which remains today one of the country's most im­ When it comes to scientific and mathematical re­ portant organizations for research. The CSIC con­ search, Spain is in many ways a developing coun­ sists mainly of a collection of institutes with per­ try. "We don't have a tradition of research in Spain," manent research staffs. In 1939, the Instituto Jorge said Manuel de Leon, a permanent researcher at the Juan de Matematicas was created in the CSIC. Al­ Consejo Superior de Investigaciones Cientificas though this institute was run more on the basis of (CSIC, High Council for Scientific Research) and influence and connections than on mathematical president of the Executive Committee for ICM2006. accomplishment, it nevertheless played an impor­ During the Middle Ages there were very good Ara­ tant role in keeping mathematics alive in Spain. So bic and Jewish mathematicians in Spain, and in it was a setback for the Spanish mathematical com­ 15 72 King Phillipe II founded the Academia de munity when the Jorge Juan Institute was shut Matematicas de Madrid. Nevertheless, Spain has tra­ down in 1984. Today mathematicians who work ditionally been known more for its arts and liter­ within CSIC are employed by institutes in other ature than for science and mathematics. In the areas. For example, de Le6n works in a Madrid­ early part of the twentieth century, some mathe­ based CSIC institute focused on theoretical and matical activity began to develop. The Real So­ fundamental physics, which is the only CSIC insti­ ciedad Matematica Espaiiola (Royal Spanish Math­ ematical Society, RSME) was founded in 1911 and tute that has a mathematics department. This de­ partment has seven permanent members, eight Allyn jackson is senior writer and deputy editor of the postdoctoral researchers, and eight doctoral stu­ Notices. Her email address is axj @ams. o rg. dents.

218 NOTICES OF THE AMS VOLUME 53, NUMBER 2 The improvement over the last couple of decades algebraic and differential geometry, partial differ­ of Spain's economic condition led to increased in­ ential equations, probability theory, and Fourier, vestment in research and education, which in turn complex, and functional analysis. Some branches improved the climate for mathematics. During this of mathematics, such as number theory and logic, time, and particularly in the last ten years, math­ have little representation in Spain. Most of the re­ ematics in Spain has undergone a revival. There are search, even in such areas as PDEs and numerical many more Spanish mathematicians working at analysis, tends toward the theoretical end of the the top levels of mathematics research than before. spectrum. According to data collected by the Institute of Sci­ Aside from the RSME, Spain has three other entific Information (lSI), the percentage of mathe­ major mathematical societies: the Societat Catalana matics research papers written by Spanish authors de Matematiques (Catalan Mathe- has grown from 0.3 percent in 1980 to close to 5 matical Society), the Sociedad percent today. "Now when you open international Espafwla de Matematica e journals, it is common to see Spanish authors," Aplicada (Spanish Society commented Carlos Andradas of the Universidad of Applied Mathemat­ •.. - Complutense de Madrid, who is the current presi­ ics), and the Sociedad dent of the RSME and vice president general of the de Estadistica e Inves­ -· ..,i ·. -~ •• ICM2006 Executive Committee. "This was not the tigaci6n Operativa (So­ ~ "· ciety for Statistics and -· (I; •• case several years ago." One also sees more Span­ Operations Research). ish mathematicians on editorial boards of jour­ • "' it'! nals, as winners of international prizes, and as In 1998 these four or­ . ganizations banded to­ participants in research programs such as the in­ •• '41 •••• • • ternational networks funded by the European gether to create a new Union. Spanish National Com­ The lSI also publishes a list of the world's most mittee for representation highly cited scientists. Among the fifteen Spaniards within the International •• •••• on this list, mathematics has the largest showing, Mathematical Union (IMU) (for with four mathematicians. The four are: David Nu­ many years, Spain's IMU represen­ • • Logo of ICM2006. alart of the Universitat de Barcelona and the Uni­ tation was handled directly by the Ministry The logo is an versity of Kansas, Jesus Maria Sanz Serna of the Uni­ of Education and Science, which is the of­ idealized image of a versidad de Valladolid, and Juan Luis Vazquez and ficial adhering organization to the IMU). sunflower. The Enrique Zuazua, both of whom are at the Univer­ These four organizations also collabo­ n_umber of spirals to sidad Aut6noma de Madrid. Vazquez will deliver rated to prepare the bid to the IMU to the right and left in a plenary lecture at ICM2006, while Nualart and hold the 2006 ICM in Madrid. Carles a sunflower are Zuazua will present section lectures. Indeed, de Casacuberta of the Universitat de Barcelona, who is the current president of consecutive Le6n pointed to the strong showing of Spanish numbers of the mathematicians among ICM2006 speakers-nine in the Catalan Mathematical Society and a vice president of the ICM2006 Executive Fibonacci sequence. all-as yet another indication of the burgeoning of The logo also mathematics in Spain. Committee, stated in an email message: "The bid's success testifies to the progress symbolizes the idea Rising Investment in Mathematics and unity of the Spanish mathematical of Spain as a Mediterranean Mathematics research in Spain is concentrated community, in spite of its rich thematic and geographical diversity. Now Spain is country. The colors mainly in the country's universities. Judging by of the logo are used, percentage of mathematics papers written, the pri­ willing and prepared to host this ICM. I doubt it would have been possible twenty to identify different mary centers are in Andalusia (19 percent), fields of ICM2006 Barcelona (21 percent), and Madrid (24 percent). years ago, or perhaps even ten years ago. Nowadays we have strong teams in al­ activity. For There are also strong groups in Granada, Santiago, example, orange Sevilla, and other places. There is one mathemat­ most every mathematical subject, linked by growing research structures, and the represents r ics research institute that operates at the interna­ scientific activity. tional level, the Centre de Recerca Matematica whole community is ready to support the (CRM), based at the Universitat Aut6noma de ICM." The four mathematical societies- Barcelona. The CRM is supported by the Institut together with two other societies in education and d'Estudis Catalans, a scholarly academy devoted to history, plus a federation of teachers' associa­ the promotion of Catalan culture. de Le6n esti­ tions-have formed the Comite Espaiiol de mates that there are about 3,000 permanent posi­ Matematicas (Spanish Committee for Mathemat­ tions for Spain's approximately 6,000 mathemati­ ics, CeMAT), which aims to coordinate Spanish ac­ cians C).nd that about one-quarter of these tivities connected with the IMU. individuals are actively doing research. Among the Right now Spain devotes just over 1 percent of main areas of strength are algebraic topology, its gross domestic product to research, while the

FEBRUARY 2006 NOTICES OF THE AMS 219 The ICM2006 Alhambra Poster. The Hall of the Two Sisters (Sal a de las dos Hermanas) derives its name from the twin marble flagstones forming part of the floor. This hall was in the center of a series of chambers where the Sultana and her family lived. The hall was built by order of Mohammed V. It is square, has interlacing ceilings and bedchambers connected with the Emperor's Chambers (Habitaciones de Carlos V) and, through a balcony, with the Gardens of the Partal Uardines del Partal). Visitors may access the hall through a semicircular festooned arch, where the original wooden doors are still preserved. A passageway leads to the high chambers, with ceilings carved in the 16th century. Three little arches, with Mozarabs on the lateral arches and arch scallops on the central arch, lead to the chamber of the mirador. You can see the Patio of the Lions (Patio de los leones) from there. The hall's paving is made of marble and has a small fountain with a jet and a little channel that carries the water to the Patio of the lions. The most impressive feature of the hall is the beautiful and perfect Mozarabic dome. Its lighting was carefully considered and it receives the light from small lateral windows. The dome is therefore a beautiful and exquisitely rich flower. Ibn Zamrak wrote a poem about this dome, and some of his verses are reproduced on a tile skirting board that has metallic iridescence. The hall's walls are covered with extremely fine plasterwork with different themes, among which we find the class-ical Nasrid motto "Only God is victorious" · and also, for example, a pair of clasped hands.

average for countries in the European Union is Euros in 2004. The grants are usually given to about 2 percent; the benchmark set by the EU is teams of researchers and function much like grants 3 percent. The current Spanish government has from the U.S. National Science Foundation, although set a target to reach 2 percent by 2010, so it seems the Spanish government does not provide any likely that funding for research in Spain will con­ salary for principal investigators. The increase in tinue to grow. The government supports research funding has had a large impact, improving the re­ primarily through the Ministry of Education and Sci­ search conditions for mathematicians and making ence, which in particular provides funding for the it easier to support students. "Every single active CSIC. Employing about 2,500 scientists in 120 in­ mathematician felt the effect" of the National Pro­ stitutes across Spain, the CSIC is the country's main gram in Mathematics, commented Casacuberta. research organization. Very few mathematicians Zuazua and others said that the National Pro­ have positions in the CSIC, and there is no single gram in Mathematics has reached a plateau and now CSIC institute devoted to mathematics. But in an­ provides sufficient support for small teams of re­ other sign of the progress of mathematics in Spain, searchers. They argue that what is needed now is plans are now being laid to launch a CSIC mathe­ a more ambitious endeavor, such as establishing matics institute, possibly in 2006, in cooperation a major national center for mathematics in Spain. with the three major universities in Madrid (the And indeed the Spanish government that was in Aut6noma, the Complutense, and the Carlos III). power before the elections in spring 2004 agreed For the past twenty years or so, the Ministry of in principle to establish a National Research Cen­ Education and Science has also supported research ter for Mathematics. But exactly what form this cen­ through grant programs. Mathematics did not have ter will take and exactly when it will come into being its own funding program but was funded through are open questions. At least at first, it will most a general program for basic research overseen by likely be a "distributed institute" consisting of a net­ a committee that also dealt with physics grants. work of university-based groups, CSIC institutes, This changed in 2001, when the government and the CRM. Deciding whether and where1to erect stepped up its support for research and decided a building that would serve as a permanent home to launch a separate mathematics program. En­ for the center is, according to Zuazua, fraught with rique Zuazua was appointed to get the new program political difficulties that the government is not yet off the ground, and after a transition period, the prepared to face. There are vague hopes that an an­ National Program in Mathematics was formally es­ nouncement about the center's establishment will tablished in 2004. (In spring 2005 a new manager be made at the ICM in August 2006, but nothing is of the program was appointed, Emique Fernan­ certain yet. Zuazua believes the government will dez-Cara of Sevilla University.) The last five years eventually fund the center, but he sees some ur­ have seen large growth in government funding for gency in getting the project going soon. "We are los­ mathematics, from just under 2 million Euros (ap­ ing important years," he noted. "There is a great proximately US$2.5 million) in 2000 to 5.5 million generation of mathematicians in Spain right now.

220 NOTICES OF THE AMS VOLUME 53, NUMBER 2 The ICM2006 Calatrava poster. This is a photograph of the City of Arts and Sciences in Valencia, Spain, designed by the Spanish architect Santiago Calatrava. The photograph depicts an example of the new Spain, a dynamic country open to science and technology.

"As the site is close to the sea, and Valencia is so dry, I decided to make water a major element for the whole site using it as a mirror for the architecture." -Santiago Calatrava

Thanks to Manuel deLeon for providing text describing the subjects of the two ICM posters.

These people are getting older, and they cannot wait a propensity for deep but somewhat narrow re­ forever to have the right tools for their research." search, and the infusion of new ideas that can come from interactions with other disciplines is Challenges Ahead missing. At the same time, there is little recogni­ The many positive developments in mathematics tion for interdisciplinary work. But this too seems in Spain seem to presage a bright future, but the to be changing. "Ten years ago there was a big ex­ mathematical community there nevertheless faces plosion of mathematics on Wall Street," Zuazua ob­ some substantial challenges. One is the declining served. "Now it is happening here in Spain." Span­ number of students pursuing mathematics- a phe­ ish companies are slowly waking up to the value nomenon that is not particular to Spain but in fact of mathematics, and industrial laboratories have seems to be worldwide in scope. When he first gradually begun hiring mathematicians. However, came to Madrid in 1990, Zuazua would have per­ the effect has not yet been large enough to lure haps fifteen students in his graduate classes. more students into the field. "Today, if I have three students, I am very happy," A third challenge for Spanish mathematics is the he said. In Spain, ties between mathematics and in­ inbred nature of the academic hiring system. It is dustry have traditionally been weak, so Spanish not only rare to find a foreigner in a Spanish math­ companies generally do not seek mathematically ematics department, it is even unusual to find trained employees. As a result, the career path for someone from outside the local area. Zuazua re­ those with advanced mathematical training points called that, when he took a position at the Univer­ inevitably to academia- where in recent years jobs sidad Complutense in Madrid, there was grum­ have been few and far between. But this situation bling that his job should have gone to a local; is poised to change. Recently Andradas helped to Zuazua is originally from Bilbao in the Basque prepare a study that concluded that about half of country. Many mathematics departments are filled all professorial positions in Spain will open up in with people who received their Ph.D.'s there or at the corning decade. "For young people starting nearby universities. While a case can be made that now, the perspectives are much better than for such a strategy helps to build cohesive research people who started ten years ago," he noted. Nev­ groups, over the long term the result can be medi­ ertheless, it remains difficult right now to con­ ocrity. Andradas noted that Spain has made some vince students to pursue and remain in mathe­ efforts to try to improve the. hiring system, but matics. de Leon noted that Spanish mathematicians change has been exceedingly difficult. "Spain is a have begun several initiatives to spark the interest country where mobility is still not very common," of young people in mathematics, such as the "Di­ especially when one is over thirty-five and has vulgamat" website of the RSME that contains vir­ one's own family, he noted. "People try to work in tual exhibitions, popularizations, mathematical po­ the neighborhood where they grew up and where etry, biographies of mathematicians, and other their family is living. Family still has a strong in­ resources. fluence here." .A second challenge, according to Zuazua, is re­ Intense local loyalties have developed hand in lated to the lack of connection to industry. Such hand with this hiring system, and big centers like connections are not easy to cultivate, so, as Zuazua Madrid are sometimes eyed with suspicion by math­ put it, "you continue to work on your inequality." ematicians in other places. de Leon and the As a resuit, Spanish mathematicians have developed ICM2006 co-organizers seem deferrnined to use fEBRUARY 2006 NOTICES OF THE AMS 221 the occasion of the Congress to bring the Spanish tree-it is not enough for the tree to flower, it must mathematical community together. "We are trying also bear fruit. "ICM06 is the flower, but we have to get every university, every mathematician, to feel to be extremely hard workers, clever and coordi­ that he or she is a part of the ICM organization," nated, and able to convince politicians if we want he said. "It is not a separate thing-it's an ICM by that to persist and to give the fruit of putting Spain the full Spanish mathematical community." To this in the first division of mathematics," he said. end, the ICM executive committee has held its "ICM06 is a proof of our success, but also the right meetings in various cities around Spain, so that they time to be extremely, but positively, critical of our­ could discuss the plans with local mathematicians. selves." It would have been easier to have had all of the meetings in Madrid, de Leon noted. But the ICM or­ ganizers wanted to make the point that "this is the ICM for Spain, not just for Madrid." Reaching Out In fact, the organizers are reaching out far beyond the borders of Spain. Because this is the first ICM to be held in a Spanish-speaking country, special efforts are being made to bring in participants from Latin America, through a program of travel grants. Because of Spain's geographical and cultural proximity to north Africa, the ICM organizers are working to foster participation by mathematicians from that area. Also in the works is a special con­ ference called "Mathematics for Peace and Devel­ opment", to be held in Cordoba in conjunction with the ICM. Spain has a unique cultural identity formed through an unusual combination of Jewish, Islamic, and Christian influences. The idea, said de Leon, is to capitalize on this heritage and "use mathematics as an instrument for peace." The con­ ference would bring together mathematics stu­ dents from Latin America, north Africa, Israel, and the Middle East. The Congress itself will be held at the Palacio Mu­ nicipal de Congresos, a convention center in the northeast of Madrid. The format is the traditional one of plenary and parallel "section" lectures. While the breakdown of areas into sections is largely the same as for previous ICMs, some tweaking has been done. Also, rather than nineteen sections, as there were at ICM2002, there are now twenty: A sec­ tion devoted to "Control Theory and Optimiza­ tion" has been added. The cultural attractions of Madrid will be on full display, and there will be spe­ cial events aimed at communicating mathematics to the wider Spanish public. At the previous ICM in 2002 in Beijing, the president of China, ]iang Zemin, presented the Fields Medals. That's a tough act to follow, but the ICM organizers have received assurances from the King of Spain that he will at­ tend the opening ceremonies. Mathematics in Spain seems poised to grow and prosper, and many mathematicians there speak with great ambition about their aspirations for the future. At the same time, they are not resting on their laurels. They see challenges ahead, and they are working to meet them. Zuazua likened the de­ velopment of mathematics in Spain to an orange

222 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Interview with Peter D. Lax Martin Raussen and Christian Skau

Peter D. Lax is the recipient of the 2005 Abel Prize of the Norwegian Academy of Science and Letters. On May 24, 2005, prior to the Abel Prize celebrations in Oslo, Lax was interviewed by Martin Raussen of Aalborg University and Christian Skau of the Norwegian University of Science and Technology. This interview originally appeared in the European Mathematical Society Newsletter, September 2005, pages 24-31.

Raussen & Skau: On behalf of the Norwegian and bued with the utter importance of computing for Danish Mathematical Societies we would like to con­ science and mathematics. Los Alamos, under the gratulate you on winning the Abel Prize for 2005. influence of von Neumann, was for a while in the You came to the U.S. in 1941 as a fifteen-year­ 1950s and the early 1960s the undisputed leader old kid from Hungary. Only three years later, in in computational science. 1944, you were drafted into the U.S Army. Instead of being shipped overseas to the war front, you Research Contributions were sent to Los Alamos in 1945 to participate in R & S: May we come back to computers later? First the Manhattan Project, building the first atomic some questions about some ofyour main research bomb. It must have been awesome as a young man contributions to mathematics: You have made out­ to come to Los Alamos to take part in such a mo­ standing contributions to the theory of nonlinear mentous endeavor and to meet so many legendary partial differential equations. For the theory and nu­ famous scientists: Fermi, Bethe, Szilard, Wigner, merical solutions of hyperbolic systems of conser­ Teller, Feynman, to name some of the physicists, and vation laws your contribution has been decisive, von Neumann and Ulam, to name some of the math­ not to mention your contribution to the under­ ematicians. How did this experience shape your standing of the propagation of discontinuities, so­ view of mathematics and influence your choice of called shocks. Could you describe in a few words how a research field within mathematics? you were able to overcome the formidable obstacles Lax: In fact, I returned for a year's stay at Los and difficulties this area of mathematics presented? Alamos after I got my Ph.D. in 1949 and then spent Lax: Well, when I started to work on it I was very many summers as a consultant. The first time I much influenced by two papers. One was Eberhard spent in Los Alamos, and especially the later ex­ Hopf's on the viscous limit of Burgers' equation, posure, shaped my mathematical thinking. First of and the other was the von Neumann-Richtmyer all, it was the experience of being part of a scien­ paper on artificial viscosity. And looking at these tific team-not just of mathematicians, but people examples I was able to see what the general the­ with different outlooks-with the aim being not a ory might look like. theorem, but a product. One cannot learn that from R & S: The astonishing discovery by Kruskal and books, one must be a participant, and for that Zabusky in the 1960s of the role of solitons for so­ reason I urge my students to spend at least a sum­ lutions of the Korteweg-de Vries (KdV) equation, and mer as a visitor at Los Alamos. Los Alamos has a the no less astonishing subsequent explanation given very active visitor's program. Secondly, it was by several people that the KdV equation is com­ there-that was in the 1950s-that I became im- pletely integrable, represented a revolutionary de­ velopment within the theory of nonlinear partial dif­ Martin Raussen is associate professor of mathematics at ferential equations. You entered this field with an Aalborg University, Denmark. His email address is ingenious original point of view, introducing the [email protected]. so-called Lax-pair, which gave an understanding of Christian Skau is professor of mathematics at Norwegian how the inverse scattering transform applies to University ofScience and Technology, Trondheim, Norway. equations like the KdV, and also to other nonlinear His email address is csk@math. ntnu. no. equations which are central in mathematical physics,

FEBRUARY 2006 NOTICES OF THE AMS 223 Now the question is: Are completely integrable systems exceptions to the behavior of solutions of non-integrable systems, or is it that other systems have similar behavior, only we are unable to ana­ lyze it? And here our guide might well be the Kolmogorov-Arnold-Moser theorem which says that a system near a completely integrable system behaves as if it were completely integrable. Now, what near means is one thing when you prove theorems, another when you do experiments. It's another aspect of numerical experimentation re­ vealing things. So I do think that studying com­ pletely integrable systems will give a clue to the be­ havior of more general systems as well. Peter D. Lax was interviewed by Martin Raussen and Who could have guessed in 196 5 that completely Christian Skau at t he Hotel Continental in Oslo. integrable systems would become so important? R & S: The next question is about your seminal like the sine-Gordon and the nonlinear Schrddinger paper "Asymptotic solutions of oscillating initial equation. Could you give us some thoughts on how value problems" from 1957. This paper is consid­ important you think this theory is for mathemati~ ered by many people to be the genesis ofFourier In ­ cal physics and for applications, and how do you tegral Operators. What was the new viewpoint in the view the future of this field? paper that proved to be so fruitful? Lax: Perhaps I should start by pointing out that Lax: It is a micro-local description of what is the astonishing phenomenon of the interaction of going on. It combines looking at the problem in the solitons was discovered by numerical calculations, large and in the small. It combines both aspects, as was predicted by von Neumann some years be­ and that gives it its strengths. The numerical im­ fore, namely that calculations will reveal extremely plementation of the micro-local point of view is by interesting phenomena. Since I was a good friend wavelets and similar approaches, which are very. of Kruskal, I learned early about his discoveries, and powerful numerically. that started me thinking. It was quite clear that R & S: May we touch upon your collaboration with there are infinitely many conserved quantities, and Ralph Phillips-on and off over a span of more than so I asked myself: How can you generate all at once thirty years- on scattering theory, applying it in a an infinity of conserved quantities? I thought if you number of settings. Could you comment on this col­ had a transformation that preserved the spectrum laboration, and what do you consider to be the most of an operator then that would be such a trans­ important results you obtained? pleasures of my formation, and that turned out to be a very fruit­ Lax: That was one of the great life! Ralph Phillips is one of the great analysts of ful idea, applicable quite widely. our time and we formed a very close friendship. We Now you ask how important is it? I think it is had a new way of viewing the scattering process pretty important. After all, from the point of view with incoming and outgoing subspaces. We were, of technology for the transmission of signals, sig­ so to say, carving a semi-group out of the unitary nalling by solitons is very important and a promis­ group, whose infinitesimal generator contained al­ ing future technology in trans-oceanic transmission. most all the information about the scatterjng This was developed by Linn Mollenauer, a brilliant process. So we applied that to classical scattering engineer at Bell Labs. It has not yet been put into of sound waves and electromagnetic waves by po­ practice, but it will be some day. The interesting tentials and obstacles. Following a very interesting thing about it is th.at classical signal theory is en­ discovery of Faddeev and Pavlov, we studied the tirely linear, and the main point of soliton signal spectral theory of automorphic function~. We €lab­ transmission is that the equations are nonlinear. orated it further, and we had a brand new approach That's one aspect of the practical importance of it. to Eisenstein series for instance, getting at spectral As for the theoretic importance: the KdV equa­ representation via translation representation. And tion is completely integrable, and then an aston­ we were even able to contemplate- following Fad­ ishing number of other completely integrable sys­ deev and Pavlov- the Riemann hypothesis peeking tems were discovered. Completely integrable around the corner. systems can really be solved in the sense that the R & S: That must have been exciting! general population uses the word solved. When a Lax: Yes! Whether this approach will lead to the mathematician says he has solved the problem he proof of the Riemann hypothesis, stating it, as one means he knows the solution exists, that it's unique, can, purely in terms of decaying signals by cutting but very often not much more. out all standing waves, is unlikely. The Riemann

224 NOTICES OF THE AMS VOLUME 53, NUMBER 2 hypothesis is a very elusive thing. You may re­ experimental facts, and, in particular, some nu­ member in Peer Gynt there is a mystical character, merical evidence. the Boyg, which bars Peer Gynt's way wherever he R & S: In the history of mathematics, Abel and goes. The Riemann hypothesis resembles the Boyg! Galois may have been the first great mathematicians R & S: Which particular areas or questions are that one may describe as "pure mathematicians", you most interested in today? not being interested in any "applied" mathematics Lax: I have some ideas about the zero dispersion as such. However, Abel did solve an integral equa­ limit. tion, later called "Abel's integral equation", and Abel gave an explicit solution, which incidentally Pure and Applied Mathematics may have been the first time in the history of math­ R & S: May we raise a perhaps contentious issue with ematics that an integral equation had been for­ you: pure mathematics versus applied mathemat­ mulated and solved. Interestingly, by a simple re­ ics. Occasionally one can hear within the mathe­ formulation one can show that the Abel integral matical community statements that the theory of equation and its solution are equivalent to the Radon nonlinear partial differential equations, though pro­ Transform, the mathematical foundation on which found and often very important for applications, is modern medical tomography is based. fraught with ugly theorems and awkward argu­ Examples of such totally unexpected practical ments. In pure mathematics, on the other hand, applications of pure mathematical results and beauty and aesthetics rule. The English mathe­ theorems abound in the history of mathematics­ matician G.H. Hardy is an extreme example of such group theory that evolved from Galois' work is an­ an attitude, but it can be encountered also today. other striking example. What are your thoughts on How do you respond to this? Does it make you this phenomenon? Is it true that deep and impor­ angry? tant theories and theorems in mathematics will Lax: I don't get angry very easily. I got angry once eventually find practical applications, for example at a dean we had, terrible son of a bitch, destruc­ in the physical sciences? tive liar, and I got very angry at the mob that oc­ Lax: Well, as you pointed out, this has very often cupied the Courant Institute and tried to burn happened: Take for example Eugene Wigner's use down our computer. Scientific disagreements do of group theory in quantum mechanics. And this not arouse my anger. But I think this opinion is def­ has happened too often to be just a coincidence. initely wrong. I think Paul Halmos once claimed that Although, one might perhaps say that other theo­ applied mathematics was, if not bad mathematics, ries and theorems which did not find applications at least ugly mathematics, but I think I can point were forgotten. It might be interesting for a histo­ to those citations of the Abel Committee dwelling rian of mathematics to look into that phenomenon. on the elegance of my works! But I do believe that mathematics has a mysteri­ Now about Hardy: When Hardy wrote A Mathe­ ous unity which really connects seemingly distinct matician's Apology he was at the end of his life, he parts, which is one of the glories of mathematics. was old, I think he had suffered a debilitating heart R & S: You have said that Los Alamos was the attack, he was very depressed. So that should be birthplace of computational dynamics, and I guess taken into account. About the book itself: There was it is safe to say that the U.S. war effort in the 1940s a very harsh criticism by the chemist Frederick advanced and accelerated this development. In what Soddy, who was one of the co-discoverers of the way has the emergence of the high-speed computer isotopes-he shared the Nobel Prize with Ruther­ altered the way mathematics is done? Which role will ford. He looked at the pride that Hardy took in the high-speed computers play within mathematics in uselessness of his mathematics and wrote: "From the future? such cloistral clowning the world sickens." It was Lax: It has played several roles. One is what we very harsh because Hardy was a very nice person. saw in Kruskal's and Zabusky's discovery of soli­ My friend Joe Keller, a most distinguished ap­ tons, which would not have been discovered with­ plied mathematician, was once asked to define ap­ out computational evidence. Likewise the Fermi­ plied mathematics and he came up with this: "Pure Pasta-Ulam phenomenon of recurrence was also a mathematics is a branch of applied mathematics." very striking thing which may or may not have Which is true if you think a bit about it. Mathematics been discovered without the computer. That is one originally, say after Newton, was designed to solve aspect. very concrete problems that arose in physics. Later But another is this: in the old days, to get nu­ on, these subjects developed on their own and be­ merical results you had to make enormously dras­ came branches of pure mathematics, but they all tic simplifications if your computations were done came from applied background. As von Neumann by hand, or by simple computing machines. And the pointed out, after a while these pure branches that talent of what drastic simplifications to make was develop on their own need invigoration by new a special talent that did not appeal to most math­ empirical material, like some scientific questions, ematicians. Today you are in an entirely different

FEBRUARY 2006 NOTICES OF THE AMS 225 situation. You don't have to put the problem on a Erdos and is related to a certain inequality for Procrustean bed and mutilate it before you attack polynomials, which was earlier proved by Bern­ it numerically. And I think that has attracted a stein. Much later in your career you studied the so­ much larger group of people to numerical problems called P6lya function which maps the unit interval of applications-you could really use the full the­ continuously onto a right-angled triangle, and you ory. It invigorated the subject of linear algebra, discovered its amazing differentiability properties. which as a research subject died in the 1920s. Sud­ Was problem solving specifically encouraged in your denly the actual algorithms for carrying out these early mathematical education in your native Hun­ operations became important. It was full of sur­ gary, and what effect has this had on your career prises, like fast matrix multiplication. In the new later on? edition of my linear algebra book I will add a chap­ Lax: Yes, problem solving was regarded as a ter on the numerical calculation of the eigenvalues royal road to stimulate talented youngsters, and I of symmetric matrices. was very pleased to learn that here in Norway they You know it's a truism that due to increased have a successful high-school contest, where the speed of computers, a problem that took a month winners were honored this morning. But after a forty years ago can be done in minutes, if not sec­ while one shouldn't stick to problem solving, one onds today. Most of the speed-up is attributed, at should broaden out. I return to it every once in a least by the general public, to increased speed of while, though. computers. But if you look at it, actually only half Back to the differentiability of the P6lya func­ of the speed-up is due to this increased speed. The tion: I knew P6lya quite well having taken a sum­ other half is due to clever algorithms, and it takes mer course with him in 1946. The differentiability mathematicians to invent clever algorithms. So it question came about this way: I was teaching a is very important to get mathematicians involved, course on real variables, and I presented P6lya's ex­ and they are involved now. ample of an area-filling curve, and I gave as home­ R & S: Could you give us personal examples of work to the students the problem of proving that how questions and methods from applied points of it's nowhere differentiable. Nobody did the home­ view have triggered "pure" mathematical research work, so then I sat down and I found out that the. and results? And conversely, are there examples situation was more complicated. where your theory of nonlinear partial differential There was a tradition in Hungary to look for the equations, especially your explanation of how dis­ simplest proof. You may be familiar with Erdos' con­ continuities propagate, have had commercial in­ cept of The Book. That's The Book kept by the terests? In particular, concerning oil exploration, Lord of all theorems and the best proofs. The high­ so important for Norway! est praise that Erdos had for a proof was that it was Lax: Yes, oil exploration uses signals generated out of The Book. One can overdo that, but shortly by detonations that are propagated through the after I had gotten my Ph.D., I learned about the earth and through the oil reservoir and are recorded Hahn-Banach theorem, and I thought that it could at distant stations. It's a so-called inverse problem. be used to prove the existence of Green's function. If you know the distribution of the densities of ma­ It's a very simple argument- ! believe it's the sim­ terials and the associated waves' speeds, then you plest-so it's out of The Book. And I think I have can calculate how signals propagate. The inverse a proof of Brouwer's Fixed Point Theorem, using problem is that if you know how signals propagate, calculus and just change of variables. It is proba­ then you want to deduce from it the distribution bly the simplest proof and is again out of l;'he of the materials. Since the signals are discontinu­ Book. I think all this is part of the Hungarian tra­ ities, you need the theory of propagation of dis­ dition. But one must not overdo it. continuities. Otherwise it's somewhat similar to R & S: There is an impressive list of great Hun­ the medical imaging problem, also an inverse prob­ garian physicists and mathematicians 'of Jewish lem. Here the signals do not go through the earth background that had to flee to the U.S. after the rise but through the human body, but there is a simi­ of fascism, Nazism and anti-Semitism in Europe. How larity in the problems. But there is no doubt that do you explain this extraordinary culture of excel­ you have to understand the direct problem very well lence in Hungary that produced people like de before you can tackle the inverse problem. Hevesy, Szilard, Wigner, Teller, von Neumann, von Karman, Erdos, Szeg6, P6lya, yourself, to name Hungarian Mathematics some of the most prominent ones? R & S: Now to some questions related to your personal Lax: There is a very interesting book written by history. The first one is about your interest in, and John Lukacs with the title "Budapest 1900: A His­ great aptitude for, solving problems of a type that you torical Portrait of a City and its Culture", and it call "Mathematics Light" yourself. To mention just a chronicles the ri&e of the middle class, rise of com­ · few, already as a seventeen-year-old boy you gave merce, rise of industry, rise of science, rise of lit­ an elegant solution to a problem that was posed by erature. It was fueled by many things: a long period

226 NOTICES OF THE AMS VOLUME 53, NUMBER 2 of peace, the influx of mostly Jewish population remember the tremendous slaughter on Okinawa from the East eager to rise, and intellectual tradi­ and Iwo Jima. The Japanese would have resisted to tion. You know in mathematics, Bolyai was a cul­ the last man. The atomic bomb put an end to all tural hero to Hungarians, and that's why mathe­ this and made an invasion unnecessary. I don't be­ matics was particularly looked upon as a glorious lieve reversionary historians who say: "Oh, Japan profession. was already beaten, they would have surrendered R & S: But who nurtured this fantastic flourish­ anyway." I don't see any evidence for that. ing of talent, which is so remarkable? There is another point which I raised once with Lax: Perhaps much credit should be given to someone who had been involved with the atomic julius Konig, whose name is probably not known bomb project. Would the world have had the hor­ to you. He was a student of Kronecker, I believe, ror of nuclear war if it had not seen what one bomb but he also learned Cantor's set theory and made could do? The world was inoculated against using some basic contribution to it. I think he was influ­ nuclear weaponry by its use. I am not saying that ential in nurturing mathematics. His son was a alone justifies it, and it certainly was not the jus­ very distinguished mathematician, Denes Konig, re­ tification for its use. But I think that is a historical ally the father of modern graph theory. And then fact. there arose extraordinary people. Leopold Fejer, for Now about scribbles changing history: Sure, the instance, had enormous influence. There were too special theory of relativity, or quantum mechanics, many to fill positions in a small country like Hun­ would be unimaginable today without scribbles. In­ gary, so that's why they had to go abroad. Part of cidentally, Ulam was a very interesting mathe­ it was also anti-Semitism. matician. He was an idea man. Most mathematicians There is a charming story about the appointment like to push their ideas through. He preferred of Leopold Fejer, who was the first Jew proposed throwing out ideas. His good friend Rota even sug­ for a professorship at Budapest University. There gested that he did not have the technical ability or was opposition to it. At that time there was a very patience to work them out. But if so, then it's an distinguished theologian, Ignatius Fejer, in the Fac­ instance ofUlam turning a disability to tremendous ulty of Theology. Fejer's original name was Weiss. advantage. I learned a lot from him. So one of the opponents, who knew full well that R & S: It is amazing for us to learn that an Fejer's original name had been Weiss, said point­ eighteen-year-old immigrant was allowed to par­ edly: This professor Leopold Fejer that you are ticipate in a top-secret and decisive weapon devel­ proposing, is he related to our distinguished col­ opment during WlVII. league Father Ignatius Fejer? And Eotvos, the great Lax: The war created an emergency. Many of the physicist who was pushing the appointment, replied leaders of the Manhattan Project were foreigners, without batting an eyelash: "Illegitimate son." That so being a foreigner was no bar. put an end to it. R & S: And he got the job? Collaboration. Work Style Lax: He got the job. R & S: Your main workplace has been the Courant Institute of Mathematical Sciences in New York, Scribbles That Changed the Course of which is part ofNew York University. You served as Human Affairs its director for an eight-year period in the 1970s. R & S: The mathematician Stanislaw Ulam was in­ Can you describe what made this institute, which volved with the Manhattan Project and is considered was created by the German refugee Richard Courant to be one of the fathers of the hydrogen bomb. He in the 1930s, a very special place from the early days wrote in his autobiography Adventures of a Math­ on, with a particular spirit and atmosphere? And is ematician: "It is still an unending source of surprise the Courant Institute today still a special place that for me to see how a few scribbles on a blackboard, differs from others? or on a sheet of paper, could change the course of Lax: To answer your first question, certainly the human affairs." Do you share this · feeling? And personality of Courant was decisive. Courant saw what are your feelings about what happened to Hi­ mathematics very broadly, he was suspicious of spe­ roshima and Nagasaki, to the victims of the explo­ cialization. He wanted it drawn as broadly as pos­ sions of the atomic bombs that brought an end to sible, and that's how it came about that applied World War II? topics and pure mathematics were pursued side Lax: Well, let me answer the last question first. by side, often by the same people. This made I was in the army, and all of us in the army expected the Courant Institute unique at the time of its to be sent to the Pacific to participate in the inva­ founding, as well as in the 1940s, 1950s, and 1960s. sion of Japan. You remember the tremendous Since then there are other centers where applied slaughter that the invasion of Normandy brought mathematics is respected and pursued. I am happy about. T"\lat would have been nothing compared to to say that this original spirit is still present at the the invasion 6f the Japanese mainland. You Courant Institute. We still have large areas of fEBRUARY 2006 NOTICES OF THE AMS 227 applied interest, meteorology and climatology these two extremes. Incidentally, I have a very good under Andy Majda, solid state and material science memory. under Robert Kohn and others, and fluid dynam­ ics. But we also have differential geometry as well Teaching as some pure aspects of partial differential equa­ R & S: You have also been engaged in the teaching tions, even some algebra. of calculus. For instance, you have written a calcu­ I am very pleased how the Courant Institute is lus textbook with your wife Anneli as one of the co­ presently run. It's now the third generation that's authors. In this connection you have expressed running it, and the spirit that Courant instilled in strong opinions about how calculus should be ex­ it-kind of a family feeling- still prevails. I am posed to beginning students. Could you elaborate happy to note that many Norwegian mathemati­ on this? cians received their training at the Courant Insti­ Lax: Our calculus book was enormously unsuc­ tute and later rose to become leaders in their field. cessful, in spite of containing many excellent ideas. R & S: You told us already about your collabo­ Part of the reason was that certain materials were ration with Ralph Phillips. Generally speaking, look­ not presented in a fashion that students could ab­ ing through your publication list and the theorems sorb. A calculus book has to be fine-tuned, and I and methods you and your collaborators have given didn't have the patience for it. Anneli would have name to, it is apparent that you have had a vast col­ had it, but I bullied her too much, I am afraid. laboration with a lot of mathematicians. Is this shar­ Sometimes I dream of redoing it because the ideas ing of ideas a particularly successful, and maybe also that were in there, and that I have had since, are joyful, way of advancing for you? still valid. Lax: Sure, sure. Mathematics is a social phe­ Of course, there has been a calculus reform nomenon after all. Collaboration is a psychologi­ movement and some good books have come out of cal and interesting phenomenon. A friend of mine, it, but I don't think they are the answer. First of all, Vera John-Steiner, has written a book (Creative the books are too thick, often more than 1,000 Collaboration) about it. Two halves of a solution are pages. It's unfair to put such a book into the hands supplied by two different people, and something of an unsuspecting student who can barely carry quite wonderful comes out of it. it. And the reaction to it would be: "Oh, my God, I R & S: Many mathematicians have a very par­ have to learn all that is in it?" Well, all that is not ticular work style when they work hard on certain in it! Secondly, if you compare it to the old stan­ problems. How would you characterize your own dards, Thomas, say, it's not so different- the order particular way of thinking, working, and writing? of the topics and concepts, perhaps. Is it rather playful or rather industrious? Or both? In my calculus book, for instance, instead of Lax: Phillips thought I was lazy. He was a prod­ continuity at a point, I advocated uniform conti­ uct of the Depression, which imposed a c ertain nuity. This you can explain much more easily than strict discipline on people. He thought I did not defining continuity at a point and then say the work hard enough, but I think I did! function is continuous at every point. You lose the R & S: Sometimes mathematical insights seem to students; there are too many quantifiers in that. But rely on a sudden unexpected inspiration. Do you the mathematical communities are enormously have examples of this sort from your own career? conservative: "Continuity has been defined point­ And what is the background for such sudden in­ wise, and so it should be!" spiration in your opinion? Other things that I would emphasize: To be sure Lax: The question reminds me of a story about there are applications in these new books. But the a German mathematician, Schottky, when he applications should all stand out. In my book there reached the age of seventy or eighty. There was a were chapters devoted to the applications, that's celebration of the event, and in an interview like how it should be- they should be featured promi­ we are having, he was asked: "To what do you at­ nently. I have many other ideas as well. I still dream tribute your creativity and productivity?" The ques­ of redoing my calculus book, and I am looking for tion threw him into great confusion. Finally he a good collaborator. I recently met someone who said: "But gentlemen, if one thinks of mathemat­ expressed admiration for the original book, so per­ ics for fifty years, one must think of something!" haps it could be realized, if I have the energy. I have It was different with Hilbert. This is a story I heard other things to do as well, like the second edition from Courant. It was a similar occasion. At his sev­ of my linear algebra book, and revising some old entieth birthday he was asked what he attributed lecture notes on hyperbolic equations. But even if his great creativity and originality to. He had the I could find a collaborator on a calculus book, answer immediately: "I attribute it to my very bad would it be accepted? Not clear. In 1873, Dedekind memory." He really had to reconstruct everything, posed the important question: "What are, and what and then it became something else, something bet­ should be, the real numbers?" Unfortunately, he ter. So maybe that is all I should say. I am between gave the wrong answer as far as calculus students

228 NOTICES OF THE AMS VOLUME 53, NUMBER 2 are concerned. The right answer is: infinidecimals. had no access to the supercomputers. At a certain I don't know how such a joke will go down. point the government, which alone had enough money to purchase these supercomputers, stopped Heading Large Institutions placing them at universities. Instead they went to R & S: You were several times the head of/arge or­ national labs and industrial labs. Unless you hap­ ganizations: director of the Courant Institute in pened to have a friend there with whom you col­ 19 72-1980, president of the American Mathemat­ laborated, you had no access. That was very bad ical Society in 19 77-1980, leader of what was called from the point of view of the advancement of com­ the Lax Panel on the National Science Board in putational science, because the most talented peo­ 1980-1986. Can you tell us about some of the most ple were at the universities. At that time accessing important decisions that had to be taken in these and computing at remote sites became possible periods? thanks to ARPANET, which then became a model Lax: The president of the American Mathemat­ for the Internet. So the panel that I established ical Society is a figurehead. His influence lies in ap­ made strong recommendation that the NSF estab­ pointing members of committees. Having a wide lish computing centers, and that was followed up. friendship and reasonable judgement are helpful. My quote on our achievement was a paraphrase of I was very much helped by the secretary of the Emerson: "Nothing can resist the force of an idea American Mathematical Society, Everett Pitcher. that is ten years overdue." As for being the director of the Courant Insti­ R & S: A lot of mathematical research in the U.S. tute, I started my directorship at the worst possi­ has been funded by contracts from DOD (Depart­ ble time for New York University. They had just ment of Defense), DOE (Department of Energy), the closed down their School of Engineering, and that Atomic Energy Commission, the NSA (National Se­ meant that mathematicians from the engineering curity Agency). Is this dependence of mutual bene­ school were transferred to the Courant Institute. fit? Are there pitfalls? This was the time when the Computer Science De­ Lax: I am afraid that our leaders are no longer partment was founded at Courant by Jack Schwartz. aware of the subtle but close connection between There was a group of engineers that wanted to scientific vigor and technological sophistication. start activity in informatics, which is the engineers' word for the same thing. As a director I fought very Personal Interests hard to stop that. I think it would have been very R & S: Would you tell us a bit about your interests bad for the university to have had two computing and hobbies that are not directly related to mathe­ departments- it certainly would have been very matics? bad for our Computer Science Department. Other Lax: I love poetry. Hungarian poetry is particu­ things: Well, I was instrumental in hiring Charlie larly beautiful, but English poetry is perhaps even Peskin at the recommendation of Alexander Chorin. more beautiful. I love to play tennis. Now my knees I was very pleased with that. Likewise, hiring are a bit wobbly, and I can't run anymore, but per­ Sylvain Cappell at the recommendation of Bob haps these can be replaced- I'm not there yet. My Kohn. Both were enormous successes. son and three grandsons are tennis enthusiasts so What were my failures? Well, maybe when the I can play doubles with them. I like to read. I have Computer Science Department was founded I a knack for writing. Alas, these days I write obitu­ should have insisted on having a very high stan­ aries- it's better to write them than being written dard of hiring. We needed people to teach courses, about. but in hindsight I think we should have exercised R & S: You have also written japanese haikus? more restraint in our hiring. We might have become Lax: You're right. I got this idea from a nice ar­ the number one computer science department. ticle by Marshall Stone-I forget exactly where it Right now the quality has improved very much­ was-where he wrote that the mathematical lan­ we have a wonderful chairwoman, Margaret Wright. guage is enormously concentrated, it is like haikus. Being on the National Science Board was my And I thought I would take it one step further and most pleasant administrative experience. It's a pol­ actually express a mathematical idea by a haiku. icy-making body for the National Science Founda­ (See Peter Lax's haiku below.) tion (NSF), so I found out what making policy R & S: Professor Lax, thank you very much for means. Most of the time it just means nodding this interview on behalf of the Norwegian, the Dan­ "yes", and a few times saying "no". But then there ish, and the European Mathematical Societies! are sometimes windows of opportunity, and the Lax Lax: I thank you. Panel was a response to such a thing. You see, I no­ ticed through my own experience and that of my Speed depends on size friends who are interested in large scale comput­ Balanced by dispersion ing (in particular, Paul Garabedian, who complained Oh, solitary splendor. about it), that university computational scientists

FEBRUARY 2006 NOTICES OF THE AMS 229 2005 Annual Survey of the Mathematical Sciences (First Report)

Report on the 2004-2005 New Doctoral Recipients Faculty Salary Survey

Ellen E. Kirkman, ]ames W. Maxwell, and Colleen Rose

Report on the 2004-2005 New The First Report of the 2005 An nual Survey gives a broad picture of 2004- 05 new doctoral recipients from U.S. departments in the math­ Doctoral Recipients ematical sciences, including their employment status in fall 200S. The This r eport presents a statistical profile of First Report also presents salary data for faculty members in U.S. de­ recipients of doctoral degrees awarded b y partments of mathematical science s in four-year colleges and uni­ departm ents in the m ath ematical sciences at ver ~ ities. This report is based on information collected from two universities in the United States during the period questionnaires distributed to departments in May 2005 . A follow-up July 1, 2004, through June 30, 2005. It includes a queistionnaire was distributed to the individual new doctoral recipi­ preliminary analysis of the fall 2005 employment ents in October 2005. This questionnaire will be used to update and plans of 2004-05 doctoral recipients and a revise results in this report, which are based on information from the demographic profile summarizin departments that p roduced the new doct orates. Those re sults will g characteristics of be citizen published in the Second Report of the 2005 Annual Survey in the August ship status, sex, and racial/ ethnic group. All 2006 issue of the Notices of the AMS. Another questionnaire concerned information came from the d epartments that with data on fall 2005 course enrollments, majors, graduate students, awarded the degrees. and departmental faculty was distributed to departments in September Table 1: Doctorates 2005. Results from this questionnaire will appear in the Third Report Granted Response Rates oftre 2005 Annual Survey in the September 2006 issue of the Notices Group I (Pu) 23 of 25 including 0 with 0 degrees of the AMS. The 2005 Annual Survey represents the forty-ninth in an annual Group I (Pr) 18 of 23 including 0 with 0 degrees seribs begun in 1957 by the American Mathematical Society. The 2005 Group II 51 of 56 including 3 with 0 degrees Survey i s conducted by staff at the American Mathematical Soci ety Group Ill 68 of 73 including 19 with 0 degrees with guidance from the Data Committee, a joint committee of the American Mathematical Society, the American Statistical Association, Group IV 63 of 87 including 1 with 0 degree s the Institute of Mathemat ical Stat istics, and the Mat he matical Group Va 17 of 23 including 2 with 0 degrees Associ ation of America. The current members of this committee are See "Def1mt1ons of the Groups" on p age 245. Amy Cohen-Corwin, Donald M. Davis, Nicholas M. Ercolani,J. Douglas Faires, Naresh Jain, Donald R. King, Ellen E. Kirkman (chair), David J. Table 1 provides the departmental response Lutzer, James W. Maxwell (ex officio), Polly Phi pps, David E. Rohrlich, rates for the 2005 Survey of New Doctoral and Henry Schenck. The committee is assisted by AMS su rvey ana­ Recipients. See page 245 for a description of the lystl Colleen Rose. Comments or suggestions regarding this Survey groups. No adjustments were made in this report Report may b e directed to the members of t he Data Committee. for nonresponding departments. This preliminary report will b e updated in the Second Report of the 2005 Annual Survey using information gather ed f rom the new doctoral Ellen E. Kirkman is professor of mathematics at Wake Forest University. recipients. The Second Report will appear in the ]ames W. Maxwell is AMS associate executive director for Membership, August 2006 issue of the Notices of the AMS. Meetings, and Programs. Colleen Rose is AMS survey analyst.

230 N OTICES OF THE AMS VOLUME 53, N UMBER 2 2005 Annual Survey of the Mathematical Sciences

Changes in the Annual Survey occur over time, and these changes need to be considered when Highlights comparing results in this report to those in prior • There were 1,116 new doctoral recipients reported for 2004-05 by years. Information about changes that occurred in departments responding in time for the 2005 First Report. This is 1997 or later can be found in the First Report for the highest number reported since 1999-2000. the 2000 Annual Survey in the February 2001 issue • Groups I (Pu) reported the largest increase (48) in new doctoral re­ of the Notices of the AMS. cipients, but the number of new doctoral recipients last year was a In this First Report's tables referring to new doc­ 1 0-year low. This year Groups Ill and IV reached seven-year highs of toral recipients, "Fall" refers to results based on 153 and 285, respectively. information about new doctoral recipients received • Only 433 (39%) of the new doctoral recipients for 2004-05 are U.S. from departments granting their degrees. This citizens. The percentage of new doctoral recipients who are U.S. cit­ information is gathered in the first fall following izens is the lowest percentage observed in the past ten years. the academic year in which the degrees were • Based on responses from departments alone, the fall 2005 granted. "Final" refers to results based on supple­ unemployment rate for the 950 new doctoral recipients whose mental information received from the new doctoral employment status is known is 7.3%, up from 5.7% for fall 2004. recipients themselves as well as additional new doc­ • Fifty-seven new doctoral recipients hold positions at the institution that granted their degree, although not necessarily in the same de­ toral recipients not reported by departments in time partment. This is 8% of the new doctoral recipients who are currently for publication in the First Report. These results are known to have jobs and 9% of those who have academic positions published each August in the Second Report. in the U.S. Twenty-three new doctoral recipients have part-time po­ sitions. Table 2: New Doctoral Degrees Awarded • The number of new doctoral recipients employed in the U.S. is 751, by Group, Fall Count up 1 2 from last year. The number of new doctoral recipients em­ ployed in academic positions in the U.S. decreased slightly to 602 Group I (Pu) I (Pr) II Ill IV Va TOTAL from 614 last year (a 2% decrease from a nine-year high). 1998-99 292 152 241 136 243 69 1133 • Of the 751 new doctoral recipients taking positions in the U.S., 115 (1 5%) have jobs in business and industry; the number of new doc­ 1999-00 256 157 223 132 284 67 1119 toral recipients taking jobs in business and industry, after oscillat­ 2000-01 233 129 203 125 237 81 1008 ing in the late 1990s, declined three consecutive years (2001, 2002, 2001-02 218 139 164 124 222 81 948 and 2003), and now shows a slight increase for the second consec­ utive year, up 16 (16%) from last year. The number of new doctoral 2002-03 258 138 170 121 239 91 1017 recipients taking jobs in government is up 8 (31 %) over fall 2004. 2003-04 195 187 215 111 243 90 1041 • Among the 751 new doctoral recipients having employment in the 2004-05 243 146 203 1 53 285 86 1116 U.S., 325 (43%) are U.S. citizens (down from 338 (46%) last year). The number of non-U.S. citizens having employment in the U.S. is 426, up 6% from 401 last year. • Among the 288 new doctoral recipients hired by U.S. doctoral­ Figure 1: New Doctoral Degrees Awarded granting departments, 38% are U.S. citizens (same as last year). by Combined Groups, Fall Count Among the 314 having other academic positions in the U.S., 5 i% are U.S. citizens. -+- I (Pu), I (Pr), II, Ill, & Va • Ofthe 1,116 new doctoral recipients, 330 (30%) are females, up just -<>-- I (Pu), I (Pr), & II 1 5 from fall 2004. Of the 433 U.S. citizen new doctoral recipients, 1000 120 (28%) are females, down 15 from fall 2004. 900 • Among the 433 U.S. citizen new doctoral recipients, 1 is American Indian or Alaska Native, 21 are Asian, 14 are Black or African Amer­ 800 ican, 12 are Hispanic or Latino, 380 are White, 3 are Native Hawai­ 700 ian or Other Pacific Islander, and 3 are Other. • Group IV produced 285 new doctorates, of which 126 (44%) are 600 females, compared to all other groups combined, where 204 (2 5%) 500 are females. In Group IV, 79 (28%) of the new doctoral recipients are U.S. citizens (while in the other groups 43% are U.S. citizens). 400 • Three hundred seventy-four new doctorates had a dissertation in 300 statistics/ biostatistics (345) or probability (29), an 1 8% increase over last year. The next highest number was in algebra and number the­ 200 ory with 161. Those with dissertations in statistics/biostatistics and 100 probability accounted for 31% of the new doctorates in 2004-05. 0

01 0 N M <:t Lr\ 01 0 0 0 0 0 0 I I I I I I I 00 01 0 N M <:t 01 01 0 0 0 0 0 01 01 0 0 0 0 0 N N N N N

FEBRUARY 2006 NOTICES OF THE AMS 231 2005 Annual Survey of the Mathematical Sciences

Table 3: Full-Time Graduate Students in Groups I, II, Ill, & Va, Fall 1995 to Fall 2004

GRADUATE STUDENTS 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 Total full-time 9761 9476 9003 8791 8838 9637 9361 9972 10444 10707 First-year full-time 2601 2443 2386 2458 2664 2839 2875 2996 2711 3004 U.S. citizen full-time 5623 5445 4947 4831 4668 5085 4631 5055 5590 5877 First-year U.S. citizen full-time 1551 1465 1316 1349 1401 1527 1517 1630 1527 1803 (Data Reprinted from Table 6B in Third Report, 2004 Annual Survey)

Doctoral Degrees Granted in 2004-05 recipients from the previous year (which was the Table 2 shows the number of new doctoral degrees lowest number for Group I (Pu) in the last 10 years), granted by the different doctoral groups surveyed while Groups III and IV also had increases that put in the Annual Survey for the past seven years. The them at their highest numbers in the last seven 1,116 new doctorates granted by these depart­ years. Groups I (Pr), II, and Va showed decreases of ments in 2004-05 is an increase of 75 from the 41, 12, and 4 respectively. fall count for 2003-04. Figure 1 presents the trends Table 3 gives historical information about var­ i:b. doctorates granted for Groups I (Pu), I (Pr), II, III, ious types of full-time graduate students in Groups and Va combined and Groups I (Pu), I (Pr), and II I, II, III, and Va combined. These data, gathered in combined. the 2004 Departmental Profile survey, are reprinted The response rates were above 90% for all groups from Table 6B of the Third Report of the 2004 except Groups I (Pr), IV and Va. Response rates de­ Annual Survey (Notices of the AMS, September creased in all groups, except Group II which remained 2005). It sheds some light on the upward trend in the same. Overall, thirteen fewer departments number of new doctorates as shown in Table 2 and Figure 1. First-year graduate emollment has responded in time for the First Report this year than been generally increasing since 1997, with rela­ responded last year. tively large increases in 1999 and 2000; these in­ The 1,116 new doctoral recipients is a prelimi­ creases in first-year graduate emollment are likely nary count. A final count will appear in the Second to be related to this year's increase in new Ph.D.'s. Report in the August 2006 issue of the Notices of The continuing increase in. graduate emollment the AMS. Efforts continue to obtain data from as shown in Table 3 suggests that numbers of new many of the nomesponding departments as pos­ Ph.D.'s will continue a generally upward trend over sible. the next few years. From Table 2 we see that Group I (Pu) showed The 2004-05 numbers in Table 2 will be broken the largest increase (48) in the number of doctoral down in various ways, such as by sex, in later sections of this report. The names of Figure 2: Percentage of New Doctoral Recipients Unemployed the 1,116 new doctoral recipients are found (as reported in the respective Annual Survey Reports 1993-2005) on pages 258-276 of this issue of the No- tices. -+-Fall --<>--Final Report Fall Final 1 6.0 ------. 1993-94 14.0 11.0 Employment Status of 2004-05 1994-95 15.0 11.0 14.0 New Doctoral Recipients 1995-96 9.4 8.1 Tables 4A, 4B, and 4C each provide a 12.0 different cross-tabulation of the 1,116 new 1996-97 6.8 3.8 doctoral recipients in the mathematical sci­ 1997-98 7.2 4.9 10.0 ences. These tables contain a wealth of in­ 1998-99 6.2 4.7 8.0 formation about these new doctoral recip­ 1999-00 4.6 3.3 ients, some of which will be discussed in this 6.0 report. Note that these tables give a break­ 2000-01 5.6 3.7 down by sex for type of employer, type of 2001-02 4.3 2.9 4.0 degree-granting department, and field of 2002-03 5.1 5.0 thesis. Keep in mind that the results in 2.0 ------. 2003-04 5.7 4.4 this report come from the departments giv­ ing the degrees and not from the degree re­ 2004-05 7.3 ~·~ 0.0 cipients themselves. These tables will be '<;j" *To appear in the Second Report. Lf"l lD 1'- 00 0\ 0 N M '<;j" Lf"l 0\ 0\ 0\ 0\ 0\ 0\ 0 0 0 0 0 0 revised using information from the doc­ Note: Prior to 1998- 99, the per· I I I I I I I I I I I I M '<;j" Lf"l lD 1'- 00 0\ 0 N M '<;j" toral recipients themselves and will appear centages include new doctoral re· 0\ 0\ 0\ 0\ 0\ 0\ 0\ 0 0 0 0 0 0\ 0\ 0\ 0\ 0\ 0\ 0\ 0 0 0 0 0 cipients from Group Vb. N N N N N

232 NOTICES OF THE AMS VOLUME 53, NUMBER 2 2005 Annual Survey of the Mathematical Sciences

Table 4A: Employment Status of 2004-05 U.S. New Doctoral Recipients in the Mathematical Sciences by Field of Thesis

FIELD OF THESIS

Real , Comp., Discr. Math./ Numerical Lin ear Differential, Algebra/ Funct., & Com bin./ Analys is/ Nonlinear Integ ral, & Number Harmonic Geometry/ Logic/ Statistics/ Applied Approxi- Optim./ Diffe rence Math. Other/ TYPE OF EMPLOYER Th eory Analysis Topology Camp. Sci. Probability Bios tat. Math. mations Control Equations Educ. Unknow n TOTAL Group I (Public) 17 8 11 8 1 0 5 5 2 16 0 0 73 Group I (Private) 12 5 14 7 0 1 4 0 1 6 0 0 50 Group II 17 7 9 4 5 3 7 4 1 9 0 0 66 Group Ill 3 8 2 6 1 11 2 3 1 3 1 1 42 Group IV 0 1 1 0 2 40 1 0 0 0 0 0 45 Group Va 1 0 0 0 0 0 4 3 2 2 0 0 12 Master's 12 2 5 6 3 16 5 3 3 13 1 0 69 Bachelor's 26 14 12 19 1 1 5 7 7 6 8 4 0 119 Two-Year College 1 0 2 2 1 1 0 0 0 0 0 0 7 Other Academic Dept. 7 1 2 5 2 53 10 8 0 6 3 0 97 Research Institute/ 3 1 0 0 0 12 2 0 1 3 0 0 22 Other Nonprofit Government 1 1 2 1 0 14 6 5 3 1 0 0 34 Business and Industry 2 3 4 3 7 75 13 3 0 5 0 0 115 Non-U.S. Academic 21 6 18 14 5 17 13 5 3 10 1 0 113 Non-U.S. Nonacademic 3 0 0 0 0 7 0 0 0 0 0 0 10 Not Seeking Employment 1 1 0 1 0 3 1 0 0 0 0 0 7 Still Seeking Employment 10 4 4 11 1 16 11 3 0 8 1 0 69 Unknown (U.S.) 9 7 6 2 0 25 17 2 1 6 1 0 76 Unknown (non-U.S.)* 1 5 4 5 5 0 36 8 4 3 9 1 0 90 TOTAL 161 73 97 94 29 345 116 55 27 105 13 1 1116 Column I Male 132 57 77 75 24 192 86 41 17 80 4 1 786 Subtotals I Female 29 16 20 19 5 153 30 14 10 25 9 0 330 *Includes those whose status is reported as "u nknown" or "s till seeking employment".

Table 4B: Employment Status of 2004-05 U.S. New Doctoral Recipients in the Mathematical Sciences by Type of Degree-Granting Department

TYPE OF DOCTORAL DEGREE-GRANTING DEPARTMENT Group I Group I Row (Public) (Private) Group II Group Ill Group IV Group Va Subtotals TYPE OF EMPLOYER Math . Math. Math . Math. Statistics Applied Math . TOTAL Male Female Group I (Public) 36 19 9 4 0 5 73 58 1 5 Group I (Private) 20 27 2 0 0 1 50 40 10 Group II 18 14 25 3 3 3 66 54 12 Group Ill 6 1 8 17 10 0 42 29 13 Group IV 0 3 2 2 37 1 45 26 19 Group Va 0 1 3 1 0 7 12 8 4 Master's 12 6 22 1 5 8 6 69 38 31 Bachelor's 27 10 41 27 12 2 119 90 29 Two-Year College 3 0 3 0 0 1 7 6 1 Other Academic Dept. 5 4 11 14 so 13 97 60 37 Research Institute/ 4 3 4 0 11 0 22 14 8 Other Nonprofit Government 6 2 6 3 11 6 34 20 14 Business and Industry 5 9 14 1 5 64 8 115 82 33 Non-U .S. Academic 42 23 14 11 17 6 133 87 26 Non-U.S. Nonacademic 2 1 0 0 7 0 10 7 3 Not Seeking Employment 1 1 1 0 3 1 7 5 2 Still Seeking Employment 13 12 13 10 11 10 69 44 25 Unknown (U.S.) 24 2 12 1 5 16 7 76 51 25 Unknown (non-U.S.)" 19 8 13 16 25 9 90 67 23 TOTAL 243 146 203 153 285 86 1116 786 330 Column I Male 192 120 158 97 1 59 60 786 Subtotals I Female 51 26 45 56 126 26 330 * In cludes those whose status is reported as "unknown" or "s till seeking employment". fEBRUARY 2006 NOTICES OF THE AMS 233 2005 Annual Survey of the Mathematical Sciences

Table 4C: Field of Thesis of 2004-05 New Doctoral Recipients by Type of Degree-Granting Department

FIELD OF THESIS 1YPE OF DOCTORAL Real, Comp., Di scr. Math./ Numerica l Linear Differential, DEGREE-GRANTING Algebra/ Fun ct., & Combin./ Analysis/ Nonlinear Integral, & Number Harmonic Geometry/ Logic/ Statistics/ Applied Approxi- Optim./ Difference Math. Other/ DEPARTMENT Theory Analysis Topology Comp. Sci. Probability Bios tat. Math. mations Control Equation s Educ. Unknown TOTAL Group I (Public) 68 20 40 25 6 12 20 8 8 35 1 0 243 Group I (Private) 42 9 32 19 5 2 13 8 2 14 0 0 146 Group II 42 21 19 23 10 6 24 16 9 33 0 0 203 Group Ill 9 23 4 20 2 33 23 9 3 15 12 0 153 Group IV 0 0 0 0 3 280 1 0 0 0 0 1 285 Group Va 0 0 2 7 3 12 35 14 5 8 0 0 86 Column Total 161 73 97 94 29 345 116 55 27 105 13 1 1116

Table SA: U.S. Employed 2004-05 New Doctoral Recipients Table 58: Number of New Doctoral by Type of Degree-Granting Department Recipients Taking Positions in Business and Industry in the U.S. by Type of Degree­ U.S. EMPLOYER I (Pu) I (Pr) II Ill IV Va TOTAL Granting Department, Fall 2001 to Fall 2005 Groups I, II , Ill, IV, and Va 80 65 49 27 50 17 288 Master's, Bachelor's, and Group I (Pu) I (Pr) II Ill IV Va TOTAL 2-Year Colleges 42 16 66 42 20 9 195 Fall 2001 24 1 5 25 21 59 24 168 Other Academic and Fall 2002 1 5 12 19 6 56 1 5 123 Research Institutes 9 7 15 14 61 13 119 Fall 2003 19 13 5 8 45 7 97 Government 6 2 6 3 11 6 34 Fall 2004 9 13 9 9 50 9 99 Business and Industry 5 9 14 1 5 64 8 115 Fall 2005 5 9 14 1 5 64 8 11 5 TOTAL 142 99 150 101 206 53 751 Table SC: Number of New Doctoral in the 2005 Second Report in the August 2006 is­ Recipients Taking U.S. Academic Positions by sue of the Notices of the AMS. Type of Degree-Granting The last column (Total) in Table 4A can be used Department, Fall 2001 to Fall 2005 to find the overall unemployment rate. In this and Group I (Pu) I (Pr) II Ill IV Va TOTAL other unemployment calculations in this report, Fall 2001 146 70 109 74 84 27 510 the individuals whose employment status is not known (Unknown (U.S.) and Unknown (non-U.S.)) are Fall 2002 120 83 9 1 86 92 31 503 first removed, and the unemployment fraction Fall 2003 123 76 117 60 118 40 534 is the number still seeking employment divided Fall 2004 110 113 130 70 142 49 614 by the total number of individuals left after the Fall 2005 131 88 130 83 131 39 602 "Unknowns" are removed. The overall unemploy­ ment rate for these data is 7.3%. This figure will be Table SD: U.S. Academic Positions Filled updated later with information gathered from the by New Doctoral Recipients by Type of individual new doctoral recipients. The figure for Hiring Department, Fall 2001 to Fall 2005 fall 2004 was 5.7%. Figure 2 shows how this unemployment rate compares with other years Group 1- 111 IV Va M&B Other TOTAL over the past decade. The unemployment rates, Fall 2001 199 41 12 161 97 510 calculated using Table 4B, vary from group to group, Fall 2002 213 46 7 138 99 503 with a high of 14.3% for Group Va and lows of 4.5% Fall 2003 203 39 9 156 127 534 and 6.5% for Groups IV and I (Pu) respectively. There are 7 51 new doctoral recipients employed Fall 2004 222 63 17 154 158 614 in the U.S. Table SA gives a breakdown of type of Fall 2005 231 45 12 188 126 602 employer by type of degree-granting department for these 751 new doctoral recipients. Of these, 602 Table SE: Females as a Percentage of 2004-05 (80%) hold academic positions, 34 (5%) are em­ New Doctoral Recipients Produced by and ployed by government, and 115 (15%) hold positions Hired by Doctoral-Granting Groups in business and industry. Percent I (Pu) I (Pr) In the First Report for 2003-04, there were 739 II Ill IV Va TOTAL new doctoral recipients employed in the U.S., of which Produced 21 18 22 37 44 30 30 614 (83%) held academic positions, 26 (4%) were in Hired 21 20 18 31 42 33 25

234 NOTICES OF THE AMS VOLUME 53, N UMBER 2 2005 Annual Survey of the Mathematical Sciences government, and 99 (13%) were in business and Table SD shows the number of positions filled industry. The number of new doctoral recipients em­ with new doctoral recipients for each type of aca­ ployed in the U.S. decreased in all categories ofTable demic employer. Increases in positions filled by new SA except "Master's, Bachelor's and Two-Year doctoral recipients were realized by all groups ex­ Colleges", "Government", and "Business and Indus­ cept Groups IV, Va, and Other. try"; "Other Academic and Research Institutes" is Infall2005, 5 7new doctoral recipients held posi­ down 17% this year over last year, and "Master's, tions in the institution that granted their degree, Bachelor's and Two-Year Colleges" is up 16% this year over last year. although not necessarily in the same department. Table SB shows the number of new doctoral This represents 6. 5% of new doctoral recipients who recipients who took positions in business and are currently employed and 9% of the U.S. academic industry by the type of department granting their positions held by new doctoral recipients. lnfall2004 degree for fall 2001 to fall 2005. The number of there were 58 such individuals making up 7% of the new doctoral recipients taking jobs in business new doctoral recipients who were employed at the and industry oscillated in the late 1990s, declined time of the First Report. Twenty-three new doctoral three consecutive years (2001, 2002, and 2003), and recipients have taken part-time positions infall2005 the past two years shows a slight increase (up 16% compared with 19 infall2004. from fall2004). The fall2005 number is down 32% from the fall2001 number. The number of new doc­ Information about 2004-05 Female toral recipients taking jobs in government is up 8 (31%) over fall 2004. New Doctoral Recipients Among the 751 new doctoral recipients known Tables 4A and 4B give male and female breakdowns to have employment in the U.S. in fall2005, Group of the new doctoral recipients in 2004-0 5 by Field of I (Pu) has the smallest percentage taking jobs in Thesis, by Type of Degree-Granting Department, and business and industry at 4% and Group IV the high­ by Type of Employer. est at 31%. Table SC shows the number of new doctoral Table SG: 2004-05 New Doctoral recipients who took academic positions in the U.S. Recipients Having Employment in the U.S. by type of department granting their degree for fall by Type of Employer and Citizenship 2001 to fall 2005. After reaching a nine-year high of 614 last year, the number of new doctoral re­ CITIZENSHIP cipients taking academic employment in fall2005 U.S . EMPLOYER U.S . Non-U.S. TOTAL has dropped 2%. Among the 751 new doctoral re­ Academic, Groups I-Va 108 180 288 cipients employed in the U.S. in fall2005, 80% have Academic, Other 160 154 314 academic positions. This percentage is highest for Nonacademic 57 92 149 Group I (Pu) at 92% and lowest for Groups IV at 64%. TOTAL 325 426 751

Table SF: Employment Status of 2004-05 U.S. New Doctoral Recipients by Citizenship Status

CITIZENSHIP NON-U.S. CITIZENS U.S. CITIZENS TYPE OF EMPLOYER Permanent Visa Temporary Visa Unknown Visa TOTAL U.S. Employer 325 61 352 13 751 U.S. Academic 268 43 280 11 602 Groups I, II, Ill, and Va 100 18 116 9 243 Group IV 8 1 36 0 45 Non-Ph.D. Department 1 55 21 114 2 292 Research Institute/Other Nonprofit 5 3 14 0 22 U.S. Nonacademic 57 18 72 2 149 Non-U.S. Employer 23 2 96 2 123 Non-U.S. Academic 21 2 89 1 113 Non-U.S. Nonacademic 2 0 7 1 10 Not Seeking Employment 6 0 1 0 7 Still Seeking Employment 20 9 40 0 69 SUBTOTAL 374 72 489 15 950 Unknown (U.S.) 53 9 14 0 76 Unknown (non-U.S.)* 6 1 74 9 90

TOTAL 433 82 577 24 1116

*Includes those whose status is reported as "unknown" or "s till seeking employment".

FEBRUARY 2006 NOTICES OF THE AMS 235 2005 Annual Survey of the Mathematical Sciences

Table 6: Sex, Race/Ethnicity, and Citizenship of 2004-05 U.S. New Doctoral Recipients

MALE FEMALE NON-U.S . CITIZENS NON-U.S. CITIZENS u.s. Permanent Temporary Unknown Total u.s. Permanent Temporary Unknown Total RACIAL/ETHNIC GROUP CITIZENS Visa Visa Visa Male CITIZENS Visa Visa Visa Female TOTAL American Indian or 1 0 0 0 1 0 0 0 0 0 1 Alaska Native Asian 14 18 205 6 243 7 15 115 4 141 384 Black or African 6 1 19 0 26 8 0 1 0 9 35 American Hispanic or Latino 8 3 24 1 36 4 3 5 0 12 48 Native Hawaiian or 1 0 0 0 1 2 0 1 0 3 4 Other Pacific Islander White 277 22 162 8 469 103 15 46 1 165 634 Unknown 3 1 3 0 7 0 1 2 0 3 10 TOTAL 310 45 413 15 783 124 34 170 5 333 1116

Overall, 330 (30%) of the 1,116 new doctoral varies by type of visa. The unemployment rate for recipients in 2004-05 are female. In 2003-04, 315 non-U.S. citizens with a permanent visa is 12.5%, (30%) of the new doctoral recipients were female. while that for non-U.S. citizens with a temporary This percentage varies over the different groups, visa is 8.2%. Among U.S. citizens whose employment and these percentages are given in the first row of status is known, 87% are employed in the U.S. Table 5E. This year the percentage of females Among non-U.S. citizens with a permanent visa produced is highest again for Group IV at 44%, whose employment status is known, 85% have jobs compared with 40% last year. While the lowest per­ in the U.S. (same as last year), while the percent­ centage last year was for Group I (Pu) at 23%, this age for non-U.S. citizens with a temporary visa is year it is for Group I (Pr) at 18%. 72% (last year the percentage was 75%). The num­ The second row of Table 5E gives the percent­ ber of non-U.S. citizens having employment in the age of the new doctoral recipients hired who are U.S. is 426, up 6% from 40llast year. female for each of the Groups I, II, III, IV, and Va. Table 5G is a cross-tabulation of the 751 new In addition, 45% of the new doctoral recipients doctoral recipients who have employment in the hired in Group M, master's departments, are U.S. by citizenship and broad employment cate­ female; 24% of the new doctoral recipients hired gories, using numbers from Table 5F. Of the 751 in Group B, bachelor's departments, are female; new doctoral recipients having jobs in the U.S., and 29% of new doctoral recipients hired in 43% are U.S. citizens. Of the 288 new doctoral re­ business and industry are female. cipients who took jobs in U.S. doctoral-granting The unemployment rate for female new doc­ departments, 38% are U.S. citizens (same as last toral recipients is 9% compared to 7% for males and year). Of the 314 who took other academic posi­ 7.3% overalL tions, 51% are U.S. citizens. Of the 149 who took The percentage of female new doctoral recipi­ nonacademic positions, 38% are U.S. citizens. Of the ents within fields of thesis ranged from 17% in 325 U.S. citizens employed in the U.S., 33% have jobs probabilty, to 44% in statistics, and 69% in mathe­ in a doctoral-granting department, 49% are in other matics education. academic positions, and 18% are in nonacademic Later sections in this First Report give more in­ positions. For the 426 non-U.S. citizens employed formation about the female new doctoral recipients in the U.S., the analogous percentages are 42%, by citizenship and the female new doctoral recip­ 36%, and 22% respectively. ients in Group IV.

Sex, Race/Ethnicity, and Citizenship Status Employment Information about 2004-05 of 2004-05 New Doctoral Recipients New Doctoral Recipients by Citizenship Table 6 presents a breakdown of new doctoral and Type of Employer recipients according to sex, racial/ethnic group, Table 5F shows the pattern of employment within and citizenship status. The information reported employer categories broken down by citizenship i n status of the new doctoral recipients. this table was obtained in summary form from the The unemployment rate for the 433 U.S. citizens departments granting the degrees. is 5.3% compared to 6.1% in fall 2004. The unem­ There were 433 (39%) U.S. citizens among the ployment rate for non-U.S. citizens is 8.5%. This 1,116 new doctoral recipients in 2004-05. Among

236 NOTICES OF THE AMS VOLUME 53, NUMBER 2 2005 Annual Survey of the Mathematical Sciences

Table 7: U.S. Citizen Doctoral Recipients Figure 3: U.S. Citizen Doctoral Recipients --+-- Total Doctorates Granted by U.S . Institutions Total Doctorates Total U.S. Granted by U.S. Citizen Doctoral ~ Total U.S. Citizen Doctoral Recipients Year Institutions Recipients % 1300 ------1980-81 839 567 68% 1200 1985-86 755 386 51% 1100 1990-91 1061 461 43% 1000 1995-96 1150 493 43% 900 1998-99* 1133 554 49% 800 1999-00 1119 537 48% 700 ------2000-01 1008 494 49% 600 2001-02 948 418 44% 2002-03 1017 489 48% 500 2003-04 1041 441 42% 400 2004-05 1116 433 39% 300 ------

~' Prior to 1998-99, the counts include new doctoral recipients from 200 ------Group Vb. In addition, prior to 1982-83, the counts include recipients 100 ------from computer science departments. 0+-+-~~~-+-+~~1-+-+-~~~-+-+~1-~

FEBRUARY 2006 NOTICES OF THE AMS 237 2005 Annual Survey of the Mathematical Sciences

Table 9: Sex and Citizenship of 2004-05 New Doctoral Recipients by Granting Department

GROUP I (Pu) I (Pr) II Ill IV Va TOTAL CITIZENSHIP Male Female Male Female Male Fem ale Male Female Male Female Male Female Male Female u.s. 93 1 5 45 11 67 24 37 27 44 34 27 9 313 120 Non-U.S. 99 36 75 1 5 91 21 60 29 11 5 92 33 17 473 210 TOTAL 192 51 120 26 158 45 97 56 159 126 60 26 786 330

Table 8 (and Figure 4) gives the historical statistics/biostatistics and probability. The other record of U.S. citizen new doctoral recipients, groups produced 91 new doctoral recipients with dis­ broken down by male and female for past years, sertations in statistics/biostatistics and probability going back to 1980-81. The number of female in 2004-05 and have averaged 82 per year over the U.S. citizen new doctoral recipients is down 67 past ten years. Information about these 91 new doc­ (36%) from an all-time high of 187 in 1998-99. toral recipients and the 28 5 new doctoral recipients Table 9 gives a sex and citizenship breakdown in Group IV is found in this section of the report. of the new doctorates within each of the six Table 10 contains information about new groups of doctoral-granting departments. Among doctoral recipients in Group IV as well as those all 1,116 new doctoral recipients, 40% of the with dissertations in statistics/biostatistics and males and 36% of the females are U.S. citizens. probability in other groups for the past seven Within the groups the percentage of the new years. The last two rows of Table 10 give doctoral recipients who are U.S. citizens is lowest a split of the 2004-05 results between the 58 in Group IV at 27% and highest in Group II at statistics departments and the 29 biostatistics 45%. The number of U.S. citizen new doctoral and biometrics departments in Group IV. This recipients is lower than the number of non-U.S. year 374 new doctorates had a dissertation in citizen new doctoral recipients in all doctoral statistics/biostatistics (345) or probability (29), granting groups for 2004-05. an 18% increase over last year's number. Those with dissertations in statistics/biostatistics and probability accounted for 31% of new doctorates in 2004-05. Quite a bit of the variation in 2004-05 New Doctoral Recipients with numbers from year to year in Table 10 is due to Dissertations in Statistics/Biostatistics the changes made in the departments in Group and Probability IV over the ten years and to the relatively low Group IV contains U.S. departments (or programs) response rate for this group. At the time of the of statistics, biostatistics, and biometrics reporting a Second Report last year, 78 of 87 (90%) of Group doctoral program. In the Annual Survey Reports, Group IV departments had responded, which is the IV is referred to as the Statistics Group. In largest percentage ever. addition, other groups in the Annual Survey produce Group IV has 87 departments for 2004-05, 14 new doctoral recipients with dissertations in more than the next largest doctoral group. It

Table 10: New Doctoral Recipients with Dissertations in Statistics/Biostatistics and Probability

New Doctoral Recipients in Statistics/Biostatistics New Doctoral Recipients New Doctoral Recipients in Group IV and Probability Hired by Group IV Depts Depts Responding Female Jobs in Percentage Other Percentage Year Surveyed (percent) Total (percent) Bus & lnd Unemployed Total Group IV Groups Unemployed Male Female 1995-96 80 54 (68%) 172 46 (27%) 55 3.9% 266 171 95 4.8% 24 6 1996-97 81 60 (74%) 197 74 (38%) 70 4.2% 292 187 105 5.1% 24 9 1997-98 82 59 (72%) 213 73 (34%) 70 3.2% 294 199 95 3.7% 25 10 1998-99 91 72 (79%) 243 87 (36%) 57 4.9% 320 240 80 5.8% 29 20 1999-00 89 75 (84%) 284 110 (39%) 79 2.4% 351 278 73 2.0% 24 22 2000-01 86 70 (81%) 237 98(41%) 59 5.1% 289 221 68 5.3% 27 14 2001-02 86 72 (84%) 222 92 (41%) 56 6.0% 288 221 67 5.4% 31 15 2002-03 86 74 (86%) 239 98(41%) 45 2.1% 302 234 68 3.3% 20 19 2003-04 87 65 (75%) 243 97 (40%) 50 3.0% 318 241 77 4.0% 48 15 2004-05 87 63 (72%) 285 126 (44%) 64 5.0% 374 283* 91 ** 5.0% 26 19 Statistics 58 43 (74%) 192 79 (41%) 43 3.0% 13 14 Biostatistics 29 20 (62%) 93 47 (51%) 21 9.0% 13 5 * Of 283, there were 280 in statistics/ biostatistics and 3 in probability. For complete details, see Table 4C. ** Of 91, there were 65 in statistics/biostatistics and 26 in probability. For complete details, see Table 4C.

238 NOTICES OF THE AMS VOLUME 53, NUMBER 2 2005 Annual Survey of the Mathematical Sciences contains 3 3% of all doctoral departments surveyed, and the 63 Group IV departments responding to the Annual Survey reported 285 new doctoral recipi­ Faculty Salary Survey ents, 26% of all new doctoral recipients in 2004-05. While this is the second lowest percentage of re­ The charts on the following pages display faculty sponding Group IV departments since 1995-96 when salary data for Groups I (Pu), I (Pr), II, III, IV it was 68%, it's the largest number of new doctoral (Statistics), IV (Biostatistics), Va, M, and B: faculty recipients reported since 1999-00 when it was 284. salary distribution by rank, mean salaries by rank, The number of new doctoral recipients in Group IV information on quartiles by rank, and the number is up 42 from the number reported at this time last of returns for the group. Results reported here are year, while the number of departments responding summaries based on the departments who re­ is down 2 from the number responding by this time sponded to this portion of the Annual Survey. This last year. is the third year that salary information has been Because of its size, the data from Group IV have reported separately for statistics departments and a large effect on the results when all doctoral groups biostatistics and biometrics departments in are combined. Furthermore, Group IV results are of­ Group IV. ten quite different from those for Groups I (Pu), I Table 11 provides the departmental response (Pr), II, III, and Va. Group IV results can mask im­ rates for the 2005 Faculty Salary Survey. Depart­ portant changes in the other doctoral groups. In the ments were asked to report for each rank the following paragraphs some of these differences number of tenured and tenure-track faculty whose are presented. The trends noted below have also 2005-06 academic-year salaries fell within given been observed in past reports. salary intervals. Reporting salary data in this Table 9 shows that for the Group IV new doctoral fashion eliminates some of the concerns about recipients, 126 of 285 (44%) are female, while 204 confidentiality but does not permit determination of of 831 (2 5%) are female in the other doctoral groups. actual quartiles. Although the actual quartiles can­ Among U.S. citizens, females accounted for 34 of not be determined from the data gathered, the 79 (43%) Group IV new doctoral recipients, while for the other groups 86 of 3 54 (24%) were fe­ male. Overall, 120 of 433 (28%) U.S. citizen new Table ll: Faculty Salary Response Rates doctoral recipients were female. In Group IV, 79 of 285 (28%) new doctoral recipi­ Department Number Percent ents are U.S. citizens, while in other groups 3 54 of Group I (Public) 23 of 25 92 831 (43%) are U.S. citizens. Of the 206 new doctoral recipients from Group IV Group I (Private) 11 of 23 48 who found employment in the U.S., 64 (31%) took Group II 45 of 56 80 jobs in business or industry. From the other groups, Group Ill 66 of 75 88 545 new doctoral recipients found employment in Group IV (Statistics) 42 of 55 76 the U.S., of which 51 (9%) took jobs in business or in­ dustry. Group IV (Biostatistics) 17 of 31 55 The employment status for 244 Group IV new Group Va 11 of 21 * 52 doctoral recipients is known, and 11 (4.5%) are un­ Group M 80 of 189 42 employed. For the other groups, the employment status of 706 is known, and 58 (8.2%) are unemployed. Group B 320 of 1010 32 Nineteen of 45 (42%) new doctoral recipients hired ' The population for Group Va is slightly less than for the Doctorates by Group IV departments were female, up from last Granted Survey, because some departments grant degrees but do not for­ year's 24%, the lowest percentage of female hires re­ mally "house" faculty and their salaries. ported since 1999-2000. The other doctoral groups reported that 54 of243 (22%)newdoctoralrecipients these quartiles have been estimated assuming that hired were female, down from last year's 2 7%. the density over each interval is uniform. Group IV had 283 new doctoral recipients with Since departments in Groups I, II, and III were fields of thesis in statistics/biostatistics (280) and changed in 1995-96 (see definitions ofthe groups probability (3), and the other doctoral departments on page 245), comparisons are possible only to had 91 with fields of thesis in statistics/biostatistics the last eight years' data. In addition, prior to the (65) andprobability(26). The distribution of these 65 1998 survey Groups Va and Vb were reported degrees among the various groups can be found in together as Group V. When comparing current and Table 4C. The number of new doctoral recipients with prior year figures, one should keep in mind that theses in statistics/biostatistics and probability (3 74) differences in the set of responding departments is substantially larger than any other field, withal­ gebra and number theory next with 161. fEBRUARY 2006 NOTICES OF THE AMS 239 2005 Annual Survey of the Mathematical Sciences

Group I (Public) Faculty Salaries Doctoral degree-granting departments of mathematics (25) 23 responses (92%) 2005-06 2004-05 Ran k No. Reported Q, Median Q, Mean Mean 70 Assi stant Professor 148 60,970 64,520 68,230 63,468 63,129 ~ 65 Associate Professor 164 65,910 70,860 79,800 72,031 70,671 s:::: I1S Full Professor 802 89,060 103,610 126,440 109,440 105,529 r:t:: 60 s:::: 55 r-- .s::::.... Assistant 50 · ~ f-- >- 45 II Associate .!: f-- :::l n 1.1 40 f-- I1S Full Ll.. 35 I """"' • iii.... 0 30 n- f- .... 25 - ....0 s:::: 20 -- Ql ...1.1 1 5 f--- Ql I ~- c.. 10 L f--- ;--- f--- - 5 -- -- - 1--- 1--- 1--- - r, 0 ·- i t~ ~ ~ f--- r--- tt. • - 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - • 0 0 0 "¢ lJ"\

2005-06 Academic-Year Salaries (in thousands of dollars)

Group I (Private) Faculty Salaries Doctoral degree-granting departments of mathematics (23) 11 responses (48%) 2005-06 2004-05 70 Rank No. Reported Median Q, Mean Mean ------1 As sistant Professor 39 54,070 62,250 67,910 62,772 v 65 + f 60,1 76 1------.... Associate Pro essor 52 72,230 78,000 85,830 80,897 76,528 ~ 60 Full Professor 204 99,570 117,690 134,700 11 8,146 11 6,379 r:t:: s:::: SSt------.s:::: ·~ 50 Assistant >- 45 +------.!: ------1 a 40+------­ • Associate ns Ll.. 35 +-----­ • Full iii 0 30 +---- - ­ ~ ------f------~~~~---- .... 25 +------1 0 c 20+-----­ ------QI ~ 15 +-----­ QI c.. 10 +------: +----r-----,.-=M --'--"-t--'-, l-n I 0 0 0 0 0 0 0 0 0 0 0 0 0 "¢ 0 0 0 0 lJ"\

240 NOTICES OF THE AMS VOLUME 53, NUMBER 2 2005 Annual Survey of the Mathematical Sciences

Group II Faculty Salaries Doctoral degree-granting departments of mathematics (56) 45 responses (80%) 2005-06 2004-05 Rank No. Reported Ql Median Q, Mean Mean 70 Assistant Professor 238 56,130 60,460 64,370 60,216 56,862 ~ 65 Associate Professor 371 61,080 66,240 72,760 67,633 65,385 s::: 1"1:1 Full Professor 918 78,750 90,930 105,740 94,650 89,664 0:: 60 s::: 55 - ..s:::.... Assistant '3: 50 - >- 45 ~ Ill Associate - .!::: :I u 40 -- r~ Full - 1"1:1 • LL. 35 -- ~.... 0 30 -- 1- ~ 25 -- 0 Fl'l .... ,....---- s::: 20 --,...... , 1--- Q) ...u 1 5 • 1--- r-- '--- Q) ~·· Cl.. 10 ·~ - -1--- r-- r-- - 5 - •'t : r-- - 0 tf W= r--""'"" ttl • - 0 0 0 0 0 0 0 0 0 0 0 0 0 - 0 0 0 0 LJ'1 1'- 00 M LJ'1 - 1'- 00 1.0 0'\ 0 N 1.0 0'\ 0'\ ""'I I I I I I ""' 0 0 0 0 0 0 I I I I I I I I I I A M LJ'1 1.0 1'- 00 0 0 0 0 0 0 0 0 0 0 ""' 0'\ 0 N M ""' LJ'1 1.0 1'- 00 2005-06 Academic-Year Salaries (in thousands of dollars)

Group Ill Faculty Salaries Doctoral degree-granting departments of mathematics (75) 66 responses (88%) 2005-06 2004-05 Rank No. Rep orted Median Q, Mean Mean 70 Ql Assistant Professor 293 50,260 55,960 61,740 56,790 54,349

~ 65 Associate Professor 446 55,390 60,800 70,220 64,956 63,297 s::: Full Professor 641 69,190 79,260 96,160 83,897 79,756 1"1:1 60 0:: s::: 55 r- ..s:::.... Assistant '3: 50 r- >- 45 i13 Associate r- .!::: :I u 40 Full r- n:l -·~ • LL. 35 ~.... ~" 0 30 1- ...... ~ 25 - 1---- ....0 s::: 20 -- - Q) - f"'· ...u 1 5 -- 0; - ··1"·· - 1--- Q) Cl.. 10 -- r~ ~ . - !"""" 1--- • ' [¥ 1"-. 5 -

IJ: c--'-- 0 tL b:l::l=l • - 0 0 0 0 0 0 0 0 0 0 0 --0 - 0 0 0 0 0 LJ'1 1.0--- =1'- 00 0'\ 0 N M LJ'1 1.0 1'- 00 0'\ 0'\ ""'I I I I I I ""' 0 0 0 0 0 0 I I I I I I I I I I A M LJ'1 1.0 1'- 00 0 0 0 0 0 0 0 0 0 0 ""' 0'\ 0 N M ""' LJ'1 1.0 1'- 00 2005-06 Academic-Year Salaries (in thousands of dollars)

FEBRUARY 2006 NOTICES OF THE AMS 241 2005 Annual Survey of the Mathematical Sciences

Group IV (Statistics) Faculty Salaries Doctoral degree-granting departments of statistics (55) 42 responses (76%) 2005-06 2004-05 Rank No. Reported Q, Median Q, Mean Mean 70 Assistant Professor 177 62,630 67,060 70,300 66,631 64,975 ~ 65 r::: Associate Professor 129 67,410 75,360 84,040 76,504 73 ,275 Full Professor 346 91,700 109,440 128,550 113,531 107,297 Ill:: 60 "'r::: 55 n r-- ..r::: ~ I Assistant "3: 50 r-- >- 45 II Associate r-- ~ ::I \J 40 Full r-- Ll.."' 35 f1· • iU lrr• ~ 0 30 1- ..... 25 0 ;~ ~r::: 20 - Cll \J ... 1 5 ... - Cll 1:1.. 10 - ~~- f-- - f-- - 5 - f-- - -. 0 I= tE ~ f-..-!!= r- :=1=1: • • 0 0 0 0 -=0 0 0 0 0 0 ~ 0 - 0 0 0 0 - 0 0 '

2005-06 Academic-Year Salaries (in thousands of dollars)

Group IV ( Biostatistics) Faculty Salaries Doctoral degree-granting departments of biostatistics and biometrics (31) 1 7 responses (55%) 2005-06 2004-05 70 Rank No. Reported Q, Median Q, Mean Mean Assistant Professor 89 63,020 68,150 75,970 69,558 66,129 65 Associate Professor 72 73,850 83,180 93,880 85,393 81,209 ~ r::: 60 Full Professor 106 95,940 116,430 138,070 120,558 113,396 Ill::"' r::: 55 ..r::: - ~ 50 Assistant r- "3: >- 45 II Associate r- ~ ::I 40 H r- \J Full Ll.."' 35 • iU r , ~ 0 30 1- I , ..... 25 0 ' ~r::: 20 ! _ J - Cll ...\J 1 5 -- - !"""" Cll ::q 1:1.. ~' 10 - t--- - t--- }l__ ~ - 1-"· - r'- r~· r- - ~ ~~; 5 - ~;~ - f-- - f-- ,...., r \-., ~i 0 ~- ~~ r= :...::.. .- c..:. ~ ,...... m ~ ±t=l - • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 '

242 NOTICES OF THE AMS VOLUME 53, NUMBER 2 2005 Annual Survey of the Mathematical Sciences

Group Va Faculty Salaries Doctoral degree-granting departments of applied mathematics (18) 11 70 Rank 65 Assistant Professor 29 52,330 61,390 66,750 59,827 54,418 .;;t. Associate Professor 39 51 ,2 50 63,250 77,700 64,472 59,123 s::: 60 n:s Full Professor 132 82,500 94,470 120,900 102,882 97,784 c:: 55 s::: .. Assistant ..r:: OJ 50 Ill Associate '3: 45 >- .::: 40 ::Iv n:s 1.1.. 35 iU OJ 30 0 ....1- 25 0 OJ 20 s::: Ql ...v 1 5 Ql c.. 10 5 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 " 0 N m " 0'> I I I "I I I " 0 0 0 0 0 0 I I I I I I I I I I 'A m " 0 N m "

Group M Faculty Salaries Master's degree-granting departments of mathematics (189) 80 responses (42%) 2005-06 2004-05 Rank No. Reported Q, Median Q, Mean Mean 55 Assistant Professor 435 46,970 51,220 56,3 40 52,139 51,972 .;;t. Associate Professor 457 54,520 61,090 69,390 62,341 61,603 s::: 50 Full Professor 630 69,060 78,700 88,540 79,350 81,785 c::n:s s::: 45 ..r:: OJ 40 '3: - 35 - ::I v • Associate n:s 30 - 1.1.. iU • Full OJ 25 - 0 1- !k ' .... 20 jl ~~ 0 ;--• OJ J' ' s::: 1 5 r- Ql ...v Ql 10 :- ·~. c.. ~·· 5 t}) ~ " •L l· nl= r~ ,.. r I I 0 n- - - 0 Lf'l 0 Lf'l 0 Lf'l• 0 Lf'l 0 Lf'l 0 Lf'l 0 Lf'l 0 Lf'l 0 Lf'l 0 Lf'l 0 Lf'l 0 0 m m " 0'> 0 0 N N m m " Lf'l 0 Lf'l 0 Lf'l 0 Lf'l 0 Lf'l " " 0'> 0 0 N N m m 2005-06 Academic-Year Salaries (in thousands of dollars) fEBRUARY 2006 NOTICES OF THE AMS 243 2005 Annual Survey of the Mathematical Sc iences

Group B Faculty Salaries Bachelor's degree-granting departments of mathematics (1 01 0) 320 responses (32%) 2005-06 2004-05 55 Rank No . Reported Q, Median Q, Mean Mean

.:;t. 50 Assistant Professor 916 42,930 47,830 53,500 48,808 48,511 1: Associate Professor 852 50,360 56,370 64,850 58,293 57,542 rtl 0:: 45 Fu ll Professor 948 62,610 73,160 86,020 76,289 73,745 1: ..1:..... 40 - ~ : Assi stant >- 35 !:! r-- :I 1..1 Ill Associate rtl 30 ,. . r-- LL II Fu ll 'iii..... 25 r-- 0 1- 1 ...... 20 - 0 i ~· ...... 1: 1 5 - '1"1- r-- Q) 1..1 .... 1:11 ' Q) 10 - :--- ·I'~ ~- c.. fF'i 5 - r-·- rt~~ 1 ~1 L '""' q !•· I - . _ < , n!l ~ · _n !"'' .,..,., nll .... n c-; 0 ~ fC n n ~- ..

0 Lri 0 Lri 0 Lri 0 Lri 0 Lri 0 Lri 0 Lri 0 Lri 0 Lri 0 Lri 0 Lri 0 0 m m

2005-06 Academic-Year Salaries (in thousands of dollars)

may be a significant factor in the change in the re­ ported mean salaries.

Previous Annual Survey Reports Other Data Sources The 2004 First, Second, and Third Annual Survey American Association of University Professors, The Annual Reports were published in the Notices of the AMS Report on the Economic Status of the Profession in the February, August, and September 2005 issues 2004-2005, Academe: Bull. AAUP (April 2005), respectively. These reports and earlier reports, as Washington, DC. well as a wealth of other information from these American Statistical Association, Business, Industry, and su rveys, are available on the AMS web site at Government 2005 Salary Survey. [http: I /www . www .ams.org/ em ployment/surveyreports.html. amstat . o r g/ publi cati o ns /am s n/200 5/ hi ghl i ghtsl 0-' 1. pd f ] Revised November 2005. Acknowledgments (Published in AMSTATNEWS, October 2005, Issue #340.) The Annual Survey attempts to provide an accurate _ _ , 2004-2005 Sa lary Report ofAcademic Statisticians. appraisal and analysis of various aspects of the aca­ [http: //www . ams t at .o rg/profess ion / demic mathematical sciences scene for the use and s a l aryre po rt_acad2004- 5. pdf] (Published in benefit of the community and for filling the infor­ AMSTATNEWS, December 2004, Issue #330.) mation needs of the professional organizations. Commission on Professionals in Science and Technology, Every year, college and u niversity departments Professional Women and Minorities, 15th ed., CPST, in the United States are invited to respond. The Washington, DC, 2004. Annual Survey relies heavily on the conscientious __, Salaries of Scientists, Engineers, and Technicians: A efforts of the dedicated staff members of these Summary of Salary Surveys, 21st ed., CPST, Wash­ departments for the quality of its information. On ington, DC, 2004. behalf of the Annual Survey Data Committee __, Employment of Recent Doctoral Graduates in S&E: and the Annual Survey Staff, we thank the many Results ofProfessional Society Surveys, CPST, Washing­ secretarial and administrative staff members in ton, DC, 1998. the mathematical sciences departments for their __, Employment Outcomes of Doctorates in Science and cooperation and assistance in responding to the Engineering: Report of a CPST Workshop, CPST, Wash­ survey questionnaires. ington, DC, 1998.

244 N OTICES OF THE AMS VOLUME 53, N UMBER 2 2005 Annual Survey of the Mathematical Sciences

__, Supply and Demand Indicators for New Science and Engineering Doctorates: Results of a Pilot Study, CPST, Definitions ofthe Groups Washington, DC, 1997. As has been the case for a number of years, much of the data in these Conference Board of the Mathematical Sciences, Statisti­ reports is presented for departments divided into groups according cal Abstract of Undergraduate Programs in the Math­ to several characteristics, the principal one being the highest degree ematical Sciences in the United States: Fall 2000 CBMS Survey, American Mathematical Society, Providence, offered in the mathematical sciences. Doctoral-granting departments Rl, 2002. of mathematics are further subdivided according to their ranking of "scholarly quality of program faculty" as reported in the 1995 publi­ __, Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States: Fal/1995 cation Research-Doctorate Programs in the United States: Continuity CBMS Survey, MAA Reports No.2, 1997. and Change.l These ran kings update those reported in a previous study published in 1 982.2 Consequently, the departments which now com­ National Opinion Research Center, Doctorate Recipients from United States Universities: Summary Report 2003, pose Groups I, II, and Ill differ significantly from those used prior to Survey of Earned Doctorates, Chicago, IL, 2004. the 1996 survey. The subdivision of the Group I institutions into Group I Public and National Research Council, Strengthening the Linkages between the Sciences and the Mathematical Sciences, Group I Private was new for the 1996 survey. With the increase in num­ National Academy Press, Washington, DC, 2000. ber of the Group I departments from 39 to 48, the Annual Survey Data Committee judged that a further subdivision of public and private __, U.S. Research Institutes in the Mathematical Sciences: Assessment and Perspectives, National Academy Press, would provide more meaningful reporting of the data for these de­ Washington, DC, 1999. partments. Brief descriptions of the groupings are as follows: National Science Board, Science and Engineering Indica­ tors-2004 (NSB 04-01), National Science Foundation, Group I is composed of 48 departments with scores in the 3.00-5.00 Arlington, VA, 2004. range. Group I Public and Group I Private are Group I departments at public institutions and private institutions respectively. National Science Foundation, Characteristics of Doctoral Scientists and Engineers in the United States: 2001 Group II is composed of 56 departments with scores in the 2.00-2.99 (NSF 03-310), Detailed Statistical Tables, Arlington, range. VA, 2003. Group Ill contains the remaining U.S. departments reporting a doc­ _ _ , Emigration of U.S.-Born S&E Doctorate Recipients toral program, including a number of departments not included (NSF 04-327), Arlington, VA, June 2004. in the 1995 ranking of program faculty. __, Graduate Students and Postdoctorates in Science and Group IV contains U.S. departments (or programs) of statistics, bio­ Engineering: Fall 2002 (NSF 05-310), Arlington, VA, statistics, and biometrics reporting a doctoral program. 2004. Group V contains U.S. departments (or programs) in applied mathe­ __ , Gender Differences in the Careers ofAcademic Sci­ matics/applied science, operations research, and management entist and Engineers (NSF 04-323), Arlington, VA, 2004. science which report a doctoral program. _ _ , Plans for Postdoctoral Research Appointments Group Va is applied mathematics/applied science; Group Vb, which Among Recent U.S. Doctorate Recipients (NSF 04-308), was no longer surveyed as of 1998-99, was operations research Arlington, VA, 2004. and management science. _ _ , Science and Engineering Degrees: 1966-2000 (NSF Group M contains U.S. departments granting a master's degree as 02-327), Detailed Statistical Tables, Arlington, VA, the highest graduate degree. 2002. Group B contains U.S. departments granting a baccalaureate degree __, Science and Engineering Degrees, by Race/Ethnic­ only. ity ofRecipient: 1992-2001 (NSF 04-318), Detailed Sta­ Listings of the actual departments which compose these groups are tistical Tables, Arlington, VA, 2004. available on the AMS website at www. ams. org/empl oyment/. __ ,Science and Engineering Doctorate Awards: 2003 (NSF 05-300), Detailed Statistical Tables, Arlington, 1Research-Doctorate Programs in the United States: Continuity and VA, 2004. Change, edited by Marvin L. Goldberger, Brendan A. Maher, and Pamela Ebert Flattau, National Academy Press, Washington, DC, 1995. __, Women, Minorities, and Persons with Disabilities in Science and Engineering: 2004 (NSF 004-317), Arling­ 2 These findings were published in An Assessment of Research­ ton, VA, 2004. Doctorate Programs in the United States: Mathematical and Physical Sciences, edited by Lyle V. ]ones, Gardner Lindzey, and Porter E. _ _ , Statistical Profiles of Foreign Doctoral Recipients in Coggeshall, National Academy Press, Washington, DC, 1982. The Science and Engineering: Plans to Stay in the United information on mathematics, statistics, and computer science was States (NSF 99-304), Arlington, VA, 1998. presented in digest form in the April1983 issue of the Notices of the AMS, pages 257-67, and an analysis of the classifications was given in the june 1983 Notices of the AMS, pages 392-3.

fEBRUARY 2006 NOTICES OF THE AMS 245 Mathematics People

Colmez and Le Gall Awarded NSF Graduate Fellowships Fermat Prize Awarded The 2005 Fermat Prize for Mathematics Research has been The National Science Foundation (NSF) has awarded its awarded jointly to PIERRE CoLMEZ, Institut de Mathema­ Graduate Fellowships for fiscal year 2005. This program tiques de Jussieu, and ]EAN-FRAN<;:Ois LE GALL, Universite supports students pursuing doctoral study in all areas of Paris VI and Ecole Normale Superieure. Colmez was hon­ science and engineering and provides a stipend of ored for his contributions to the study of L-functions and US$18,000 per year for three years of full-time graduate p-adic Galois representations. Le Gall was chosen for his study. Following are the names of the awardees in the math­ contributions to the fine analysis of planar Brownian mo­ ematical sciences for 2005, followed by their undergrad­ tion and his invention of the Brownian snake and its ap­ uate institutions (in parentheses) and the institutions at plications to the study of nonlinear partial differential which they plan to pursue graduate work. equations. ]EFFREYM. ARISTOFF (Massachusetts Institute of Technol­ The Fermat Prize is presented every two years and car­ ogy), Massachusetts Institute of Technology; ETHAN P. ATKINs ries a monetary award of 20,000 euros (approximately (Rensselaer Polytechnic Institute), New York University; US$23,500). The prize rewards the research work of one REm W. BARTON (Massachusetts Institute of Technology), or more mathematicians in fields in which the contribu­ Massachusetts Institute of Technology; ] ONAH BLASIAK tions of Pierre de Fermat have been decisive: calculus of (Princeton University), University of California, Berkeley; variations, foundations of probability and analytic geom-· ]EREMY S. BRANDMAN (Yale University), University of Cali­ etry, and number theory. The award is given by the Uni­ fornia, Los Angeles; MooREA L. BREGA (University of Colorado versite Paul Sabatier, Toulouse. at Boulder), Courant Institute of Mathematical Sciences, Previous recipients of the Fermat Prize are: Abbas Bahri New York University; DAVID M. BROWN (University of Ari­ and Kenneth A. Ribet (1989), Jean-Louis Colliot-Thelene zona), University of California, Berkeley; ALEJANDRO L. (1991), Jean-Michel Coron (1993), Andrew]. Wiles (1995), CANTARERO (University of Colorado at Boulder), University Michel Talagrand (1997), F. Bethuel and F. Helein (1999), of California, Los Angeles; MARGARET I. DOIG (University of Richard Taylor and Wendelin Werner (2001), and Luigi Notre Dame), University of California, Berkeley; DAMIR D. Ambrosio (2003). DZHAFAROV (Purdue University), University of California, Berkeley; JoHN N. FRANCIS (Harvard University), Massachu­ - Elaine Kehoe setts Institute of Technology; ELENA D. FucHs (University of California, Berkeley) Princeton University; ANTON I. GERASCHENKO (Brandeis University), University of California, AAAS Fellows Elected Berkeley; ]ANAL. GEVERTZ (Rutgers University), Princeton Uni­ versity; STACY L. HoEHN (Xavier University), University of Five individuals whose work involves the mathematical Notre Dame; JEFFREY N. HooD (Reed College), University of sciences have been elected as fellows of the American British Columbia; KENNETH N. KAMRIN (University of Cali­ Association for the Advancement of Science (AAAS). The fornia, Berkeley), Massachusetts Institute of Technology; n ew fellows are JENNIFER TouR CHAYES, Microsoft Research; ADAM W. MARcus (Georgia Institute of Technology), Geor­ ROBERT M. MIURA, New Jersey Institute of Technology; gia Institute of Technology; CARLS. McTAGUE (University of LINDA R. PETZOLD, University of California, Santa Barbara; Cincinnati), Courant Institute of Mathematical Sciences, T. CHRISTINE STEVENS, St. Louis University; and ROBERT WILLIAMS, New York University; AARoN C. NABER (Pennsylvania State University of Texas, Austin. University), Pennsylvania State University; SARAH A. NowAK (Massachusetts Institute of Technology), University of - From an AAAS announcement California, Los Angeles; MARIBETH B. OscAMou (Santa Clara

246 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Mathematics People

University), University of Colorado at Boulder; VICTOR M. PANARETOS (Athens University of Economics and Business), University of California, Berkeley; ROBERT C. RHOADES (Buck­ nell University), Massachusetts Institute of Technology; ERic M. ScHOENFELD (Williams College), Stanford University; ALEXEY N. SPIRIDONOV (Princeton University), Massachusetts TENURE TRACK FACULTY Institute of Technology; KARnK VENKATRAM (Harvard Uni­ STATISTICS- MATHEMATICAL versity), Princeton University; RAcHEL A. WARD (University of Texas at Austin), Princeton University; WILLIE W. WONG SCIENCES (Princeton University), Stanford University; CARL R. YERGER The Mathematical Sciences Department of Worcester Polytechnic Institute (WPI) invites applications for one anticipated tenure-track faculcy position in applied (Harvey Mudd College), University of California, San Diego; statistics in 2006. Candidates at the assistant professor level will be considered. YEVGENY K. ZAYTMAN (Massachusetts Institute of Technol­ An earned Ph.D. or equivalent degree is required. Successful candidates must be able to contribute strongly w both rhe department's research activities and its ogy), Princeton University. innovative, project-based educational programs. Applications are especially encouraged in rhe areas of biostatistics, computational statistics, experimental -From an NSF announcement design, Bayesian methods, or time series analysis. WPI is a private and highly selective technological university with an enrollment of 2700 undergraduates and about 1100 full- and part-time graduate students. Worcester, located forty miles west of Boston, offers ready access to the diverse economic, cultural and recreational resources of the region. The Mathematical Sciences Department has 24 renured!renure-rrack facu lty and supports BS, MS, and Ph.D. programs in applied and computational mathematics and applied statistics. For additional information, see http://www.wpi.edu/+math. Qualified applicants should send a derailed curriculum vitae, a one-page statement of specific teaching and research objectives, and the names of four references with mail/email addresses and telephone/fax numbers to Statistics Search Committee, Mathematical Sciences Department, WPI, 100 Institute Road, Worcester, MA 01609-2280, USA. Applications will be considered on a continuing basis beginning December 1, 2005 until the position is filled. To enrich education through diversity, WPI is an affirmation action, equal opportunity employer. NO PHONE CALLS PLEASE

2006 AMS Sectional Meetings

Aprill-2, 2006 Florida International University, Miami, FL April 8-9, 2006 University of Notre Dame, Notre Dame, IN (features the Erdos Memorial Lecture by Bela Bollobcis) April 22-23, 2006 REMINDER! University of New Hampshire, Durham, NH April 29-30, 2006 San Francisco State University, San Francisco, CA Ensure that you continue to (features the Einstein Public Lecture in Mathematics receive your AMS publications by Benoft Mandelbrot) and communications. October 7-8, 2006 University of Utah, Salt Lake City, UT Renew October 21-22, 2006 your University of Cincinnati, Cincinnati, OH membership October 28-29, 2006 today! University of Connecticut, Storrs, CT November 3-4, 2006 For more information, see University of Arkansas, Fayetteville, AR https://www.ams.org/dues-renewal/ For more information, see http://www.ams.org/amsmtgs/sectional .html

fEBRUARY 2006 NOTICES OF THE AMS 247 Mathematics Opportunities

email: dav@math. ksu. edu; website: http: I lwww. math. NSF-CBMS Regional ksu.edulmainleventslconvex-geom. Conferences, 2006 Probabilistic and Combinatorial Approach in Analysis, Mark Rudelson, lecturer. August 6-12, 2006; Kent State With funding from the National Science Foundation (NSF), University. Organizers: Artem Zvavitch, telephone: 330-672- the Conference Board of the Mathematical Sciences (CBMS) 3316, email: zvavi tch@math. kent. edu; Per Enflo, tele­ will hold four NSF-CBMS Regional Research Conferences phone 330-672-9095, email: enfl o@math. kent. edu; and during the summer of 2006. Andrew Tonge, telephone: 330-672-9046, email: These conferences are intended to stimulate interest and tonge@math. kent. edu; website: http: I lwww. math. activity in mathematical research. Each five-day conference kent.edulmathiCBMS.cfm. features a distinguished lecturer who will deliver ten lec­ tures on a topic of important current research in one -From a CBMS announcement sharply focused area of the mathematical sciences. The lec­ turer subsequently prepares an expository monograph based on these lectures. Depending on the conference Call for Proposals for 2007 NSF­ topic, the monograph will be published by the American Mathematical Society, by the Society for Industrial and CBMS Regional Conferences Applied Mathematics, or jointly by the American Statistical To stimulate interest and activity in mathematical re­ Association and the Institute of Mathematical Statistics. search, the National Science Foundation (NSF) intends to Support for about thirty participants will be provided support up to seven NSF-CBMS Regional Research Con­ for each conference. Established researchers and interested ferences in 2007. A panel chosen by the Conference Board newcomers, including postdoctoral fellows and graduate of the Mathematical Sciences will make the selections from students, are invited to attend. among the submitted proposals. Information about an individual conference may he ob­ Each five-day conference features a distinguished tained by contacting the conference organizer. The four lecturer who delivers ten lectures on a topic of important conferences to be held in 2006 are as follows. current research in one sharply focused area of the math­ Mathematical and Numerical Treatment of Fluid Flow ematical sciences. The lecturer subsequently prepares an and Transport in Porous Media, Zhangxin (John) Chen, lec­ expository monograph based on these lectures, which is turer. May 22-26, 2006; University of Nevada, Las Vegas. normally published as a part of a regional conference se­ Organizers: Jichun Li, telephone: 702-895-0365, email: ries. Depending on the conference topic, the monograph ji chun@unlv. nevada. edu; and Yi-Tung Chen, telephone: will be published by the American Mathematical Society, 702-895-1202, email: uuchen@nscee. edu; website: by the Society for Industrial and Applied Mathematics, or http:llwww.ncacm.unlv.edulcbmsl. jointly by the American Statistical Association and the In­ Cluster Algebras and Applications, Andrei Zelevinsky, stitute of Mathematical Statistics. Support is provided for lecturer. June 13-17, 2006; North Carolina State Univer­ about thirty participants at each conference, and the con­ sity. Organizer: Naihuan Jing, telephone: 919-513-3584, ference organizer invites both established researchers and email: j i ng@uni ty. ncsu. edu; website: http: I lwww. interested newcomers, including postdoctoral fellows and math.ncsu.edul-jinglconfiCBMSicbms06.html. graduate students, to attend. The Interplay between Convex Geometry and Harmonic The proposal due date is April 7, 2006. For further in­ Analysis, Alexander Koldobsky, lecturer. July 29- formation on submitting a proposal, consult the CBMS August 2, 2006; Kansas State University. Organizers: Dmitry website, http: I lwww. cbmsweb. orgiNSF12007 _call . htm, Ryabogin, telephone: 785-532-6750, email: ryabs@math. or contact: Conference Board of the Mathematical Sci­ ksu. edu; and David Auckly, telephone: 785-532-6750, ences, 1529 Eighteenth Street, NW, Washington, DC 20036;

248 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Mathematics Opportunities telephone: 202-293-1170; fax: 202-293-3412; email: from June 5 through August 11, and in the fall, from Sep­ [email protected] or [email protected]. tember 11 through November 17. Applications for the fellowships are invited from schol­ -From a CBMS announcement ars from graduate through postdoctoral levels in any physical, biological, or social science field or any field of engineering, medicine and health, or veterinary medicine, National Academies Research as well as business, law, education, and other graduate and professional programs. Postdoctoral scholars should have Assodateship Programs received their Ph.D.'s within the past five years. The stipend for both ten-week programs is US$4,800. The Policy and Global Affairs Division of the National The fellowship stipend is intended to cover all living ex­ Academies is sponsoring the 2006 Postdoctoral and Senior penses for the period. In addition, a travel stipend of up Research Associateship Programs. The programs are meant to US$500 will be provided. to provide opportunities for Ph.D., Sc.D., or M.D. scientists and engineers of unusual promise and ability to perform Deadlines for receipt of materials for the summer pro­ research at more than one hundred research laboratories gram is March 1, 2006, and for the fall program, June 1, throughout the United States and overseas. 2006. More information and application forms and in­ Full-time associateships will be awarded for research in structions can be found on the website http: I lwww7 . the fields of mathematics, chemistry, earth and atmospheric nationalacademies.orgl policyfellows or by con­ sciences, engineering, applied sciences, life sciences, space tacting National Academies Christine Mirzayan Science sciences, and physics. Most of the laboratories are open to and Technology Policy Graduate Fellowship Program, 500 both U.S. and non-U.S. nationals and to both recent doctoral Fifth Street, NW, Room 508, Washington, DC 20001; tele­ recipients and senior investigators. phone: 202-334-2455; fax: 202-334-1667. Awards are made for one or two years, renewable for a maximum of three years. Annual stipends for recent Ph.D. - From a National Academies announcement recipients range from US$30,000 to US$50,000, depending on the sponsoring laboratory; the awards for senior recipi­ ents will be higher. Support is also provided for allowable ONR Young Investigator relocation expenses and for limited professional travel during the period of the award. Program Awards will be made four times during the year, in The Office of Naval Research (ONR) sponsors a Young In­ February, May, August, and November. The deadline for vestigator Program to support academic scientists and application materials to be postmarked or for electronic engineers who have recently received Ph.D. or equivalent submissions for the February 2006 review is February 1, degrees and who show exceptional promise for doing cre­ 2006. ative research. The ONR expects to make up to twenty-four For further information and application materials, see new awards in fiscal year 2006. Awards of up to US$100,000 the National Academies website at http: I lwww4. nas. edul per year for three years are made, and additional funds pgal rap. nsfIW ebDocumentsiHome+Page, or contact Re­ may be provided based on need. search Associateship Programs, Keck Center of the National Proposals are sought that address the following priority Academies, 500 Fifth Street, NW, GR322A, Washington, DC research areas in mathematical, computer, and information 20001; telephone 202-334-2760; fax 202-334-2759; email: sciences: inverse problems arising from electromagnetic rap@nas. edu. and acoustic wave propagation and scattering; mathemati­ cal foundations for imaging, image analysis, and image -From an NRC announcement processing; mathematical optimization; fundamentals of software and systems; and intelligent systems. The program is open to United States citizens, nationals (native residents National Academies Graduate of a U.S. possession), and permanent residents who hold tenure-track or permanent faculty positions at U.S. univer­ Fellowship Program sities and who received their graduate degrees on or after The Christine Mirzayan Science and Technology Policy November 1, 2000. Graduate Fellowship Program of the National Academies Proposals in mathematical, computer, and information is designed to engage graduate science, engineering, med­ sciences should be sent to: Office of Naval Research (FY06 ical, veterinary, business, and law students in the analy­ YIP BAA No. 06-002), Attn: YIP Coordinator, Mathematical, sis and creation of science and technology policy and to Computer, and Information Sciences Division, ONR Code familiarize them with the interactions of science, 311, Room 1106, 875 North Randolph Street, Suite 1425, technology, and government. As a result, students de­ Arlington, VA 22203-1995; telephone: 703-696-4313. velop essential skills different from those attained in acad­ Proposals must be received by 4:00 p.m. Eastern Standard emia and make the transition from graduate student to pro­ Time on January 12, 2006. For further information and fessional. In 2006 programs will be held in the summer, instructions for proposal preparation, see the ONR

FEBRUARY 2006 NOTICES OF THE AMS 249 Mathematics Opportunities

NATIONAL SECURITY AGENCY website, http: I jwww. onr. navy. mil /sci_tech/ industrial/363/docs/baa_06_002.doc.

-From an ONR announcement

Clay Mathematics Institute 2006 Summer School The Clay Mathematics Institute (CMI) Summer School on Arithmetic Geometry will be held at the Mathematisches Institut, Georg-August-Universitiit Gbttingen, Germany, from July 17 to August 11, 2006. Designed for graduate students and mathematicians within five years of receipt of the Ph.D., the program will introduce the participants to modern techniques and out­ standing conjectures at the interface of number theory and algebraic geometry. The main focus is rational points on Put Your Math algebraic varieties over nonalgebraically closed fields. Do they exist? If not, can this be proven efficiently and algo­ Intelligence to Work rithmically? When rational points do exist, are they finite in number and can they be found effectively? When there When you join NSA, you join a highly are infinitely many rational points, how are they distrib­ talented group of Mathematicians who deduce uted? For curves, a cohesive theory addressing these questions structure where it is not apparent, find patterns has emerged in the past few decades. Highlights include in seemingly random sets, and create order out Faltings's finiteness theorem and Wiles's proof of Fer­ of chaos. They apply Number Theory, Group mat's last theorem. Key techniques are drawn from the Theory, Finite Field Theory, Linear Algebra, theory of elliptic curves, including modular curves and parametrizations, Heegner points, and heights. Probability Theory, Mathematical Statistics, The arithmetic of higher dimensional varieties is equally Combinatorics, and more to a world of rich, offering a complex interplay of techniques, includ­ challenges. They exchange ideas and work with ing Shimura varieties, the minimal model program, mod­ uli spaces of curves and maps, deformation theory, Galois some of the finest minds and most powerful cohomology, harmonic analysis, and automorphic func­ computers in the country. And you can too, tions. However, many foundational questions about the when you put your math intelligence to structure of rational points remain open, and research work at NSA. tends to focus on properties of specific classes of varieties. This school will offer three core courses (on curves, sur­ faces, and higher-dimensional varieties), supplemented by seminars on computational and algorithmic aspects of NSA: Securing Tomorrow T~Cia arithmetic geometry and by minicourses on more ad­ vanced topics. Lecturers include Dan Abramovich, Fedor For more information and to apply Bogomolov, Antoine Chambert-Loir, Ching-Li Chai, Henri online, visit our Web site. Darmon, David Harari, Brendan Hassett, Andrew Kresch, Yuri Manin, Frans Oort, Jason Starr, Yuri Tschinkel, and others. The organizers of the summer school are Jim Carl­ son, Henri Damon, David Ellwood, Brendan Hassett, and Yuri Tschinkel. Funding is available to graduate students and post­ doctoral fellows who are within five years of receipt of the Ph.D. Standard support amounts will include funds for local expenses and accommodations plus economy travel. www.NSA.gov/Careers The deadline for application is February 28, 2006. WHERE INTELLIGENCE GOES TO WORK For more information and an application form, see http://www.claymath.org/summerschool or contact

U.S. citizenship is required. NSA is an equal opportunity emplo!;jer. All applicants for em ployment summerschoo l @cl aymath. org; telephone: 617-995-2600. are considered without regard to race, colo r, religion, sex, national origin, age, marital status, handicap, sexual orientation, or status as a parent. -CMI announcement

250 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Inside the AMS

AMS Congressional Briefing: How Mathematics Helps Predict Storm Surges On November 3, 2005, the AMS sponsored its eighth Con­ gressional Briefing, a yearly event that brings together senators, congressional representatives, and their staffs for presentations about using mathematics to address is­ sues of national importance. The title of the latest brief­ ing was "From Katrina Forward: How Mathematics Helps Predict Storm Surges". The briefing featured two speakers: Clint Dawson, pro­ fessor of aerospace engineering and engineering mechanics and a member of the Center for Subsurface Modeling in Left to right: Congresswoman Eddie Bernice johnson the Institute for Computational Engineering and Sciences (D-TX) with Joannes Westerink and Clint Dawson. at the University of Texas, and Joannes Westerink, asso­ ciate professor of civil engineering and geological sciences discussed what potential research is still necessary to at the University of Notre Dame. The presentations focused make these predictions more accurate and timely. on data from Hurricane Katrina and other costly U.S. For more information on activities of the AMS Wash­ storms. ington Office, visit the webpage http: I lwww. ams. o rgl Mathematical modeling and computer simulation are es­ government. sential tools for both forecasting and hindcasting storm surges due to hurricanes and tsunamis. Dawson and Wes­ -Anita Benjamin, AMS Washington Office terink described research that has taken place over the past decade, which allows for predictions of the extent and mag­ nitude of flooding as a storm makes landfall. They also 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 lwww. ams. o rgl amslemai l. html. [email protected] for questions regarding a particular abstract. [email protected] to contact the AMS Acquisitions Department. [email protected] to contact the Society's headquarters in Providence, Rhode Island. Left to right: Congressman Vernon Ehlers (R-MI), talks with Clint Dawson and Joannes Westerink at the [email protected] congressional briefing. to contact the Society's office in Washington, DC. fEBRUARY 2006 NOTICES OF THE AMS 251 Inside the AMS

AMS journal-specific questions should be directed to [email protected] the following email addresses: for information on AMS employment and career services. [email protected]: for questions regarding a paper to [email protected] appear in Bulletin of the AMS. for technical questions regarding AMS electronic prod­ ucts and services. [email protected]: for questions regarding a paper to appear in journal of the AMS. [email protected] for authors to submit research announcements to Electronic [email protected]: for questions regarding a paper Research Announcements of the AMS. to appear in Mathematics of Computation. [email protected] [email protected]: for questions regarding a paper to to send information to be included in the "Mathematics appear in Proceedings. Calendar" section of the Notices. [email protected]: for questions regarding a paper to [email protected] appear in Transactions. for user questions about the job application website, http://www.mathjobs.org. [email protected] [email protected] to request information about membership in the AMS or to submit reviews to Mathematical Reviews and to send about dues payments, or to ask any general membership correspondence related to reviews or other editorial ques­ questions; may also be used to submit address changes. tions. [email protected] [email protected] for information or questions about the AMS-ASA-IMS-MAA to request general information about Society meetings Annual Survey of the Mathematical Sciences or to request and conferences. reprints of Survey reports. [email protected] [email protected] for questions regarding the Society's overseas book to request email meeting registration forms. donation program. [email protected] [email protected] to submit completed email meeting registration forms. for inquiries related to the online AMS Bookstore. [email protected] [email protected] for information or questions about registration, housing, to submit classified advertising for the Notices. and exhibits for the Joint Mathematics Meetings (Mathe­ matics Meetings Service Bureau). [email protected] for general information about AMS products (including [email protected] electronic products); to send address changes, place credit for technical questions regarding MathSciNet. card orders for AMS products, or conduct any general [email protected] correspondence with the Society's Customer Services to send correspondence to the managing editor of the Department. Notices, including items for the news columns. The editor [email protected] (noti ces@math. ou. edu) is the person to whom to send for information about giving to the AMS, including the articles. Requests for permission to reprint from the Epsilon Fund. Notices should be sent to [email protected] (see below). [email protected] for general information and questions about Employment [email protected] Information in the Mathematical Sciences (ElMS). For dead­ to submit paid display ads electronically for the Notices. lines, rates, and the advertising submission form, go to (Hard copy of the ad should also be faxed or sent via http://www.ams.org/eims. postal mail.) [email protected] [email protected] to submit papers to Representation Theory and Conformal to submit suggestions for books to be included in the Geometry and Dynamics, electronic journals of the AMS. Book List in the Notices. Each submission must be accompanied by the journal [email protected] template. A copy of the template is available by sending to submit letters and opinion pieces to the Notices. email to ejour-submit@ams. org. Putthe word TEMPlATE in the subject field of the email message. To get additional [email protected] help, put the word HELP in the subject field in a separate to comment on or send suggestions for topics for the mail message. WHAT IS ... ? column to the Notices.

252 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Inside the AMS [email protected] JoHN P. HUNEKE, professor, Ohio State University, Colum­ to contact the AMS Public Awareness Office. bus, died on October 1, 2004. Born on April16, 1942, he was a member of the Society for 38 years. [email protected] LEE M. SoNNEBORN, professor, Michigan State University, to contact the president of the AMS. East Lansing, died in August 2004. Born on December 2 7, [email protected] 1931, he was a member of the Society for 49 years. to send correspondence about AMS professional programs CHUNG-TAO YANG, professor emeritus, from Springfield, and services. VA, died on September 15, 2005. Born in May 1923, he was a member of the Society for 34 years. [email protected] to send correspondence to the AMS Publication Division. [email protected] to submit accepted electronic manuscripts to AMS publi­ cations (other than Abstracts). See http: I jwww. ams. org/ submi t-book-j ournal to electronically submit accepted manuscripts to the AMS book and journal programs. [email protected] to request permission to reprint material from Society publications. [email protected] to inquire about royalty statements or payments. [email protected] to inquire about reselling or distributing AMS publications, or to send correspondence to the AMS sales department. [email protected] to contact the secretary of the AMS. [email protected] to correspond regarding a balance due shown on a monthly statement. AMERICAN MATHEMATICAL SOCIETY [email protected] for questions relating to student programs and services. in [email protected] Math Moscow to contact the Society's typesetting Technical Support group. Scholarships [email protected] to request examination copies or to inquire about using The AMS invites undergraduate AMS publications as course texts. mathematics and computer science majors in the U.S. to apply for a [email protected] special scholarship to attend a Math in for general information or for assistance in accessing and Moscow semester at the Independent University of using the AMS website. Moscow. Funding is provided by the National Science Foundation and is administered by the AMS. . Deaths of AMS Members The application deadline for spring semesters is September 30, and for fall semesters is April 15. MICHAEL E. BRECKENRIDGE, from Solomon, KS, died on Febru­ For more information, see ary 13, 2005. Born on October 3, 1951, he was a member of the Society for 5 years. www.ams.org/employment/mimoscow.html. NELSON A. BRIGHAM , retired, from Eugene, OR, died on Contact: Membership and Programs Department, June 14, 2005. Born on November 6, 1915, he was a American Mathematical Society, 201 Charles Street, member of the Society for 59 years. Providence, Rl 02904-2294, USA; KAZIMIERZ GLAZEK, professor, Technical University of tel. 800-321-4267, ext. 4170; Zielona Gora, Poland, died in September 2005. Born on email: [email protected]. AMS February 20, 1939, he was a member of the Society for 9 years.

FEBRUARY 2006 NOTICES OF THE AMS 253 Reference and Book List

The Reference section of the Notices "Mathematics Opportunities" in this fax: 202-588-1853; email: amsdc@ is intended to provide the reader with issue. ams. org. frequently sought information in January 13, 2006: Proposals for NSF January 26, 2006: Proposals for an easily accessible manner. New Program on Mathematical Sciences: NSF Scientific Computing Research information is printed as it becomes Innovations at the Interface with the Environments for the Mathematical available and is referenced after the Physical and Computer Sciences and Sciences (SCREMS). See the website first printing. As soon as information Engineering: Chemistry. See the web­ http://www.nsf.govlpublicationsl is updated or otherwise changed, it site http: I /www. nsf. gov /pubs/ pub_summ.jsp?ods_key=nsf05627. will be noted in this section. 2005/nsf05622/nsf05622.htm. January 27, 2006: Proposals for January 15, 2006: Applications Partnerships for Adaptation, Imple­ Contacting the Notices for AMS-AAAS Mass Media Fellow­ mentation, and Dissemination Awards The preferred method for contacting ships. See http: I /www. a aas. o rg/ of the NSF ADVANCE Program. See the Notices is electronic mail. The programs/education/MassMedia/ editor is the person to whom to send index. shtml, or contact Stacey Pasco, the website http: I lwww. nsf. gov I articles and letters for consideration. Manager, Mass Media Program, AAAS fundinglpgm_summ.jsp?pims_id= Articles include feature articles, Mass Media Science and Engineering 5383. memorial articles, communications, Fellows Program, 1200 New York January 31,2006: Applications for opinion pieces, and book reviews. The Avenue, NW, Washington, DC 20005; postdoctoral fellowships at the Insti­ editor is also the person to whom to telephone 202-326-6441; fax 202- tut Mittag-Leffler. See the website send news of unusual interest about 371-9849. Also see the website http:llwww.mittag-leffler.se/ other people's mathematics research. http://www.ams.org/government/ grants. The managing editor is the person massmedi aann. html or contact February 1, 2006: Applications for to whom to send items for "Mathe­ the AMS Washington Office, 1527 February review for National Acade­ matics People", "Mathematics Op­ Eighteenth Street, NW, Washington, mies Postdoctoral and Senior Re­ portunities", "For Your Information", DC 20036; telephone 202-588-1100; search Associateship Programs. See "Reference and Book List", and "Math­ ematics Calendar". Requests for Where to Find It permissions, as well as all other inquiries, go to the managing editor. A brief index to information that appears in this and previous issues of the Notices. The electronic-mail addresses are AMS Bylaws-November 2005, p. 1239 noti ces@math. ou. edu in the case of AMS Email Addresses-February 2006, p. 251 the editor and noti ces@ams. org in AMS Ethical Guidelines-June/July 2004, p. 675 the case of the managing editor. The AMS Officers 2004 and 2005 (Council, Executive Committee, fax numbers are 405-325-7484 for Publications Committees, Board of Trustees)-May 2005, p. 564 the editor and 401-331-3842 for the AMS Officers and Committee Members-October 2005, p. 1073 managing editor. Postal addresses Conference Board of the Mathematical Sciences-September 2005, may be found in the masthead. p. 892 Information for Notices Authors-]une/]uly 2005, p. 660 Mathematics Research Institutes Contact Information-August 2005, Upcoming Deadlines p. 770 January 10, 2006: Applications for National Science Board-January 2006, p. 62 AAUW Educational Foundation Fel­ lowships and Grants. See http: I I New journals for 2004-]une/]uly 2005, p. 662 www.aauw.org/fga/fellowships_ NRC Board on Mathematical Sciences and Their Applications-March 2005, grants/selected. cfm or contact the p. 361 AAUW Educational Foundation, 1111 NRC Mathematical Sciences Education Board-April 2005, p. 465 Sixteenth St., N.W., Washington, DC NSF Mathematical and Physical Sciences Advisory Committee-February 20036; telephone 800-326-2289 2006,p. 255 (AAUW); fax 202-872-1425; email: Program Officers for Federal Funding Agencies-October 2005, i nfo@aauw. org. p. 1069 (DoD, DoE); November 2005, p. 1223 (NSF) january 12, 2006: Proposals for Stipends for Study and Travel-September 2005, p. 900 ONR Young Investigator Program. See

254 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Reference and Book List

"Mathematics Opportunities" in this 934-0163; email: awm@ math. umd. Luis Echegoyen (10106) issue. edu; or contact Association for Department of Chemistry February 1, 2006: Applications for Women in Mathematics, 11240 Waples Clemson University AWM Travel Grants and Mentoring Mill Road, Suite 200, Fairfax, VA Travel Grants. See http: I lwww. awm­ 22030. Mostafa El-Sayed (10106) math.orgltravelgrants.html; June 1, 2006: Applications for fall School of Chemistry and telephone 703-934-0163; email: awm@ program of the Christine Mirzayan Biochemistry math. umd. edu; or contact Associa­ Science and Technology Policy Grad­ Georgia Institute of Technology tion for Women in Mathematics, uate Fellowship Program of the Na­ 11240 Waples Mill Road, Suite 200, tional Academies. See "Mathematics Lucy Fortson (10106) Fairfax, VA 22030. Opportunities" in this issue. Department of Astronomy February 10, 2006: Applications Adler Planetarium for Math for America Foundation New­ MPS Advisory Committee ton Fellowships. See the website Following are the names and affilia­ Sol M. Gruner (10107) http: llwww.mathforamerica.orgl. tions of the members of the Advisory Department of Physics February 15, 2006: Nominations Committee for Mathematical and Cornell University for Clay Mathematics Institute Physical Sciences (MPS) of the National (CMI) Liftoff Program. See http: I I Science Foundation. The date of the Frances Hellman (10106) claymath.orglfaslliftoff_ expiration of each member's term is Department of Physics fell owsl; telephone 617-995-2600; given after his or her name. The web­ University of California, San Diego email:[email protected]. site for the MPS directorate may be February 28, 2005: Applications found at http:llwww.nsf.govl john Huchra (10106) for Clay Mathematics Institute (CMI) homelmpsl. The postal address is Harvard-Smithsonian Center Summer School. See "Mathematics Directorate for the Mathematical and for Astrophysics Opportunities" in this issue. Physical Sciences, National Science Harvard University March 1, 2006: Applications for Foundation, 4201 Wilson Boulevard, summer program of the Christine Arlington, VA 22230. Rhonda Hughes (10108) Mirzayan Science and Technology Pol­ Douglas N. Arnold (10108) Department of Mathematics icy Graduate Fellowship Program of Institute for Mathematics and its Bryn Mawr College the National Academies. See "Mathe­ Applications matics Opportunities" in this issue. University of Minnesota Raymond L. johnson (10106) March 1, 2006: Proposals for NSF Department of Mathematics Program on Mathematical Sciences: Lars Bildsten (10107) University of Maryland, College Park Innovations at the Interface with the KITP Physical and Computer Sciences and University of California, jon R. Kettenring (10106) Engineering: Computer Science. See Santa Barbara Charles A. Dana Research Institute the website http: I lwww. nsf. gov I Drew University pubsi200Sinsf05622lnsf05622. Cynthia j. Burrows (10108) htm. Department of Chemistry Robert V. Kohn (10107) March 1, 2006: Applications for University of Utah Courant Institute EDGE Program. See the website New York University http:llwww.edgeforwomen.orglor Claude R. Canizares (10108) contact the EDGE Program, Depart­ Office of the Provost Steven E. Koonin (10107) ment of Mathematics, Bryn Mawr Massachusetts Institute Chief Scientist College, 101 North Merion Avenue, of Technology BP, plc Bryn Mawr, PA 19010; email: edge@ edgeforwomen. org; telephone 610- janet M. Conrad (10106) W Carl Lineberger (chair) (10106) 876-3527. Department of Physics Department of Chemistry March 31, 2006: Nominations for Columbia University and Biochemistry Third World Academy of Sciences Joint Institute for Laboratory Prizes. See http: I lwww. twas . o rgl. Susan Coppersmith (10107) Astrophysics April 7, 2006: Proposals for 2007 Department of Physics University of Colorado, Boulder NSF-CBMS Regional Conferences. See University of Wisconsin "Mathematics Opportunities" in this Venkatesh Narayanamurti (10106) issue. Larry R. Dalton (10108} Division of Engineering and Applied May 1, 2006, October 1, 2006: Ap­ Department of Chemistry Sciences plications for AWM Travel Grants. See University of Washington Harvard University http:llwww.awm-math.orgl travel grants. html; telephone 703-

FEBRUARY 2006 NOTICES OF THE AMS 255 Reference and Book List

Monica Olvera de la Cruz (10/ 08) Action This Day, edited by Michael The Equation That Couldn't Be Department of Materials Science Smith and Ralph Erskine. Random Solved (How Mathematical Genius Dis­ and Engineering House of Canada, February 2003. covered the Language of Symmetry), Northwestern University ISBN 0-593-04910-1. by Mario Livio. Simon and Schuster, Beyond Reason: Eight Great Prob­ September 2005. ISBN 0-743-25820-7. jose N. Onuchic (10/08) lems That Reveal the Limits ofScience, ''M. C. Escher's Legacy: A Centennial Department of Physics by A K. Dewdney. Wiley, April 2004. Celebration, edited by Doris University of California, San Diego ISBN 0-471-01398-6. Schattschneider and Michele Emmer. The Book of Presidents. London Springer, September 2005 (paperback Eve Ostricker (10/07) Mathematical Society, 2005. ISBN 0- edition). ISBN 3-540-20100-9. Department of Astronomy 950-27341-4. The Essential Turing, edited by University of Maryland, College Park A Brief History of Infinity, by Paolo B. Jack Copeland. Oxford University Zellini. Penguin Books (paperback), Press, September 2004. ISBN 0-198- David W Oxtoby (10/07) March 2005. ISBN 0-141-00762-1. 25080-0. Office of President The Calculus Gallery: Masterpieces Experimentation in Mathematics: Pomona College from Newton to Lebesgue, by William Computational Paths to Discovery, by Dunham. Princeton University Press, Jonathan Borwein, David Bailey, and Marcia]. Rieke (10/ 07) December 2004. ISBN 0-691-09565-5. Roland Girgensohn. A K Peters, March Steward Observatory 262 Chance: A Guide to Gambling, Love, 2004. ISBN 1-56881-136-5. (Reviewed University of Arizona the Stock Market and just About Every­ September 2005.) thing Else, by Amir D. Aczel. Thun­ The Fermat Diary, by C.]. Mozzochi. Elizabeth H. Simmons (10/07) AMS, August 2000. ISBN 0-8218- Department of Physics and der's Mouth Press, October 2004. ISBN 1-56858-316-8. (Reviewed August 2670-0. Astronomy The Fermat Proof, by C.]. Mozzochi. Michigan State University 2005.) ''Change Is Possible: Stories of Trafford Publishing, Inc., February 2004. ISBN 1-412-02203-7. Michael Witherell (10/ 08) Women and Minorities in Mathematics, by Pat Kenschaft. AMS, September Geometry and Meaning, by Dominic Department of Physics Widdows. Center for the Study of Lan­ University of California, 2005. ISBN 0-8218-3748-6. Coincidences, Chaos, and All That guage and Information, November Santa Barbara 2004. ISBN 1-5 75-86448-7. Math jazz: Making Light of Weighty God Created the Integers, by Stephen Ideas, by Edward B. Burger and Michael Book List Hawking. Running Press, October 2005. Starbird. W. W. Norton, August 2005. ISBN 0-762-41922-9. The Book List highlights books that ISBN 0-393-05945-6. ''Godel's Theorem: An Incomplete have mathematical themes and are The Colours ofInfinity: The Beauty Guide to Its Use and Abuse, by Torkel aimed at a broad audience potentially and Power of Fractals, by Michael including mathematicians, students, Franzen. A K Peters, May 2 00 5. ISBN 1- Barnsley, Nigel Lesmoir-Gordon, and the general public. When a book 568-81238-8. Benoit B. Mandelbrot, Ian Stewart, has been reviewed in the Notices, a The Golden Ratio: The Story of Phi, Gary Flake, Robert Prechter, and reference is given to the review. Gen­ the World's Most Astonishing Number, Arthur C. Clarke. Clear Press, March erally the list will contain only books by Mario Livio. Broadway Books, published within the last two years, 2004. ISBN 1-904-55505-5. September 2003. ISBN 0-7679-0816-3. though exceptions may be made in Complexities: Women in Mathe­ (Reviewed March 2005.) cases where current events (e.g., the matics, edited by Bettye Anne Case Graphic Discovery: A Trout in the death of a prominent mathematician, and Anne M. Leggett. Princeton Uni­ Milk and Other Visual Adventures, by coverage of a certain piece of mathe­ versity Press, January 2005. ISBN Howard Wainer. Princeton University matics in the news) warrant drawing 0-691-11462-5. Press, October 2004. ISBN 0-691- readers' attention to older books. Sug­ Converging Realities: Toward a 10301-1. gestions for books to include on the list Common Philosophy of Physics and Incompleteness: The Proof and may be sent to noti ces-bookl i st@ Mathematics, by Roland Omnes. Paradox of Kurt Godel, by Rebecca ams .org. Princeton University Press, November Goldstein. W. W. Norton, February ''Added to "Book List" since the 2004. ISBN 0-691-11530-3. 2005. ISBN 0-393-05169-2. list's last appearance. The Curious Incident of the Dog in ''The Infinite Book: A Short Guide to the Nighttime, by Mark Haddon. Vin­ the Boundless, Timeless and Endless, by A 3 & His Algebra: How a Boy from tage, May 2004. ISBN 1-400-03271-7. John D. Barrow. Pantheon, August Chicago's West Side Became a Force in Dark Hero of the Information Age: 2005. ISBN 0-375-42227-7. American Mathematics, by Nancy E. In Search of Norbert Wiener, by Flo Introducing Game Theory and Its Albert. iUniverse, Inc., January 2005. Conway and Jim Siegelman. Basic Applications, by Elliott Mendelson. ISBN 0-595-32817-2. (Reviewed De­ Books, December 2004. ISBN 0-738- CRC Press, July 2004. ISBN 1-584- cember 2005.) 20368-8. 88300-6.

256 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Reference and Book List

]dnos Bolyai, Euclid, and the Mathematics in Nature: Modeling Reality Conditions: Short Mathe­ Nature of Space, by Jeremy ]. Gray. Patterns in the Natural World, by matical Fiction, by Alex Kasman. Math­ MIT Press, May 2003. ISBN 0-262- John A. Adam. Princeton University ematical Association of America, May 57174-9. (Reviewed October 2005.) Press, November 2003. ISBN 0-691- 2005. ISBN 0-88385-552-6. john Pell (1611-1685) and His Cor­ 11429-3. (Reviewed June/July 2005.) The Road to Reality: A Complete respondence with Sir Charles Meta Math! The Quest for Omega, by Guide to the Laws of the Universe, by Cavendish: The Mental World of an Gregory Chaitin. Pantheon, October Roger Penrose. Knopf, February 2005. Early Modern Mathematician, by Noel 2005. ISBN 0-375-42313-3. ISBN 0-679-45443-8. Malcolm and Jacqueline Stedall. The (Mis)Behavior of Markets: A Oxford University Press, second Fractal View of Risk, Ruin and Reward, Saunders Mac Lane: A Mathemati­ edition, January 2005. ISBN 0-198- by Benoit Mandelbrot and Richard cal Autobiography, by Saunders 56484-8. Hudson. Basic Books, August 2004. Mac Lane. A K Peters, May 2005. ISBN The Knot Book: An Elementary ISBN 0-465-04355-0. 1-568-81150-0. (Reviewed December Introduction to the Mathematical The­ More Damned Lies and Statistics: 2005.) ory of Knots, Colin C. Adams. AMS, How Numbers Confuse Public Issues, Science in the Looking Glass, by September 2004. ISBN 0-8218-3678-1. by Joel Best. University of California E. Brian Davies. Oxford University (Reviewed September 2005.) Press, August 2004. ISBN 0-520- Press, August 2003. ISBN 0-19- Knots and Links, by Peter R. 23830-3. 852 543-5. (Reviewed December 2005.) Cromwell. Cambridge University Press, More Mathematical Astronomy Sneaking a Look at God's Cards: October 2004. ISBN 0-691-10301-1. Morsels, by Jean Meeus. Willmann­ Unraveling the Mysteries of Quantum Luck, Logic, and White Lies: The Bell, 2002. ISBN 0-943396-743. Mechanics, by Giancarlo Ghirardi, Mathematics of Games, by Jbrg Musings of the Masters: An An­ translated by Gerald Malsbary. Prince­ Bewersdorff. Translated by David thology of Miscellaneous Reflections, Kramer. A K Peters, November 2004. edited by Raymond G. Ayoub. ton University Press, revised edition, ISBN 1-568-81210-8. Mathematical Association of Amer­ January 2005. ISBN 0-691-12139-7. Math and the Mona Lisa: The Art ica, 2004. ISBN 0-88385-549-6. Spaceland, by Rudy Rucker. Tor and Science of Leonardo da Vinci, by ''New Mexico Mathematics Contest Books, june 2002. ISBN 0-765-30366- Bulent Atalay. Smithsonian Books, Problem Book, by Liong-shin Hahn. 3. (Reviewed August 2005.) April2004. ISBN 1-588-34171-2. University of New Mexico Press, No­ Stalking the Riemann Hypothesis: The Math Instinct: Why You're a vember 2005. ISBN 0-8263-3534-9. The Quest to Find the Hidden Law of Mathematical Genius (Along with Lob­ The Newtonian Moment: Isaac New­ Prime Numbers, by Dan Rockmore. sters, Birds, Cats, and Dogs), by Keith ton and the Making ofModern Culture, Pantheon, April 2005. ISBN 0-375- Devlin. Thunder's Mouth Press, March by Mordechai Feingold. New York 42136-X. 2005. ISBN 1-560-25672-9. Library and Oxford University Press, A Tour through Mathematical Mathematical Adventures for Stu­ December 2004. ISBN 0-195-17735-5. Logic, by Robert S. Wolf. Mathemati­ dents and Amateurs, David F. Hayes Numbers, the Language of Science, cal Association of America, January and Tatiana Shubin, editors. Mathe­ by Tobias Dantzig. Pi Press, fifth edi­ 2005. ISBN 0-88385-036-2. matical Association of America, 2004. tion, March 2005. ISBN 0-131-85627-8. ISBN 0-88385-548-8. The Oxford Murders, by Guillermo The Transformation of Mathemat­ Mathematical Illustrations: A Man­ Martinez. Abacus, January 2005. ISBN ics in the Early Mediterranean World: ual of Geometry and PostScript, by Bill 0-349-11721-7. (Reviewed November From Problems to Equations, by Reviel Casselman. Cambridge University 2005.) Netz. Cambridge University Press, Press, December 2004. ISBN 0-521- The Pea and the Sun: A Mathe­ June 2004. ISBN 0-521-82996-8. 54788-1. matical Paradox, by Leonard M. Using the Mathematics Literature, A Mathematician at the Ballpark: Wapner. A K Peters, April2005. ISBN by Kristine K. Fowler. Marcel Dekker, Odds and Probabilities for Baseball 1-568-81213-2. june 2004. ISBN 0-824-75035-7. Fans, by Ken Ross. Pi Press, July 2004. ''PopCo, by Scarlett Thomas. Har­ The Works of Archimedes: Trans­ ISBN 0-131-47990-3. vest Books, October 2005. ISBN 0-156- lation and Commentary. Volume I: Mathematicians under the Nazis, by 03137-X. (Reviewed in this issue.) The Two Books On the Sphere and Sanford L. Segal. Princeton University Probability Theory: The Logic of The Cylinder. Edited and translated by Press, July 2003. ISBN 0-691-00451-X. Science, by E. T. Jaynes. Edited by G. Reviel Netz. Cambridge University (ReviewedApril2005.) Larry Bretthorst. Cambridge Univer­ Mathematics by Experiment: Plau­ sity Press, April 2003. ISBN 0-521- Press, April2004. ISBN 0-521-66160- sible Reasoning in the 21st Century, by 59271-2. (Reviewed January 2006.) 9. (Reviewed May 2005.) Jonathan Borwein and David Bailey. R. L. Moore: Mathematician and A World without Time: The Forgot­ A K Peters, December 2003. ISBN Teacher, by John Parker. Mathemati­ ten Legacy of Godel and Einstein, by 1-56881-211-6. (Reviewed September cal Association of America, 2004. ISBN Palle Yourgrau. Basic Books, January 2005.) 0-88385-550-X. 2005. ISBN 0-465-09293-4.

FEBRUARY 2006 NOTICES OF THE AMS 257 Doctoral Degrees Conferred 2004-2005

ALABAMA Kwon, Miyeon, A class of operation on Kim, Sangil, Ensemble filtering methods Hardy space in Schatten-von Neumann for nonlinear dynamics. Auburn University (2) class and its properties. Kondrashov, Dmitry, Protein control of a Simmons, Carolyn, A comparison of poly­ ligand: Modeling nitric oxide release in MATHEMATICS AND STATISTICS nomial preconditioners for solving lin­ nitrophorin 4. Das, Kumer, Ruin estimates under inter­ ear systems. Lehovich, Andre, List-mode SPECT recon­ est force. Zhang, Xinjun, A matrix version of corona struction using empirical likelihood. Granado, Michael, On the moving off theorem for algebras of functions on Lu, Yixia, The integrability of second property and weak additivity of local reproducing kernel Hilbert spaces. order nonlinear ordinary differential connectedness and metrizability. equations with Painleve properties and University of Alabama, ARIZONA Lie symmetries. Park, Subok, Signal detection with ran­ Birmingham (3) Arizona State dom backgrounds and random signals. BIOSTATISTICS University (6) Sviercoski, Rosangela, Multiscale ana­ lytical solutions and homogenization Richman, joshua S., Sample entropy MATHEMATICS AND STATISTICS of n-dimensional generalized elliptic statistics. Dueck, Amy/au, Robust imputation in equations. multivariate hierarchical data. MATHEMATICS Gordillo, Luis, Q-Hausdorff summability. Lee, Young-Ran, Spectral properties of Lant, Timothy, Transition kernels, inte­ ARKANSAS a polyharmonic operator with limit­ gral semigroups on spaces of mea­ periodic potential in dimension two. sures, and perturbation by cumulative University of Arkansas, Lesort, Claire, Statistical efficiency and outputs. Fayetteville (3) complexity of curve fitting algorithms. Li, ]iaxu, The dynamics of glucose-insulin endocrine metabolic regulatory system. MATHEMATICAL SCIENCES University of Alabama, Murakami, ]unko, Parameter estimate of Karber, Kristen, Star-shift invariant sub­ Tuscaloosa (10) a hidden Markov chain. spaces of H 2(IlJi). Rahman, Mohammad Mahbuber, Numer­ INFORMATION SYSTEMS, STATISTICS AND Shores, Emily, Regularity theory for weak ical approximations to stochastic dif­ solutions of systems in Carnot groups. MANAGEMENT SCIENCE ferential equations with applications to Singh, Pramod, Fan, Guangzhe, Regression and survival mathematical neurosciences. Decomposition of non­ tree analysis using TARGET. linear operators on Banach lattices. Hong, Bo, Multivariate surveillance schemes University of Arizona (11) for infectious diseases on multiple lo­ MATHEMATICS CALIFORNIA cations. Lozano, Guadalupe, Poisson geometry of Howington, Eric, A genetic algorithm the Ablowitz-Ladik equations. California Institute of for computing the minimum volume ellipsoid estimates. Per/is, Alexander, The projective geom­ Technology (13) etry of curves of genus one, and an Yadav, Prashant, Collaborative forecast­ algorithm for the jacobian of such a APPLIED AND COMPUTATIONAL ing and supply chain coordination. curve. MATHEMATICS Yu, ]ing, Space-time interaction models Shipmar, Patrick, Plant patterns. for mortality data. Stredie, Valentin Gabriel, Mathematical PROGRAM IN APPLIED MATHEMATICS modeling and simulation of aquatic MATHEMATICS and aerial animal locomotion. Alvarez-Sierra, Oliverio, Acoustic reso- Eddins, Melanie, Variation of M/G/1 nance in a cavity under a subsonic Westhead, Andrew, Upscaling for two­ queues with batch services. flow. phase flows in porous media. Gong, Minqing, Waiting time in a com- Frey, Sarah, Characterization of instabil­ Yu, Xinwei, Localized non-blowup condi­ bined first-come-first-served and ities in the problem of elastic planetary tions for 3D incompressible Euler flows shortest-time-first queue. tides. and related equations.

contains the name of the recipient and the thesis title. The number The above list contains the names and thesis titles of recipients of in parentheses following the name of the university is the number of doctoral degrees in the mathematical sciences (July 1, 2004, to June 30, degrees listed for that university. A supplementary list containing names 2005) reported in the 2005 Annual Survey of the Mathematical Sciences by 215 departments in 152 universities in the United States. Each entry received since compilation of this list will appear in a summer 2006 issue of the Notices.

258 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Doctoral Degrees Conferred

CONTROL AND DYNAMICAL SYSTEMS Terentyev, Sergiy, Asymmetric counter­ Sullivant, Seth, Toric ideals in algebraic Bhat, Harish S., Lagrangian averaging, party relations in default modeling. statistics. nonlinear waves, and shock capturing. Wang, Pei, Statistical methods for CGH Tseng, Hsian-Hua, Quantum Riemann­ Del Vecchio, Domitil/a, State estimation array analysis. Rock, Lefschetz and Serre theorems for in multi-agent decision and control Xiaohu, Zhang, Thin blue noise sampling orbifold Gromov-Witten theory. systems. and its application to antialiasing in Van Luijk, Ronald, Rational points on K3 Gregory, Irene, Design and stability analy­ computer graphics. surfaces. sis of an integrated controller for highly Villareal, Oscar, Countable unions of flexible advanced aircraft utilizing the University of California, subvarieties of semiabelian varieties. novel nonlinear dynamic inversion. Berkeley (37) Voight, john, Quadratic forms and quater­ Papachristodoulou, Antonis, Scalable anal­ ilion algebras: Algorithms and arith­ ysis of nonlinear systems using convex BIOSTATISTICS metic. optimization. Neugebauer, Romain, Double robust Yu, Yifeng, Loo variational problems, Prajna, Stephen, Optimization-based estimation of causal parameters in Aronsson equations and weak KAM methods for nonlinear and hybrid sys­ marginal structural models. theory. tems verification. Tai, Yu Chuan, Multivariate empirical Bayes models for replicated microarray STATISTICS MATHEMATICS time course data. Chen, Aiyou, Semiparametric inference Cai, Kaihua, Dispersive property of Xing, Biao, Statistical methods for detect­ for independent component analysis. Schrodinger operators. ing cis-regulatory motifs and construct­ Collin, Francois, Analysis of oligonu­ johnson, Jennifer, Artin L-functions for ing transcriptional regulatory networks. cleotide data with a view to data quality abelian extensions of imaginary quadrat­ assessment. ic fields. MATHEMATICS Hallgrimsdottir, Ingileif, Statistical meth­ Katz, Daniel, On p-adic estimates of Bejenaru, Joan, Quadratic derivative non­ weights in Abelian codes over Galois ods for gene mapping in complex linear Schrodinger equation. diseases. rings. Corn, Patrick, Del Pezzo surfaces and the Nenciu, Irina, Lax pairs for the Ablowitz­ Liang, Gang, Statistical inference in net­ Braner-Marrin obstruction. work tomography. Ladik system via orthogonal polynomi­ Ealy, Clifton, Thorn forking in simple als on the unit circle. Ng, Vivian, Univariate and bivariate vari­ theories and a Manin-Mumford theorem able selection in high dimensional data. Whitehouse, David, The twisted weighted for T-modules. fundamental lemma for the transfer Roginsky, Michael, Modeling of transient Esty, Norah, Orbit structures of groups of automorphic forms from GSp(4) to processes in Markov chains with an GL(4). of homeomorphisms on S 1 . application to the Internet traffic de­ Ghioca, Dragos, The arithmetic of Drin­ scription. Claremont Graduate feld modules. Shi, Tao, Polar cloud detection using University nJ Hall, H. Tracy, Counterexamples in dis­ satellite data with analysis and applica­ crete geometry. tions of kernel learning algorithms. SCHOOL OF MATHEMATICAL SCIENCES Hogan, Apollo, General topology under Zhao, Xiaoyue, Statistical methods for Le, Hieu, Delamination detection in com­ the axiom of determinacy: The beauty elucidating DNA motifs and modules. posite laminates using genetic algo­ of topology without choice. rithm optimization. Kamnitzer, joel, Mirkovic-Vilonen cycles University of California, and polytopes. Davis (9l Stanford University (14l Kirkup, George, Examples of decomposi­ STATISTICS tion of ideals. MATHEMATICS Arias-Castro, Ery, Graphical structures Levin, Aaron, Generalizations of Siegel's Dieng, Momar, Distribution functions for for geometric detection. and Picard's theorems. edge eigenvalues in orthogonal and Bair, Eric, Methods of predicting patient Levy, Dan, Applications of graph theory symplectic ensembles: Painleve repre­ survival based on DNA microarray data. to chromosome rearrangements and sentations. phylogenetics. Chatterjee, Sourav, Concentration in­ ]erdonek, Christopher, The girth of a equalities with exchangeable pairs. Milanov, Todor, Singularity theory and Heegaard splitting. integrable hierarchies. Elkaroui, Noureddine, Extended validity Tamaresis, John, Mathematical modeling of Tracy-Widom limiting law, with sta­ Miranian, Luisa, Matrix valued orthogonal of arterial endothelial cell responsive­ tistical application. polynomials. ness to flow. Finkelman, Matthew, Statistical issues in Nguyen, Nghi, Whitney theorems and computerized adaptive testing. Lefschetz pencils over finite fields. STATISTICS Hooker, Giles, Diagnostics and extrapola­ Pribik, Peter, Integrable soliton hierar­ Branscum, Adam, Bayesian nonparamet­ tion in machine learning. chies for so&d14, 2n via intertwining ric and semiparametric inferences for Liu, Ruixue, New findings of functional operators. disease risk and ROC curves. ANOVA with applications to computa­ Roberts, Lawrence, Heegaard-Floer ho­ Cui, Jiang, Regularized estimation in the tional finance and statistics. mology and d-based links in three high-dimension and low-sample size Paul, Debashis, Nonparametric estima­ manifolds. settings with applications to genomic tion of principal components. Shvets, Yelena, Problems of flooding in data. Peng, ]ie, Score statistics to map genes in porous and fissured porous rock. Last, Michael, Detecting abrupt changes humans. Siegel, Aaron, Loopy games and compu­ in time-varying power spectra. Qing Feng, Zhang, A basis function tation. Tseng, Yi-Kuan, Joint modelling of time­ approach to interest rate derivative Sinton, Andrew, The spherical trans­ to-event and longitudinal data. valuation. form on projective limits of symmetric Wai, Newton, Change trees and muta­ Stone, Eric, Statistical advances in inter­ spaces. grams for the visualization of local specific data analysis. Speyer, David, Tropical geometry. changes in sequence data.

FEBRUARY 2006 NOTICES OF THE AMS · 259 Doctoral Degrees Conferred

Zhou, Lei, A new expression index based Yu, Tianwei, Study of the transcription Zhang, Yu, Global and local multiple on the generalized logarithm and differ­ regulation in Saccharomyces cerevisiae. sequence alignment by an Eulerian path ential expression analysis of affymetrix approach. GeneChip arrays. University of California, Riverside (5) University of California, COLORADO MATHEMATICS Los Angeles (24) Carrion-Alvarez, Miguel, Loop quantiza­ Colorado School of MATHEMATICS tion versus Fock quantization of p-form Mines (3) Bene, Alex, Intersections of cycles in the electromagnetism on static spacetimes. combinatorial moduli space. Chung, ]ae-Wook, The algebraic structure MATHEMATICS AND COMPUTER SCIENCES of n-punctured ball tangles. Biswas, Kingshook, On the geometry of Abushama, Abeer, Modified nodal cubic hedgehogs and log-Riemann surfaces. Culhan, Dustin, Associated primes and primal decomposition in modules and spline collocation for Poisson's and bi­ Caston, Laurent, Super Lie groups, their harmonic equations in the unit square. actions and applications. lattice modules, and their duals. Overholser, Eric, Boundary behavior of Feng, Yan, Interactive floorplanning in Chung, Tsz Shun Eric, Finite volume and VLSI. discontinuous Galerkin methods for an infinitesimal metric and intrinsic the numerical approximation of wave measure on domains and moduli space. Hayes, Timothy, Multiple choice program­ ming. propagation problems. STATISTICS Cotta, Brian, Numerical methods for stiff reaction-diffusion equations with Chu, Li Ping, Robustness of the respon- Colorado State applications to cardiological modeling. dents-generated interval. University (3) Garibaldi, Julia, Erdos distance problem University of California, MATHEMATICS in other convex metrics. San Diego (8) ]ones, Nathan, Almost all elliptic curves Grande, Beau, Time-stepper based nu­ are Serre curves. MATHEMATICS merical bifurcation analysis: An appli­ cation to the Taylor-Couette problem. Kostadinov, Boyan, The Picard-Fuchs Donohue, Michael, Rank regression and equation and its monodromy for a synergy assessment. STATISTICS family of Calabi-Yau hypersurfaces in Ericksen, Stefan, New settings of the first cpN-1_ order Stark conjectures. Gilleland, Eric, Statistical models for Lee, Sunmi, Artificial boundary condi­ Griffin, Joshua D., Interior-point methods quantifying the spatial distribution of tions for linear elasticity and atomistic for large-scale nonconvex optimization. seasonally derived ozone standards. strain models. Hazel, Graham P., Triangulating Teich­ Hess, Ann, Models and methods for the Li, Xiaosheng, Inverse scattering problem mtiller spaces using the Ricci flow. analysis of microarray data: Before and for system of differential operators. Juhlin, Robert, Normal forms and conver­ after the fold change calculation. Mocanasu, Mona, Borel-Moore homology gence of formal CR mappings. and algebraic oriented theories. Shaheen, Anthony M., Finite planes and University of Colorado, Molnar, Stephanie, Sharp growth esti­ finite upper half planes: Their geometry, Boulder (15) mates for T(b) theorems. a trace formula, modular forms, and APPLIED MATHEMATICS Nguyen, Lan, The Ramanujan conjecture Eisenstein series. for Hilbert modular forms. Suaray, Kagba, On kernel density esti­ Burrell, Neil, Merger and alignment Peng, Pan, Integrality structure in the mation for censored data. of three-dimensional quasigeostrophic Gromov-Witten theory. Yu, Li, Superalgebraic interpretation of vortices. Soderlund, Christina, Characterizing fixed quantization maps of Weil algebras. Carvalho, Marcio, Applying perfect sim­ point sets of maps homotopic to a given ulation to solve stochastic difference map. University of California, equations that arise from certain time Somogyi, Zoltan, Stability of an imploding Santa Barbara (5) series models. spherical wave in a van der Waals gas. MATHEMATICS Hwang, Feng-Nan, Some parallel linear Staecker, Peter Christopher, The Reide­ and nonlinear Schwarz methods and meister trace: Computation by nilpotent­ Delp, Kelly, Almost periodic flows on applications in computational fluid dy­ ization and extension to coincidence 3-manifolds. namics. theory. Lyons, William, Fast algorithms with Maclachlan, Scott, Improving robustness applications to PDEs. Tornquist, Asger, The Borel complexity of in multiscale methods. Miller, Jeffrey, A 3rd order accurate pos­ orbit equivalence. Mullowney, Paul, Lagrangian particle itive scheme for hyperbolic systems of transport/mixing in roll switching sys­ Virdol, Cristian, Zeta functions of twisted conservation laws in multi-dimensions. quaternionic Shimura varieties. tems. Wills, Michael, Extension of spectral Weisbart, David, Schrodinger operators scales to unbounded operators. Petersen, Mark, A study of geophysi­ with matrix potentials and convergence cal and astrophysical turbulence using of quantum systems on grids. STATISTICS AND APPLIED PROBABILITY reduced equations. Yakes, Christopher, Composition opera­ Kulkarni, Priya, Bootstrap methods for Roehrle, Oliver, Multilevel first order tors on L-domains. time series. system least squares for quasi-linear Yip, Andy Ming Ham, Mathematical mod­ elliptic partial differential equations. els for data clustering. University of Southern Tearle, Matthew, Optimal perturbation (2) analysis of stratified shear flow. STATISTICS California Thaler, Eric, An evaluation of the opera­ Tranbarger, Katherine, Point process MATHEMATICS tional use of numerical solutions to the prototypes and other applications of Wan, Xuhu, Dynamic principal-agent quasigeostrophic diagnostic equations point processes distance metrics. problem in continuous time. by weather forecasters.

260 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Doctoral Degrees Conferred

Vadlamani, Srinath, An algorithmic unifi­ Wesleyan University (5) Makhlouf, Fairouz, Regional scores for cation of particle-in-cell and continuum localizing genes. MATHEMATICS AND COMPUTER SCIENCE methods and a wave particle descrip­ Rishmawi, Shireen, Fitting concentration tion for the electron temperature gradi­ Coe, Russell, Variational principles for data with stable distributions. ent (ETG) instability saturation. relative d-bar pressure. Safi, Samir, The efficiency of OLS in Westphal, Chad, First-order system least Krishnan, Ayalur, Universal quantifiers the presence of auto-correlated distur­ squares for geometrically-nonlinear elas­ in logic programming via indexed cate­ bances in regression models. ticity in nonsmooth domains. gories. Rokicki, Anna, Finiteness results for George Washington MATHEMATICS definite ry-regular and almost ry-regular University (2) Brown, Christopher, Connectedness and Hermitian forms. reflections in symmetry algebras of Roychowdhury, Mrinal, Finitary orbit MATHEMATICS differential equations. equivalence. Togha, Ataollah, On automorphisms of Cohen, Robert, Construction of an order Wynne, Brian, Continuous functions on structures in logic and orderability of theoretic duality for certain groups. essential P-spaces: A model-theoretic groups in topology. Horne, jennifer Anne, Cardinal functions analysis of some non-projectable lattice­ on pseudo-tree algebras, and a general­ ordered groups. STATISTICS ization of homogeneous weak density. George, Barbara jane, Bayesian regres­ Yale University (6) McAlister, Erich, Noncommutative CW­ sion for circular data. complexes arising from crystallographic BIOSTATISTICS DIVISION (3) groups and their K-theory. Buenconsejo-Sinfuego, joan, A Bayesian Howard University hierarchical model for estimation of MATHEMATICS University of Colorado, disease incidence using two surveil­ lance datasets. Farrier, Sandra, Fixed point and ergodic Denver (2) theorems for nonexpansive mappings Duan, Fenghai, Analysis of microarray on ultrametric Banach spaces. MATHEMATICS data. Syafrida, An approach to approximation Busch, Arthur, III, Feng, Rui, A latent variable model for Arc-traceable tourna­ of (0, q) meromorphic forms on a stem ments. ordinal traits. manifold. Stewart, Dustin, Domination and matrix Liu, Nianjun, Statistical methods for haplotype analysis in genetic studies. Tankersley, Barbara, Some algebraic and properties in tournaments and general­ combinatorial interpretations of lower ized tournaments. Wu, Yu- Te, Detecting rare adverse events triangular matrices from the Hankeliza­ in post-marketing studies: Sample size tion of sequences. University of Northern considerations. Colorado nl STATISTICS FLORIDA MATHEMATICAL SCIENCES Valaitis, Eduardas, Testing the biomodal­ ity of normal mixtures. Duvall, Sally, Students' concept images of Florida Institute of parameters in a multi-representational Technology

Edwards, Heather, Measures of concor­ MATHEMATICS AND COMPUTER SCIENCE University of Idaho (2l dance of polynomial type. Garten, Heather, Satellite graphs. MATHEMATICS Masino, Aaron, Wave structure function and temporal frequency in weak to Schmitt, john, On potentially P-graphic Abdo, Zaid, Computationally intensive strong optical turbulence. degree sequences and saturated graphs. methods for choosing, assessing and validating statistical models describing Salman-Mohamed, Mohamed, Utilization Siggers, Mark, Hypergraph packings and Galois cohomology. polymorphism, with applications in of total mass as a control in diffusion population genetics, phylogenetics and processes. Wilson, Ulrica, Cyclicity of division alge­ microbial ecology. bras over an arithmetically nice field. Sampson, Koffi, Structured coalescent University of Florida (lOl Georgia Institute of with nonconservative migration. MATHEMATICS Technology (2l Huang, Feng, Applications of variational ILLINOIS PDE models in medical image process­ SCHOOL OF MATHEMATICS Illinois State University (Sl ing. Sammer, Marcus, A transportation ap­ Huang, Shu-]en, Multiscale discretization proach to the concentration of measure. MATHEMATICS of electric-field equations. Song, Zixia, The extremal function for K 9 Adeyemi, Cheryl, Semiotic chaining: Pre­ Sheu, Yuan-Chyuan, Partition properties minors. service teacher beliefs and instructional and Halpern-Lauchli theorem on the practices. cmin forcing. University of Georgia noJ Carter, john, Effects of lesson study Smith, Rebecca, Combinatorial algorithms on the beliefs and practices of novice involving pattern containing and avoid­ MATHEMATICS mathematics teachers. ing permutations. Almeida, Paulo, Sign changes of error Seidelmann, A ntoinette, Students' con­ Warren, Daniel, Optimizing the pack­ terms related to certain arithmetic ceptions of zero. ing behavior of layered permutation functions. Tomas Ferreira, Rosa, Portuguese mathe­ patterns. Blair, ]ames, On the embedding of trian­ matics student teachers' evolving teach­ gles into integer lattices. ing models: A modified teacher devel­ STATISTICS opment experiment. Gwena, Tawanda, Degenerations of Prym Yu, Paul, Prototype development and dis­ Hitchcock, David, Smoothing functional varieties and cubic threefolds. course among middle school students data for cluster analysis. Matthews, Graham, Computing genera­ in a dynamic geometry environment. Klingenberg, Bernhard, Regression mod­ tors and relations for matrix algebras. els for discrete time series data. Nash, Milton, Special values of Hur­ Northern Illinois Marchev, Dobrin, Monte Carlo methods witz zeta functions and Dirichlet L­ University (2) for posterior distributions associated functions. MATHEMATICAL SCIENCES with multivariate student's t data. Pooh, Charles, Capacity theory and alge­ Sinha, Karabi, Some contributions to braic integers. Fowler, Kari, Normal functions, the MacLane class and complex differen­ small area estimation. Shumbusho, Rene-Michel, Elliptic curves tial equations in the unit disc. Sinha, Samiran, Bayesian inference for with prime conductor and a conjecture matched case-control studies. of Cremona. Haertze n, Kevin, Geometric aspects of Sturm-Liouville problems. University of South STATISTICS Northwestern (3) Florida Jiang, Yan, Semiparametric ANCOVA us­ University (9) ing shape restrictions. MATHEMATICS Yang, Ying, Nonparametric Bayesian in­ ENGINEERING SCIENCE AND APPLIED Chen, Zhao, Bayesian and empirical Bayes ference in biostatistics. MATHEMATICS on power law process and microarray Zhang, Zhengang, Marginal models for Comissiong, Donna, A stability analysis analysis. zero-inflated clustered data. of polymerization fronts. Mahalingam, Kalpana, Involution codes: Norman, Catherine, A level set method With application to DNA strand design. to numerically determine the dynamics Tookos, Ferenc, Holder continuity of HAWAII of gas bubbles in inclined channels. Green's functions. MATHEMATICS University of Hawaii (2l Chen, ]un, Transonic shocks and gas GEORGIA MATHEMATICS dynamics. Cheng, Xuezhi, Transferring Coo-structures. Seffrood, ]iajia, Non-Desarguesian planes. Emory University (?l Clay, Lisa, Some conjectures about the Xiong, ]ianfei, Some topics on geometry slopes of modular forms. and singularities. BIOSTATISTICS Kim, Young-Heon, Holomorphic exten­ sions of Laplacians and their determi­ Chen, Ying, Evaluation of a diagnostic test nants. with partially missing gold standard IDAHO information based on the test ignorance Saghin, Radu, Generic properties of La­ region. grangian systems and conservative dif­ Idaho State University nl feomorphisms. Guo, Ying, Assessing agreement for sur­ Yang, Zaiyong, Laminations and connect- vival outcomes. MATHEMATICS ing orbits on lattice. · Yang, Yang, Design and analysis of Moon, Bonnie, Radius of injectivity for a Zhu, Dianwen, Euler equations and steady infectious disease intervention trials. quarter plane. supersonic flows.

262 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Doctoral Degrees Conferred

University of Chicago (16) Wang, Yusong, Computing dynamic out­ INDIANA put feedback laws with Pieri homo­ MATHEMATICS topies on a parallel computer. Indiana University, Barakat, Aliaa, On the moduli space of Yan, Xu, Optimal designs in stability Bloomington (12) deformations of bihamiltonian hierar­ studies. chies of hydrodynamic type. Yao, Haishen, Asymptotic analysis of the MATHEMATICS Cherkashin, Dmitriy, Perception game. infinite server shortest queue problems. Carter, Nathan, Logics that prove their Dani, Pallavi, Statistical properties of own completeness. elements in infinite groups. University of Illinois, Cheskidov, Alexey, The Navier-Stokes­ Draganescu, Andrei, Two investigations Urbana-Champaign (22) alpha model and boundary-layer turbu­ in numerical analysis: Monotonicity pre­ lence. serving finite element methods and MATHEMATICS Ellett, Andrew, Portfolio management multigrid methods for inverse para­ Chan, Song Heng, On cranks partitions, toward optimal consumption and ter­ bolic problems. generalized Lambert series, and basic minal wealth. Duchin, Moon, Geodesics track random hypergeometric series. Gu, Wentao, Fixed design regression for walks in Teichmiiller space. David, Murphy, Equivariant embeddings associated random fields. Fedorov, Roman, Algebraic and Hamil­ of algebraic groups. Himpel, Benjamin, A splitting formula for tonian approaches to isostokes defor­ Demeter, Ciprian, Qualitative and quan­ spectral flow on closed 3-manifolds. mations. titative analysis of weighted ergodic Im, Bo-Hae, The rank of elliptic curves Leyenson, Maxim, On some questions of theorems. over large fi elds. the Brill-Noether theory for K3 surfaces. Galway, William Floyd, Analytic compu­ Kong, Maiying, Nonparametric statistical Ogilvie, David, Isomorphisms of Heeke tation of the prime-counting function. techniques in bioassay. algebras and deformation rings in the Giarlotta, Alfio, Lexiographic products of Kudzin, Matthew, Cohomogeneity one function field case. linear orderings. manifolds of non-negative curvature. Pereira, Rochelle, Higher order cohomol­ Groisman, Pavel, New family of constant Martinez, Maricarmen, Common sense ogy operations and minimal atomicity. mean curvature surfaces with non­ reasoning via product state spaces. Spice, Loren, Supercuspidal characters of coplanar ends. Mersch, John, Equational logic of recur­ SL1 over a p-adic field, l a prime. Hahn, Heekyoung, Einstein series, ana­ sive program schemes. Toumpakari, Eve/in, On the abelian sand­ logues of the Roger-Ramanujan func­ Qian, Lei, Message dependence and for­ pile model. tions, and partitions identities. mal verification of authentication pro­ Winn, Brandy, Traveling fronts in a ]egdic, Katarina, Analysis of spacetime tocols. reactive Boussinesq system: Bounds discontinuous Galerkin method for sys­ Wen, Su-Chi, Hyperbolic extensions of and stability. tems of conservation laws. algebras with involution. STATISTICS Kang, Jeong Hyun, Coloring of metric spaces and L(2, 1)-labeling of graphs. Purdue University (20l Clifford, David, The nature of spatial variation in crop yields. Kulosman, Hamid, Ideals of linear type MATHEMATICS and c-sequences. Min, Wanli, Inferences on time series Butske, William, Computational aspects of driven by dependent innovations. Mileti, Joseph, Partition relations and the endomorphism ring of the Jacobian computability theory. Sen, Rituparna, Modeling the stock price of a curve of genus two. process as a continuous time jump Nakprasit, Kittikorn, Coloring and pack­ Enoch, Ruth, Formal power series solu­ process. ing problems ford-degenerate graph. tions for Schroeder's equation in several Tong, Liping, Statistical inference for Petracovici, Boris, Analysis of a space­ complex variables. multi-color optical mapping data. time discontinuous Galerkin method Glotov, Dmitry, Current and vortices in for elastodynamics. the three-dimensional thin-film Ginzburg­ University of Illinois, Petrenko, Bogdan, Primitive elements in Landau model of superconductivity. finite fields. Chicago (10) Gower, Jason, Square form factorization. Sa no, Akira, The geometry of finite lattice Mangasuli, Anandateertha, Eigenvalues MATHEMATICS, STATISTICS AND varieties over Witt vectors. of the Laplacian for certain Riemannian COMPUTER SCIENCE Selvakumaran, T. V., Morita stable equiv­ metrics on 5 2 and 5 3 . Booton, Barry, Norm inequalities for alence of certain algebras. Oh, Byung-Geun, Curvature and hyper­ certain classes of functions and their Shebalov, Sergey, Polyhedra study of bolicity of surfaces. Fourier transforms. mixed integer programs with variable Rogers, Mark, The index of reducibility Chang, Li, Statistical analysis of high upper bounds. of parameter ideals. frequency intraday security prices. Wong, Kittipat, Intrinsic ultracontractivity Sun, ]ianzhong, Long-time limit for the Chen, ]ian, Growth rates with paths, and other properties of mixed barrier Ginzburg-Landau system with pinning. non-commuting loops and Thurston's Brownian motion. Veliche, Dana, Homological dimensions compactness theorem. Yesi/yurt, Hamza, Contributions to theory for modules and complexes. Ding, ]unfeng, Efficient association ruling of Q-series and mock theta functions. Veliche, Razvan, Some results on funda­ mining among infrequent items. mental groups of Kahler manifolds. STATISTICS Radin, Dale, Unidimensional Zariski­ Ward, Mark, Analysis of an error resilient type structures and applications to Georgescu, Constantin, Finite population Lempel-Ziv algorithm via suffix trees. the model theory of compact complex quantile estimators. spaces. Wei, Ying, Longitudinal growth charts STATISTICS Takata, Ken, Listing algorithms for com­ based on the semiparametric quantile Chakrabarti, Arijit, Model selection for binatorial objects and related combina­ regression. high dimensional problems with appli­ torial problems. Xu, Xueli, Computerized adaptive testing cations to function estimation. Unlu, Fatih, On explicit representations and equating methods with nonpara­ Collevecchio, Andrea, Limit theorems for of the Grothendieck fundamental class. metric IRT models. reinforced random walks on trees.

FEBRUARY 2006 NOTICES OF THE AMS 263 Doctoral Degrees Conferred

Florescu, Ionut, Stochastic volatility stock STATISTICS STATISTICS price-coefficient estimation and option Ferraz, Cristiano, Sample design for qual­ Perrett, ]amis, Using information on the pricing using a recombining tree and ity monitoring and measurement error intra-class correlation coefficient for sharp estimation of the almost-sure evaluation of large-scale longitudinal hypothesis testing in unreplicated and Lyapunov exponent for the Anderson surveys. under-replicated experiments. model in continuous space. Furukawa, Kyoji, Development of Markov Jiang, Hongmei, A two-step procedure Sy, Oumar, Multilevel mediation analysis: random field models based on expo­ Applications and estimation. for multiple pairwise comparisons in nential family conditional distributions. microarray experiments. University of Kansas (2) Liu, Yali, Incorporating time-dependent Landes, Reid, Statistical methods for application to calibration problems. covariate in the Cox proportional haz­ MATHEMATICS ards models: The LV AR approach. Sun, Shuxia, Bootstrapping the sample Caviglia, Giulio, Koszul algebras, Castel­ Qin, Yu, A study of random field models quantile based on weakly dependent observations. nuovo-Mumford regularity and generic in fitting unspecified data generating initial ideals. processes: Theory and applications. Zhang, Zhongqi, Statistical analysis of Epstein, Neil, Closure operators in com­ Sea, ]eonggang, Some classical and gene expression profiles. mutative algebra: Tight closure, phan­ Bayesian nonparametric regression meth­ ods in a longitudinal marginal model. University of Iowa Cl3) tom depth, and *-spread. Stevens, john, Meta-analytic approaches APPLIED MATHEMATICAL AND Wichita State University C2l for microarray data. COMPUTATIONAL SCIENCES MATHEMATICS AND STATISTICS Vitek, Olga, An inferential approach to Boston, Viorel, A posteriori error analysis protein backbone nuclear magnetic res­ and adaptive finite element solution of Bunck, Benjamin, Fast pseudospectral al­ onance assignment. variational inequalities of the second gorithms for boundary value problems University of Notre kind. for the Laplace equation on a rectangle. Del Valle, Sara, Effects of behavioral Treinen, Ray, A study of floating drops. Dame C7J changes and mixing patterns in mathe­ MATHEMATICS matical models for smallpox epidemics. KENTUCKY Bergner, julia, Three models for the Han, Xiaoxu, Local Z buffer algorithms homotopy theory of homotopy theories. in real time rendering of large complex University of Kentucky csJ Calvert, Wesley, Algebraic structure and systems. computable structure. Zhang, Li, The P-hub center allocation MATHEMATICS problem and Q-upgrading arc problem. Heidenreich, jacob, Stability theory mod­ Dobranski, Michael, Construction of ex­ ulo a predicate. BIOSTATISTICS ponentially growing solutions to first­ Hubbard, Keith, The notion of vertex order systems with non-local potentials. Yang, Xinqun, The posterior probability operator coalgebra: A construction and Elliott, Steve, Simple homotopy theory for geometric characterization. of linkage allowing for linkage dis­ equilibrium and a new estimate of cell complexes. jackson, Daniel, Birational maps of sur­ disequilibrium between a trait and a Hoffnung, Leonard, Subspace projection faces with invariant curves. marker. methods for the quadratic eigenvalue Maican, Mario, Vector bundles of finite problem. order on affine manifolds. MATHEMATICS Noble, Leigh, Recovery of through-thick­ Markert, Elke, Connective 1-dimensional Dutkay, Dorin, Wavelet representations. ness texture profiles in orthorhombic euclidean field theories. Farthing, Cynthia, C* -algebras of higher- sheets of cubic metals. rank graphs: Desingularization and Ragland, Matthew, On generalizations of IOWA groupoid methods. groups in which normality is a transitive Hong, Doojin, Spectra of higher spin position. Iowa State University C14l operators. Sharrow Pinzon, Kathrine, Absolutely MATHEMATICS Hou, Xiaojie, Traveling wave solutions of pure modules. Aydinyan, Ruben, Loop transversal codes the nonlinear diffusion-reaction equa­ Stepp, Elizabeth, Large Whitney levels and over finite rings. tion. finite antichains. Babyonyshev, Sergei, Metatheories of de­ Marrero, Alberto, A groupoid approach Wesley, Molly, Torsion free covers of ductive systems. to ultragraph C*-algebras. graded and filtered modules. Bhatt, Chan, Nonseparable multivariate Stuffelbeam, Ryan, The theta correspon­ wavelets. dences for U(1) and the quasi-split LOUISIANA Campbell, ]essie, Enumeration and sym­ U(2). metry of edit metric spaces. Winders, Michael,. Idealization. Louisiana State Kim, Eun-Youn, Analysis of game playing agents with fingerprint. STATISTICS AND ACTUARIAL SCIENCE University C7J Kiounge, Benard, Sedenion extension Kim, Chulmin, Unconstrained models for MATHEMATICS loops and frames of hypercomplex the covariance structure of multivariate Ionita, Coste/, Class groups and norms of 2n-ons. longitudinal data. units. Maxwell, Mandi, Almost perfect nonlinear functions and related combinatorial KANSAS johansen, Troels, Orbit structure on the structures. Silov boundary of a tube domain and the Plancherel decomposition of a causally Mutungi, Patrick, Simple ternary complex Kansas State University C3J compact symmetric space, with empha­ Grassman algebras. MATHEMATICS sis on the rank one case. Wangsness, Amy, The matrix completion Kovacs, Mihaly, On qualitative properties problem regarding various classes of Kim, Sang Hyun, On the structure of and convergence of time-discretization Po,r -matrices. finite AW* -algebras. methods for semigroups.

264 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Doctoral Degrees Conferred

Mihai, Claudiu, Asymptotic Laplace trans­ Jiang, Xiaoou, Single-point and complete MATHEMATICS forms. quenching for degenerate semilinear Krebs, Michael, Toledo invariants in 2- Mihai, Vochita, The Radon-Gauss trans­ parabolic first initial-boundary value orbifolds. form. problems. Lee, Eun K., On certain cohomological Ortiz, Norma, Dynamical systems with Kim, Mihye, Hybrid interval march­ invariants of algebraic number fields. time delay. ing/branch and bound method for Tinaglia, Giuseppe, Multi-valued graphs parametrized nonlinear systems. Rios, Vinicio, Dissipative Lipschitz dy­ in embedded constant mean curvature namics. Melton, Tanya, The generalized quasilin­ disks. earization method and higher order of louisiana Technical convergence for nonlinear problems. University of Maryland, (8) University West, Janna, Monotone iterative method Baltimore County (8) MATHEMATICS AND STATISTICS PROGRAJvl for nonlinear problems. MATHEMATICS AND STATISTICS Feng, Zongwen, Modeling of solid layer Yang, ]ie, Generalized iterative and faster Hang, Yarning, Statistical analysis of two­ growth at a constant speed in a binary convergence methods for nonlinear dy­ dimensional electrophoresis gel images. melt crystallization process. namical systems. Korostyshevskiy, Valeriy, A Hermite spec­ Gao, Wenzhi, Intelligent control of non­ Yu, ]ianQi, Inference on the difference tral approach to homoclinic solutions linear systems with actuator saturation between two normal means vectors: using neural networks. Complete and missing data cases. of ODEs. Hughes, joshua, Obstruction sets for Liu, Xing, Interior point methods for classes of cubic graphs. sufficient LCPs and their applications in bioinformatics. Lan, Hong, Integrated modeling and MARYLAND parallel computation of laser-induced Paul, Gitanjali, P-values for testing in­ axisymmetric rod growth. dividual bioequivalence and variance Johns Hopkins bioequivalence. Su, Shengjun, Numerical simulation of University (16) nanapulse penetration of biological Tao, ]iyuan, Some P-properties for linear transformations on the Lorentz cone. matter using the Z-transform. APPLIED MATHEMATICS AND STATISTICS Tymofyeyev, Yevgen, Yu, Haofeng, A high-order finite dif­ Optimal allocation ference method for solving bioheat Castello, Beryl, Semi-obnoxious multi­ for multiarmed clinical trials. transfer equations in three dimensional facility location problems: Models and Zhang, ]ialu, Prediction model selection: triple-layered skin structure. methods. Correlated data and CART. Zhang, Le, A numerical method for ob­ Ceyhan, Elvan, An investigation of prox­ Zhang, Yanqiong, Sequential monitoring taining an optimal temperature distri­ imity catch digraphs in Delaunay tes­ for randomization tests. bution on 3D triple-layered cylindrical sellations. skin structure. john, Majnu, A data-adaptive methodol­ University of Maryland, Zheng, Bin, Computational approaches to ogy for finding the optimal weighted College Park (21) the design and analysis of stability of generalized Mann-Whitney-Wilcoxon polypeptide multilayer thin films. statistic. MATHEMATICS May, William, Computational improve­ Abbiw-]ackson, Roselyn, Discrete opti­ Tulane University (6l ments in the substitution method for mization models in data visualization. BIOSTATISTICS bounding percolation thresholds. Al-Khal, ]awad, New examples of S unimodal maps with a sigma-finite ab­ Wu, Xiaoling, Some statistical and compu­ Broyles, Stephanie, Addressing missing solutely continuous invariant measure. data in public health: An empirical tational problems in pedigree linkage. Cheng, Yang, Maximum likelihood esti­ comparison of strategies. BIOSTATISTICS mation and computation in a random Diaz, Rafael, Power and bias analyzing effect factor model. the logistic normal likelihood ratio test. Choi, Leena, Modeling biomedical data Cohen Freue, Gabriela, On robustness in Lin, Hui-Yi, A comparison of goodness­ and the foundations of bioequivalence. some extended regression models. of-fit tests for binomial generalized estimating equations models. Griswold, Michael, Complex distributions, Dai, Shibin, Universal bounds on coars­ hmmmm... hierarchical mixtures of ening rates for some models of phase Sabel-Soteres, Allison, Missing data tech­ marginalized multilevel models. transitions. niques with Likert scales: An imputation study. Uu, Dongmei, Application of hierarchical Frommer, Ian, Modeling and optimization of transmission networks. Shafer, Leigh Anne, Comparison of meth­ models in microarray data analysis. ods in regression analysis with longitu­ Robinson, john, A hierarchical multi­ Gagnon, Richard, Certain computational dinal data: A simulation study. variate two-part model for profil­ aspects of power efficiency and of state space models. Xin, Xue, Performance assessment of ing providers' effects on healthcare shrinkage estimators for prediction in charges. Gomez, Hector, Binormal motion of curves and surfaces in a manifold. multiple regression with future random Shardell, Michelle, The analysis of in­ X. formatively coarsened discrete time-to­ Jiang, Xiaoping, Nonparametric quasi­ event data. likelihood in longitudinal data. Kalb, Virginia, University of louisiana at Varadhan, Ravi, The role of the design, Low-dimensional models lafayette (8l analysis, and computation in address­ for fluid flow. ing aetiology in three types of studies Kebo, Andrew, Quantum detection and MATHEMATICS in public health. finite frames. Cai, Yang, Improved inferential methods Wu, Zhijin, Probe level models for DNA Lance, Ryan, Network state estimation for some discrete distributions. microarrays. via passive traffic marketing. Hu, Shuhua, Structured population mod­ Uu, Kexue, Nonlinear evolutionary PDEs els: Well-posedness, approximation and Zhou, Hongling, Change point problems in image processing and computer parameter estimation. in generalized linear models. vision. fEBRUARY 2006 NOTICES OF THE AMS 265 Doctoral Degrees Conferred

Malekpour, Shirin, Predicate product Harvard University (26) Zheng, Lu (Summer), Contributions to logic and embeddings of ordered analysis of randomized multi-center abelian group. BIOSTATISTICS clinical trials: The role of conditioning. Rapatski, Brandy, The non-linear trans­ Christensen, jared, Likelihood methods Zhong, Sheng (Richard), Computational mission dynamics of HIV I AIDS. for clustered discrete and continuous and statistical approaches to study Ren, Huaizhong, Autonomous stochastic outcomes in developmental toxicology. gene regulation and gene function. Cook, Andrea, perturbations of Hamiltonian systems. Detecting spatial cluster­ ENGINEERING AND APPLIED SCIENCES Restrepo, juan, Synchronization in net­ ing for discrete, censored, or longitudi­ works of coupled oscillators. nal outcomes. Kirsanov, Danil, Minimal discrete curves and surfaces. Schafer, farad, Borcherds forms and Fang, Xuemin, Probe-level microarray generalizations of singular moduli. analyses: A random effect model to Lauga, Eric, Slip, swim, mix, pack: Fluid estimate cross-hybridization in expres­ mechanics at the micron scale. Trehan, Amit, Lifting of characters and Nickerson, ]ill, Reference specification in orbital integrals on metaplectic groups. sion index computation. Graham, Dionne, Statistical methods for multilingual document production. Yang, Zhihui, Exit problems and stochas­ the analysis of HIV drug-resistance Rusnak, john, ]r., The design structure tic resonance for a class of random data. analysis system: A tool to analyze perturbations. ]emiai, Yannis, Semiparametric meth­ software architecture. Yen, ]u-Yi, Multivariate Levy processes Volpe, Anthony, Modeling flexible supply for financial returns. ods for inferring treatment effects on outcomes defined only if a post­ options for risk-adjusted performance randomization event occurs. evaluation. MASSACHUSETTS Kao, Ming-Chih, Computational and sta­ Weber, Griffin, Data representation and tistical approaches to the study of the algorithms for biomedical informatics applications. Boston University (8) genetic bases of human diseases. Kim, Ryung Suk, Microarray analysis: MATHEMATICS AND STATISTICS Choice of metric, new clustering algo­ Massachusetts Institute of Technology (30) Kary, Michael, Evenness and its applica­ rithm and identification of transcription tions. factors. MATHEMATICS Leon, Larry, Robust inference and model Look, Daniel, Singular perturbations of Boulet, Cilanne, Partition identity bijec­ complex polynomials and circle inver­ checking techniques for censored linear regression models. tions related to sign-balance and rank. sion maps. Caines, Ian, Lin, Ming, Statistical methods in SNP­ New examples of four di­ Lozano-Robledo, Alvaro, On elliptic units mensional AS-regular algebras. and p-adic Galois representations at­ array-based loss-of-heterozygosity stud­ ies. Charbonneau, Benoit, Analytic aspects of tached to elliptic curves. periodic instantons. Litman, Heather, Estimation of marginal Mencattini, Igor, The structures of inser­ Ching, Michael, Bar constructions for tion elimination Lie algebra. regression models with multiple source predictors. topological operads and the Goodwillie Paso/, Vicentiu, p-adic modular symbols derivatives of the identity. attached to C.M. forms. Loecke, David, Mixed effects mean score method, optimal design for two-stage Choi, ]aehyuk, Transport-limited aggre­ Shor, Caleb, On towers of function fields longitudinal studies in a GEE frame­ gation and dense granular flow. and the construction of the correspond­ work, and addition of covariates to De Silva, Daniela, Existence and regu­ ing Goppa codes. a Markov model approach for char­ larity of monotone solutions to a free Stoev, Stilian, Stable self-similar and acterizing progression of HIV genetic boundary problem. locally self-similar random processes: mutations. Dolgushev, Vasil/y, A proof of Tsygan's Stochastic properties, parameter esti­ Martin, Emily, Survival analysis under formality conjecture for an arbitrary mation and simulation. dependent truncation of failure time. smooth manifold. Zagaris, Antonios, Analysis of reduction Matthews, Abigail, Analysis of family Dong, Yu-An, Statistical analysis of pro­ methods for multiscale problems. studies of disease. tein interaction network topology. Douglas, Christopher, Twisted stable ho­ Page, john, Doubly robust estimation: motopy theory. Boston University School Structural nested cumulative failure of Public Health (2) time models, correction of the diag­ Francisco, Sandra, Symplectic isotopy for nostic likelihood ratio for verification cuspidal curves. BIOSTATISTICS bias. Guth, Lawrence, Area-contracting maps Leip, Eric, Adapting a method for ap­ Shubina, Maria, On maximum attainable between rectangles. plying the Cox proportional hazards correlation for the Sarmanov family of Hajiaghayi, Mohammad Taghi, The bidi­ model when the change time of a bi­ bivariate distributions, Bayesian analy­ mensionality theory and its algorithmic nary time-varying covariate is interval sis for markers and degradation, and applications. censored. threshold models with markers mea­ He, Xuhua, Some subvarieties of the Zhang, Fang, Age dependent QTL analy­ sured before observed event times. De Concini-Procesi compactification. sis using Gibbs sampling for random Wager, Carrie, Mixed-model smoothing Henriques, Andre, Orbispaces. effects models. for replicated spatial point patterns in Hansen, Morten, A compact moduli space brain microscopy. for Cohen-Macaulay curves in projective Brandeis University (2) Wruck, Lisa, Statistical issues in the eval­ space. Kleinberg, Robert, Online decision prob­ MATHEMATICS uation of tests for diagnosing disease and monitoring disease progression. lems with large strategy sets. Linshow, Andrew, Vertex algebras and Zhang, Bin, Statistical methods with un­ Lam, Thomas, Combinatorics of ribbon invariant theory. recognized heterogeneity in survival tableaux. Paksoy, Vehbi Emrah, The A-series of the data analysis, identifying family re­ Mirrokni, Vahab, Approximation algo­ tangent bundles of flag manifolds and a lationships in genetic studies, and rithms for distributed and selfish generalization of Hori-Vata conjecture. response-related incomplete data. agents.

266 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Doctoral Degrees Conferred

Oblomkov, Alexei, Double affine Heeke al­ MICHIGAN Milanov, Valentin, Search procedure for gebras and noncommutative geometry. identifying gene-gene interaction based Oprea, Dragos, The tautological classes Central Michigan on entropy measures. of the moduli spaces of stable maps to University (2) Senaratne, Maddumage Dona, Develop­ flag varieties. ment and analysis of a micro-macro Persson, Per-Olaf, Mesh generation for MATHEMATICS simulation. implicit geometries. Abu Ghneim, Omar, Nonabelian McFar­ Sha, Qiuying, Multi-locus association test Robinson, Hugh, Maps and localizations land and Menan-Hadamard difference for detecting complex disease genes. in the category of Segal spaces. sets. Yapa, Gaitri, Covariate measurement er­ Rochon, Frederic, Bott periodicity for Kong, Lingji, A study of the properties, ror in dual systems models. fibred cusp operators. estimations and applications for the Rosenblum, Michael Aaron, Approximat­ beta-gamma distribution. Oakland University nl ing fluid schedules in packet-switched MATHEMATICS AND STATISTICS networks. Michigan State Zhang, Rachea/, Some analytical charac­ Sutton, Brian, The stochastic operator University (15) teristics of the ridge regression trace. approach to random matrix theory. MATHEMATICS Testa, Damiano, The Severi problem for University of Michigan, rational curves on del Pezzo surfaces. A/pay, Nimet, Global existence of solu­ Ann Arbor nsl Vondrak, ]an, Probabilistic methods in tions to nonlinear wave equations by combinatorial and stochastic optimiza­ weighted Strichartz inequalities. BIOSTATISTICS tion. Buyukbozkirli, Bulent, Modeling dynamics An, Hyonggin, Robust model-based anal­ Williams, Lauren, Combinatorial aspects of genetic algorithms for one max and ysis of multivariate data with missing of total positivity. deceptive functions. values. Wu, Dam in, Higher canonical asymptotics Cui, Changjun, Local regularization meth­ Liu, Lei, Modeling recurrent events and of Kahler-Einstein metrics on quasi­ ods for n-dimensional first-kind inte­ medical cost data in the presence of a projective manifolds. gral equations. correlated terminating event. Wu, Hao, Tight contact structures on Freidovich, Leonid, Logic-based switching Luo, Wen-Lin, General linear model for small Seifert spaces. control of nonlinear systems using FMRI time series data: Model formula­ high-gain observers. tion, covariance estimation, and model Northeastern Go, ]aegwi, Bucking arch under normal selection. pressure. University (1) McClure, Leslie, Analysis of clinical trial Novozhilova, Lydia, Axisymmetric prob­ data where treatments favor different MATHEMATICS lems in nonlinear elasticity: Existence outcomes. Seven, Ahmet, Combinatorial aspects of and global injectivity of energy mini­ Min, Sung-joan, Group sequential meth­ double Bruhat cells and cluster alge­ mizers and new classes of exact solu­ ods for nonlinear models in clinical bras. tions. trials. Slavin, Leonid, Bellman function and Xie, Dawei, Combining information from Tufts University (1) BMO. multiple surveys for small-area estima­ Sarto, Maria, Prospective middle school tion: Bayesian approaches. MATHEMATICS teachers' knowledge about data analysis Beltukov, Aleksei, Sonar transforms. and its application to teaching. MATHEMATICS Vasi/iu, Daniel, Constrained lower semi­ Chiang, Sylvia Pek- Yin, On vacuum prob­ University of continuity problems in the calculus of lems for different systems of conserva­ Massachusetts, variations. tion. Amherst (7) von Bergmann, ]ens, Pseudo-holomorphic Keen, Benjamin, A kinetic scheme for gas maps in folded symplectic manifolds. dynamics on arbitrary grids. BIOSTATISTICS AND EPIDEMIOLOGY Yu, ]ui-Ling, A fully explicit optimal Kennedy, Christopher, An exploration of Sturdivant, Rod, Goodness-of-fit in hier­ two-stage scheme to solve the reaction­ deep matrix algebras. archical logistic regression models. diffusion-chemotaxis system. Kuronya, Alex, Asymptotic cohomologi­ Yuce, Huseyin, The fundamental frequen­ cal functions on projective varieties. MATHEMATICS AND STATISTICS cies of plates with a core. Lilov, Krastio, Fatou theory in two dimen­ Cullinan, John, Local global properties sions. STATISTICS AND PROBABILITY of torsion points on three-dimensional Mitavskiy, Boris, A mathematical model Abelian varieties. Li, Fang, Testing for the equality of two of evolutionary computation and some Curran, Raymond, Toric ideals and dis­ autoregressive and regression func­ consequences. criminants in codimensions greater tions. Nguyen, Quang-Minh, Entropic graphs than two. Sirbu, Carina Mihaela, Assessing medical for image registration. Eisner, Adam, A numerical exploration costs from a longitudinal model. Tung, Yan-Chun ]ames, Fock spaces. of the statistical behavior of the dis­ Sirbu, George, Adaptive designs with Woods, Kevin, Rational generating func­ cretized nonlinear Schrodinger equa­ covariates. tions and lattice point sets. tion. Hattaway, Amanda, Modelling tubu­ Michigan Technological STATISTICS loglomerular feedback in coupled neph­ University (6) Dyson, Gregory, New techniques in clus­ rons. tering and microarray data analysis. MATHEMATICAL SCIENCES Rapti, Zoi, Modular instabilities of per­ Vartivarian, Sonya, For the formation of turbed Schrodinger-type equations. Keranen, Melissa, Transverse Steiner weighting class adjustments for unit Tzirakis, Nikolaos, Global well-posedness quadruple systems. nonresponse in sample surveys. for some dispersive partial differential Kodippli, Asitha, Analysis of intraday Xi, Bowei, Estimating internal link loss equations. dynamics of options trading B. rates using active network tomography. fEBRUARY 2006 NOTICES OF THE AMS 267 Doctoral Degrees Conferred

Wayne State University (7) Rayner, Ellen Gibson Johnston, The ex­ NEBRASKA changeable negative binomial distribu­ MATHEMATICS tion and its applications. University of Nebraska, Aouina, Mokhtar, The moduli space of Tyler, Benton, Tilings and packings of lincoln (3) thickenings. n-dimensional cubes. Geremew, Wondimagegneau, Metric reg­ MATHEMATICS ularity in variational analysis. Baeth, Nicholas, Representation theory Habte, Aychiluhim, Application of varia­ MISSOURI of one-dimensional local rings of finite tional analysis to welfare economics. Cohen-Macaulay type. Ion, Cristina, Recursive estimation algo­ St. louis University nl Duncan, Benton, Universal operator alge­ rithms using stochastic approximation bras of directed graphs. methods. MATHEMATICS AND COMPUTER SCIENCE Koetz, Matthew, Algebraic constructions Lin, Runchang, Natural superconver­ of low-density parity check codes. gence in two- and three-dimensional Ohashi, Ryo, The isometry groups on finite element methods. prism manifolds. Liu, Yuanjin, Two-time-scale systems NEW HAMPSHIRE with Markovian regime switching. University of Missouri, Dartmouth College (3) Wang, Dong, Optimal control of differ­ Columbia (4) ential inclusions in infinite dimensional MATHEMATICS spaces and semilinear evolution inclu­ STATISTICS sions. Cole, Daniel, On minimal surfaces in Nashimoto, Kane, Multiple comparison Martinet-type spaces. techniques for order restricted models. Ryan, Nathan, Satake parameters of MINNESOTA Rabie, Huwaida, Optimal designs for Siegel modular forms. dose-finding in contingent response Williams, B. Venus, The mathematics of University of Minnesota, models. the coordinated and precise dance that Twin Cities (IOJ Zhang, Zhigang, Nonproportional haz­ keeps us alive. DIVISION OF BIOSTATISTICS, SCHOOL OF ards regression models for survival analysis. University of New PuBLIC HEALTH Zhao, Qiang, Nonparametric treatment Hampshire (4) Huang, Xiaohong, Statistical methods for comparisons for interval-censored fail­ MATHEMATICS AND STATISTICS sample classification with microarray ure time data. gene expression data. Alghanem, Maher, Evaluating the mid- ]in, Xiaoping, Multivariate lattice mod­ dle school mathematics teacher prepa­ els for areal data with application to University of Missouri, ration program at Riyadh Teachers' multiple disease mapping. Rolla (Il College. Zhi, Xin, Likelihood ratio tests for corre­ Bannon, ]on, Burnside factors, amenabil­ lated time-to-event data using gamma MATHEMATICS AND STATISTICS ity defects and transitive families of frailty. Kytmanov, Alexey, Integral representa­ projections in factors in type III. tions and holomorphic extension on Gao, Ming Chu, Free products of operator SCHOOL OF STATISTICS toric varieties. spaces and free Markov processes. Chen, Chao-Yin, Improving the chemical Yousefi, Hassan, Stable invariant sub­ mass balance model. spaces, reflexivity, and BMO. de Ia Vega Gongora, jorge, A power study MONTANA of inverse regression methods. NEW JERSEY Lazar, Radu, Methods for implementing Montana State Bayesian inference for some problems involving linear constraints. University (3) New Jersey Institute of Pontiggia, Laura, Topics in stochastic Technology (7) games. MATHEMATICAL SCIENCES MATHEMATICAL SCIENCES St. Clair, Katherine, Some objective Graham, Kimberly, An examination of Bayesian methods for finite popula­ the integration of graphing calculators Ambrosio, Christina, The control of tion sampling. in formal assessments that accompany frequency of a conditional oscillator Wen, Xuerong (Meggie), Optimal sufficient high school mathematics textbooks. simultaneously subjected to multiple oscillating inputs. dimension reduction in regression with Hyde, Scott, Robust methods for mul­ categorical predictors. tivariate linear models with spectral Champanerkar, ]yoti, Pitchfork bifurca­ Yang, Rang, Statistical modeling of mul­ models for scatter matrices. tions of invariant manifolds. tivariate longitudinal binary data. Lukyanov, Valery, Scattering matrix anal­ Kosiak, jennifer, Using asynchronous dis­ ysis of photonic crystals. cussions to facilitate collaborative prob­ lem solving in college algebra. Mileyko, Yuriy, Theory and algorithms MISSISSIPPI for swept manifolds intersections. Muhammed, Hameed, (2) Influence of sur­ University of University of Montana factant on the breakup of a fluid jet in Mississippi (4) MATHEMATICAL SCIENCES viscous surrounding. MATHEMATICS Tran, . Hoa, Numerical simulation of mi­ Perkins, David, Investigations of a chip­ crowave heating of a target with temper­ Kuhl, ]aromy, On completing and avoid­ firing game. ature dependent electrical properties in ing partial Latin squares. Sloan, Deborah, A conflict in values: a single mode cavity. Page, Robert, ]r., On bilinear maps of The dilemma of equity, diversity, and Zhou, Lin, Perturbation analysis on dis­ order bounded variation. participation in higher mathematics. persive properties of micros trip.

268 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Doctoral Degrees Conferred

Princeton University (8) Stevens Institute of Nouri, Fereydoun, Graph homology. Technology (1) Pineiro, jorge, Mahler formula for dy­ APPLIED AND COMPUTATIONAL namical systems on pn. MATHEMATICS MATHEMATICAL SCIENCES Ushakov, Alexander, Fundamental search Downs, Oliver B., Learning, adaptive and Kahl, Nathan, Enumerator polynomials problems in group theory. optimization: The nonnegative Boltz­ and the enumeration of subgraphs of Zucker, Marc, Studies in cryptological mann machine and the tunneling sales­ multigraphs. combinatorics. man algorithm. Dum, Sang-i/, Graphs of bounded rank­ Columbia University (20l width. NEW MEXICO BIOSTATISTICS MATHEMATICS New Mexico State Cheng, ]ianfeng, Evaluating and cor­ Alexakis, Spyros, Local and global aspects University, Las Cruces (2l recting guess effect in not perfect of conformal geometry. double-blinded clinical trials. MATHEMATICAL SCIENCES Asok, Aravind, Geometry of simple G­ Li, Huiling, Analysis of incomplete HRQoL varieties. Al-Ayyoub, Ibrahim, The Ratliff-Rush clo­ data in the REMATCH trial. Wang, Cuiling, Regression analysis with Brumley, Farrell, Distinguishing cusp sure and a minimal Groebner basis for forms on the general linear group. certain affine monomial curves. missing data. Garcia, Rebecca, On the minors of Wong, Kam-Fai, Statistical analysis of Bufetov, Alexander, Decay of correlations current status data. for the Rauzy-Veech-Zorich induction catalecticant matrices and on the coad­ map and the central limit theorem for unation of generalized crowns. Wu, Songmei, Nonlinear modeling strate­ the Teichmuller geodesic flow. gies for metabolism rate data in brain University of New imaging studies. De Sanctis, Luca, Structural approaches to spin glasses and optimization prob­ Mexico (9) Wu, Ya-Chi, Linear regression with in­ complete dependent variable. lems. MATHEMATICS AND STATISTICS Gressman, Philip, LP - L q estimates for MATHEMATICS Radon-like operators. Aden, ]ames, Model selection in kernel machine classification with application Hedden, Matthew, Knot Floer homology Rutgers University, New in bioinformatics. and cabling. Andries, Erie, Regularized least square Mcinroy, Adam, Orbifold mirror symme­ Brunswick (14l classifiers: Application to leukemia dis­ try for complex tori. MATHEMATICS ease classification. Moser, Harriet, Proving a manifold to be hyperbolic once it has been approxi­ Blue, Pieter, Decay estimates and phase DeCastro, Manuela, Stability of parabolic systems on a half-space and theoretical mated to be so. space analysis for wave equations on Niccolai, John, Triple product L-functions. some black hole me tries. aspects of radiation. Degnan, ]ames, Gene tree distributions Qiu, Yannan, Special cycles on Siegel Burdges, Jeffrey, Simple groups of finite 3-folds. Morley rank of odd type: Toward an under the coalescent process. Dohnal, Tomas, Optical bullets in (2 + 1) Sherman, Morgan, The infinitely near endgame. Borel-fixed points on the Hilbert scheme. Chel/uri, Thyagaraju, Bragg resonant periodic structures and Equidistribution of Van Steirteghem, Bart, A classification of roots of quadratic congruences. their interaction. Doliga, Stanislaw, Real algebraic geome­ affine smooth spherical varieties. Ciobanu, Laura Joana, On the complexity Wambach, Eric, Integral representations of the endomorphism problem in free try. Glubokov, Andrey, Jet spaces of the on U(2) x U(3) and geometric applica­ groups. tions. Curry, Eva, Characterization of low-pass quantum plane. filters for multivariable wavelets and Justo, Dagoberto, High order mimetic STATISTICS some related questions. methods and absorbing boundary con­ Hadjiliadis, Olympia, Change-point direc­ Dalili, Kia, Cohomological methods for ditions. tion of two-sided alternatives in the determining numerical invariants of Nazarov, Igor, A mathematical analysis Brownian motion model and its connec­ algebras and modules. for sustainable management of ecosys­ tion to the gambler's ruin problem with Hartke, Stephen, Graph-theoretic models tems II. Perfectly matched layers for relative wealth perception. of spread and competition. Euler's linearized equation. Hernandez del-valle, Gerardo, First pas­ Lauve, Aaron, A quasideterminantal ap­ sage time densities of Brownian motion proach to quantized flag varieties. NEW YORK and applications to credit risk. Li, Xiaoqing, The orthogonality of Heeke Ruiz-Mata, jesus, Modeling credit and eigenvalues of automorphic forms. City University of New market risk and validation of models. Wang, Hui, A new approach of detect­ Medville, Kai, Existence and blow up York, Graduate Center (8l behavior of planar harmonic functions ing influential markers for complex satisfying certain nonlinear Neumann PROGRAM IN MATHEMATICS phenotypes with genotype data. boundary conditions. Diop, Serigne, Non-Gaussian models of Wang, Yuanjia, Non-parametric estima­ Ponce, Augusto, Some elliptic problems financial markets: Paths simulation via tion of distribution functions from with singularities. series representation. Kin-Cohort data. Rios, Alfredo jose, Some problems on the Kahrobaei, Delaram, Residual solvability, Yan, Xin, Discriminant analysis using pointwise convergence of wavelet series generalized free products, finitely gen­ multi-gene profiles in molecular classi­ and Riesz products. erated nilpotent groups, free groups, fication of breast cancer. and one-relator groups. Sundberg, Eric, Fair and biased positional Cornell University (18) games. La Luz, Jose, The Bousfield-Kan spectral Xu, Yongzhong, On the Morse index of sequence for Moravalk-theory. APPLIED MATHEMATICS a functional arising in contact form Leibman, George, Consistency strengths Grasso, Catherine, Partial order graphs geometry. of modified maximality principles. for multiple sequence alignment.

FEBRUARY 2006 NOTICES OF THE AMS 269 Doctoral Degrees Conferred

Guzman, johnny, Pointwise estimates for State University of New Lee, Taewon, Statistical error analysis in discontinuous Galerkin methods and York, Albany (I) numerical solutions of shock physics for the standard finite method with problems. numerical integration. MATHEMATICS AND STATISTICS Li, juan, Longitudinal, survival and joint He, Chang hong, Estimation of volatilities Kures, Osman, The Bergman projection modeling analysis with Bayesian appli­ under a Merton's jump-diffusion model and related integral operators on the cations. and an uncertain volatility model. unit ball in en. Tintle, Nathan, Reclassification as a cost Henniger, jay, Small portfolio selection effective sample design for estimation for benchmark tracking and option State University of New and testing association when misclassi­ hedging under basis risk. fication errors are present. York, Binghamton (4) Shontz, Suzanne, Numerical methods for Yu, Yan, Errors in numerical solutions of problems with moving meshes. MATHEMATICAL SCIENCES shock physics problems. Singer, Michael, Efficient time splitting Koban, Lori jean, Two generations of MATHEMATICS methods for reacting flow calculations. biased graphs: Circuit signatures and Chiose, Ionut, On the embedding of MATHEMATICS modular triples of matroids and biased q-complete manifolds. expansions of biased graphs. Belk, ]ames, Thompson's group F. Friedman, joshua, The Selberg trace Palmatier, Joshua, M-zeroids: Structure formula and Selberg zeta-function for Charalambous, Nelia, On the LP spectrum and categorical equivalences. cofinite Kleinian of the Hodge Laplacian and logarithmic groups with finite­ Saldarriaga, Omar Daria, Fusion alge­ dimensional unitary. Sobolev inequalities on non-compact bras, symmetric polynomials, orbits of manifolds. Gonzalez, Eduardo, Quantum cohomol­ N-groups and rank level duality. op: and symplectomorphism type of Ciubotaru, Dan, Unitary representations S -manifolds with isolated fixed point. of exceptional p-adic groups. Sperber, Ron, A comparison of assembly maps in algebraic K-theory. ]anks, Gregory, Some remarks on local Cortissoz, jean, On the Ricci flow in connectivity at the Feigenbaum point. rotationally symmetric manifolds with State University boundary. of New ]avaheri, Mohammad, Conformally com­ York, Buffalo (9) pact Einstein metrics with symmetry in Francisco, Christopher, Hilbert functions dimension 5. and graded free resolutions. MATHEMATICS Kim, Young Deuk, The Thurston bound­ Gabay, Yuval, Double jump inversions Agarwal, Anurag, Some quartic Diophan­ ary of Teichmuller space and complex and strong minimal covers in the of curve. Turing degrees. tine equations. Blanariu, Mihaela, Asymptotic analysis Liu, Yuan, Einstein metrics of positive Greenberg, Noam, The role of true finite­ sectional curvature on weighted projec­ ness in the admissible recursively enu­ of patterns and islands in strained alloy films. tive planes. merable degrees. Moraru, Dan, A new construction of Ku, ]a Eun, Least-squares methods for Cheptea, Dorin, A topological quan­ tum field theory for the Le-Murakami­ anti-self-dual 4-manifolds. second-order elliptic partial differential Namazi, Hossein, Heegaard splittings and equations. Ohtsuki invariant of three-dimensional manifolds. hyperbolic geometry. Leykekhman, Dmitriy, Pointwise weighted Fan, Jiangnan, Decorated link invariants. Radulescu, Anca, The connected isen­ error estimates for parabolic finite ele­ tropes conjecture in a space of quartic ment equations. Georgescu, Catalin, The boundary map polynomials. Lin, Yi, Equivariant symplectic Hodge and the connecting set in Conley index theory. Valdez, Rogelio, Self-similarity of the theory and strong Lefschetz manifolds. Mandelbrot set and parabolic bifurca­ Schwartz, Fernando, Scalar curvature Huynh, Vu, Reidemeister torsion, twisted tion. Alexander polynomial, the A-polynomial, problems on manifolds with bound­ Xu, Ming, Bauer-Furuta and the colored Jones invariant and co- ary. polynomial of homotopy some classes of knots. refined Ruberman invariant. Zhou, Hilibin, Minimax estimation with thresholding and asymptotic equiva­ Kuppum, Srikanth, Edge polynomials, University of Rochester (2) Newton and norm polygons of a family lence theory for Gaussian variance MATHEMATIC regression. of hyperbolic manifolds. S Li, Yuan, Symmetric Boolean functions Qiu, Xing, On stochastic flows and back­ Rensselaer Polytechnic and their extension to finite fields. ward stochastic differential equations with reflections. Institute (6) Tekalign, Wondimu, Evolution equation for a thin epitaxial film on a deformable Tang, Wan, Decay rates of oscillatory MATHEMATICAL SCIENCES substrate. integral operators. ]i, Xiaoyun, Clique partition problem with minimum size requirement. State University of New NORTH CAROLINA Peng, ]ufeng, Multiple robot coordina­ York, Stony Brook (20) tion: A mathematical programming ap­ Duke University (11) APPLIED MATHEMATICS AND STATISTICS proach. INSTITUTE OF STATISTICS AND D ECISION Scherzer, David, Multi-dimensional cellu­ Curry, Michael, Applications of stochastic SCIENCES lar chords. methods for periodic scheduling. Gunn, Laura, Bayesian order restricted Thorp Kusel, Elizabeth, New parabolic Greene, Nataniel, Reconstructing piece­ methods with biomedical applications. equation solutions for high frequency wise smooth functions from their spec­ Rappold, Ana, Using expert knowledge and elastic media problems. tral data. when the data model is not known Xin, ]ianguo, Aspects on discontinuous Kim, ]ieun, Path analysis of the visual in modeling the mixed layer of the Galerkin solutions of hyperbolic con­ attention network using fMRI data. Atlantic Ocean. servation laws. Kim, Youngeun, Bidomain simulation of Rigat, Fabio, A beta-Stacy proportional Xue, Yonggang, Hermite subdivision spiral waves of cardiac tissue in electri­ hazards model and Bayesian Weibull schemes and jet subdivision surfaces. cal cardiology. survival trees.

270 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Doctoral Degrees Conferred

MATHEMATICS STATISTICS Wang, Lily, Some statistical aspects of the analysis of genomic sequences. Buckingham, Robert, Long-time asymp­ Chen, Li, Bayesian hierarchical spatial­ totics of the nonlinear Schrodinger temporal models for wind prediction. MATHEMATICS equation shock problem. Feng, Sheng, Statistical studies of ge­ nomics data. Chang, Soo-Ah, Factorizations in some Cain, John, Issues in the one-dimensional special block monoids. dynamics of a paced cardiac fiber. Gosky, Ross, Bayesian analysis and match­ ing errors in closed population capture DiFranco, Jeffrey, Gibbs phenomenon for Curto, Carina, Matrix model superpoten­ recapture models. the defocusing nonlinear Schrodinger tials and Calabi-Yau spaces: An ADE equation. classification. Hwang, Sang Pil, Dynamic time series analysis using logistic function. University of North Feist, Andrew, Two problems in delay Li, Erning, Estimation for geneni.lized lin­ differential equations. ear models when covariates are subject Carolina at Charlotte (7) Fox, Daniel, Second order families of specific parameterina mixed models MATHEMATICS AND STATISTICS coassociative 4-folds. with longitudinal measurements. Guo, Xunxtang, On frame wavelets. Yang, Guoqiang, Quantitative models for Lin, ]tang, Topics in application of non­ parametric smoothing. Herron, John, Weighted conditional ex- dorsal closure in drosophila embryos. pectation operators on LP space. Yasaki, Dan, On the existence of spines Lokhnygtna, Yuliya, Topics in design and analysis of clinical trials. Hill, David, Time delayed dynamical sys­ for IQl-rank 1 groups. tems and the Duffing equation. Ytng, Wenjun, A multilevel adaptive ap­ Lu, Na, Statistical issues in coherent risk management. Hill, jennifer, An inventory optimization proach for computational cardiology. model with Markov-modulated com­ Rao, Harshavardhana, Contagion in fi­ modity prices. nancial markets: Two statistical ap­ North Carolina State proaches. ]ang, Bong Soo, Homogenization of ir­ University (27) regular shaped composite materials in Remlinger, Katja, Statistical design and periodic structures. analysis of high throughput screening MATHEMATICS data using pooling experiments and ]in, Xiaodong, Contributions to kernel data mining techniques. methods and estimation of extreme Bidwell, John, Discrete nonautonomous value index. Wang, ling, An optimization approach dynamical systems, periodic dynamical Xiong, Huatyu, Nonparametric and semi­ systems. for the parameter estimation of the nonlinear mixed effects models. parametric functional coefficient in­ Cook, William, Affine Lie algebras, vertex strumental variable models. operator algebras and combinatorial Wu, Yujun, Controlling variable selection by the addition of pseudo-variables. identities. OHIO Dozier, Richard, Existence and analysis University of North of the limiting spectral distribution Bowling Green State of large dimensional information-plus­ Carolina at Chapel Hill (14) (6) noise. BIOSTATISTICS University Finkel, Daniel, Global optimization with Ahn, Chaehyung, Detecting linked changes MATHEMATICS AND STATISTICS the DIRECT algorithm. in fast evolving genomes. Grtnevttch, Oxana, Student understand- Gibson, Nathan, Terahertz-based electro­ Begum, Munni, Statistical TK/TK dose ing of abstract algebra: A theoretical magnetic interrogation techniques for response modeling of toxicity. examination. damage detection. Capuano, George, A joint latent autore­ - Harrar, Solomon, Linear models under Hatch, Andrew, Model development and gressive model for patient dropout and non-normality. control design for high speed atomic longitudinal health related quality of Kerns, (Gary) jay, Signed measures in force microscopy. life subject to informative missingness. exchangeability and infinite divisibility. He, Taiping, Reaction-diffusion systems Deng, Shibing, Some aspects on linear Rolli, William, Frames and operator de­ with discontinuous reaction functions. model analysis of microarray gene compositions in Hilbert spaces. expression data. Hillman, Rebecca, Relationship between Sanders, Rebecca, Hypercyclic and super­ symmetric brace algebras and pre-Lie Gurka, Matthew, The Box-Cox transfor­ cyclic operators in the weak topology algebras. mation in the general linear mixed of Banach spaces. model for longitudinal data. Xu, ]in, Robustness study of some mul­ jackson, Farrah, Characterization of in­ ]ung, Inkyung, Robust inference in unbal­ volutions of SP(2N,K). tivariate tests in generalized linear anced heteroscedastic one-way random models. Kyei, Yaw, Numerical method and control effects models using rank-based meth­ theory. ods. Case Western Reserve Levy, Rachel, Partial differential equa­ Lu, Bing, Estimating correlation parame­ University (12) tions of thin liquid films: Analysis and ters in cluster intervention trials with bi­ numerical simulation. nary responses using estimating equa­ EPIDEMIOLOGY AND BIOSTATISTICS Perry, john, Combinatorial criteria for tions. Beaird, Heather, Putative DNRH agonist Grabner bases. Nee/on, Brian, Bayesian order restricted therapy and dementia: An application inference. Taylor, Dewey, Fine Bruhat intersections of medicare hospitalization claims data. for reductive monoids. Pan, Zhiytng, Regression analysis for Kasehagen, Laurin, Duffy-negativity and complex longitudinal survey data. vivax malaria epidemiology: A study Wood, Lisa, Solvable length in Lie alge­ Robbins, Tania, Combining microarrays of dual and multiple-record system bras, associative algebras and matrix with QTL analysis. estimation and patterns of association groups. Schwartz, Todd, A study of sample in Papua New Guinea. Yang, Xingzhou, Immersed interface size recalculation with particular focus Mascha, Edward, Assessing individual method for elasticity problems with on active- and placebo-controlled non­ treatment effect heterogeneity for bi­ interfaces. inferiority trials. nary outcomes.

FEBRUARY 2006 NOTICES OF TilE AMS 271 Doctoral Degrees Conferred

Nock, Nora, Development and application STATISTICS Ou, Ye-Lin, P-harmonic morphisms, mini­ of DNA damage and DNA repair indices Chen, Haiying, Ranked set sampling for mal foliations, and conformal deforma­ to prostate cancer. binary and ordered categorical variables tions of metrics. Orloff, Mohammed, Analysis of genes as­ with applications in health survey data. Xu, Tao, Model-data synthesis in ter­ sociated with focal segmental glomeru­ Duncan, Kristin, Case and covariate in­ restrial ecosystem modeling: Inverse losclerosis. fluence: Implications for model assess­ analysis and uncertainty analysis. Stein, Catherine, Genetic and environ­ ment. mental influences on tuberculosis sus­ Gibe/lata, Marilisa, Stochastic modeling OREGON ceptibility. of the sleep processes. Traore, Fatoumata, A conceptual model Pavlicova, Martina, Thresholding in fMRI Oregon State University (2l for understanding sexual risk among images. STATISTICS persons living with HIV I AIDS. Sun, ]unfeng, Stochastic models for com­ Zhu, Guohua, Ascertainment in two­ pliance analysis and applications. Amer, Safaa, Neural network imputation: A new fashion or a good tool. phase sampling designs for segregation Wang, Tao, Statistical analysis of gene and linkage analysis. expression experiments. ]ia, Siwei, Optimization, conservation and valuation of contingent claims in MATHEMATICS Ohio University (4l economic resource management under uncertainty. Hahn, Philip, Origination and propagation MATHEMATICS of reaction diffusion waves in three Al-Hazmi, Husain, A study of CS and L-CS Portland State spatial dimensions. rings and modules. University (2) STATISTICS Alsu lami, Saud, On evolution in Banach spaces and commuting semigroups. MATHEMATICS AND STATISTICS Kitska, David, Simultaneous inference for Castillo, Rene, Generalized non-autono­ Fish, Daniel, Metriplectic systems. functional linear models. mous Kato classes and nonlinear Bessel Santoro, Emanuele, Thermodynamic met- Piryatinska, Alexandra, Inference for the potentials. rics and the geometry of equilibrium Levy models and their applications in Constantin, Ele na, Optimization and flow surfaces. medicine and statistical physics. invariance via high order tangent cones. (5l Snyder, Scott, Evaluation of an im­ University of Oregon plantable medical device: Design and University of Akron (1) MATHEMATICS modeling of a three dimensional work­ THEORETICAL AND APPLIED MATHEMATICS Harker, Hayden, Cohomology of a sub­ space. Kim, Shinuk, A numerical study of param- Hopf algebra of a Steenrod algebra. Loft, Brian, Connected components of Kent State University (2l eter identification in linear and nonlin­ ear elastic and viscoelastic plates. the space of positive scalar curvature MATHEMATICAL SCIENCES metrics on spheres. University of Cincinnati (4) Merchant, Eric, Structural properties of Fontes, Natacha, Multi-dimensional poly­ Hadamard designs. MATHEMATICAL SCIENCES nomial inequalities; norms of interpola­ Nordstrom, Hans, Associated primes over tion operators. Galstyan, Anahit, Existence and number Ore extensions and generalized Weyl Ze ibig, Gerd, Categorical methods in of global solutions to model nonlinear algebras. functional analysis. partial differential equations. Ruiz, Efren, A classification theorem for Oh, ]iyeon, Error analysis of the exponen­ direct limits of extensions of circle Ohio State University (15l tial Euler method and the mathematical algebras by purely infinite C* -algebras. modeling of the retinal waves in neuro­ MATHEMATICS science. PENNSYLVANIA Antal, Tamas, Cyclic homology and Hopf Zhao, Shuhong, Statistical inference on algebras. binomial proportions. Zhou, Rang, Bayesian analysis of log­ Carnegie Mellon Ghazaryan, Anna, Nonlinear convective binomial models. University (14) instability of fronts: A case study. Guloglu, Ahmet M., On low-lying zeros of MATHEMATICAL SCIENCES automorphic L-functions. OKLAHOMA Baia, Margarida, Variational multiscale Herbig, Anne-Katrin, A sufficient condi­ Oklahoma State problems and applications to thin films. tion for subellipticity of the a-Neumann Brown, Chad, Set comprehension in problem. University-Stillwater (1l Church's type theory. Kaygun, Atabey, Bialgebra cyclic homol­ STATISTICS Janecek, Karel, Futures trading model ogy with coefficients. with transaction costs. Bagour, Ali, Probability proportional to Ojakian, Kerry, Combinatorics in bounded Liu, Xing, Rigorous exponential asymp­ size sampling. totics for a nonlinear third order differ­ arithmetic. Pankavich, Stephen, ence equation. University of Oklahoma (4) The Vlasov Poisson system with infinite mass and energy. Manukian, Vahagn, Existence and stabil­ ity of multi-pulses with applications to MATHEMATICS Petrelli, Luca, Variational principle for nonlinear optics. Borovikova, Marina, Partial regularity of general diffusion problems. Pirvu, Traian, Maximizing portfolios Roman, Cosmin, Baer and quasi-Baer weak solutions of quasilinear elliptic modules. systems and weak Harnack inequalities. growth rate under risk constraints. Gomarteli, Mamouka, On the normal ac­ Popovici, Cristina, Coupled singular per­ Wang, ]in, A numerical approach for cessibility property of actions on man­ turbations and homogenization. the interfacial motion between two ifolds: Ramifications in pseudo semi­ immiscible incompressible fluids. Rivera, juan, Portfolio choice under risk groups of local diffeomorphisms. limits: A coherent approach.

272 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Doctoral Degrees Conferred

Tudorascu, Adrian, Optimal mass trans­ Wang, Shao/i, Dimension reduction in STATISTICS portation methods for gradient flows in regression. the weak topology. Greery, Robert Alan, ]r., Noncompliance, Yang, Ke, Using the Poisson kernel in covariance adjustment, and matching Winger, Aris, On pattern formation in model building and selection. in randomized controlled trials. a one dimensional viscoelastic system Zhan, Xiaojiang, Bayesian semiparamet­ with numerical computation. Liu, Naiping, Covariance selection and ric inference based on ranks. estimation through modified Cholesky STATISTICS decomposition and the value/growth Temple University (8) spreads as predictors of returns. Araneda, Anita, Statistical inference in mapping and localization for mobile MATHEMATICS Wang, Liang, A new adaptive variable robots. selection criterion and its applications Mamma, Behai/u, A mean value theorem in financial markets. Dunn, Michelle, Applying particle-filter for discriminants of abelian extensions and path-stack methods to detecting of a number field. Zhang, Liangyue, Efficient estimation in marginal partially linear models anomalies in network traffic volume. Nguyen, Truyen Van, On Mange-Ampere Slavkovic, Aleksandra, Statistical disclo­ type equations arising in optimal trans­ for longitudinal/clustered data using sure limitation beyond the margins: portation problems. splines. Characterization of joint distributions Tesemma, Mohammed Seid, Reflection University of for contingency tables. groups and semigroup algebras in mul­ tiplicative invariant theory. Pittsburgh (17) lehigh University (1) Wen, Xiangdong, Rigorous experimental BIOSTATISTICS MATHEMATICS mathematics applied to the Goulden­ Jackson method, construction of sym­ Dang, Qianyu, Using trajectories from a Moller, Trisha, t-Split interval orders. metric chains and the Sprague-Grundy bivariate growth curve of covariates in Pennsylvania State function. a Cox model analysis. He, Shui, Generalized additive models for University, University STATISTICS data with concurvity: Statistical issues Park (18) Cai, Gengqian, Further results on Simes and a novel model fitting approach. test and Benjamin-Hochberg false dis­ Sang, Wei/ian, Empirical comparison of MATHEMATICS covery rate procedure. U.S. Census Bureau population esti­ Damjanovic, Danijela, Local rigidity of Deng, Ling, Heterogeneous and space­ mates used in morality and population partially hyperbolic higher rank Abelian dependence of substitution rates- an data system of the University of Pitts­ actions on the torus. application of zero-inflated models GEE burgh, Department of Biostatistics. Gerenrot, Dmitry, Residue formulation of and composite likelihood methods. Chern character on smooth manifolds. Li, Li, Design and analysis of DNA MATHEMATICS Handzy, Nestor, Experimental observa­ microarray data-model validation and Cross, Wesley, Principal value volumes of tions and mathematical description of sensitivity analysis. p-adic rational polyhedra. micellar fluid flow. Zhang, Hongyan, A Cox proportional Domokos, Andras, On the regularity of Krat, Svetlana, Approximation problems hazard model for monotonic severity p-harmonic functions in the Heisenberg in length geometry. marked failures. group. Lee, Young-]u, Modelling and simulations Dunca, Argus Adrian, Space averaged of non-Newtonian fluid flows. University of Navier-Stokes equations in the presence Raven, jeffrey, An equivariant bivariant Pennsylvania (14) of walls. Chern character. Grigoryan, Vahan, Multimodal biometric Saunders, Christopher, Floer homology MATHEMATICS analysis for monitoring of wellness. for almost Hamiltonian isotopies. Bana, Gergely, Soundness and complete­ Kaya, Songul, Numerical analysis of a Shoenthal, David, Several results con­ ness results for the formal model of variational multiscale method for tur­ cerning low-dimensional length spaces. symmetric encryption. bulence. Sostarecz, Michael, Experiments and mod­ Barwick, Clark, (oo, n)-Cat as a closed Krisner, Ed, Multi-bump solutions of a eling in viscoelastic fluids: Dimpled model category. one dimensional Wilson-Cowan type drops and beaded filaments. Byun, ]ungyoon, A generalization of model. Ugarcovici, Jlie, Symbolic dynamics for Connes-Kreimer Hopf algebra. Merdan, Huseyin, Renormalization group geodesic flows, hyperbolic measures Hindawi, Mohamad, Asymptotic invari­ methods in applied mathematical prob­ and periodic orbits. ants of Hadamard manifolds. lems. STATISTICS Lee, Dong Uk, p-Adic monodromy of the Pahlevani, Faranak, Sensitivity analysis ordinary subscheme of Picard modular of eddy viscosity models. Antoniou, Efi, Nonparametric imputation variety. and (mid-)rank test for mixed effects Scott-Pomerantz, Colleen, The k-epsilon Maxim, Laurentiu, Alexander invariants model. models with missing data. of hypersurface complements. Bai, Steven, Cluster analysis of high dimensional data and dimension reduc­ Mehrotra, Sukhendu, Triangulated cate­ STATISTICS tion for regression. gories of singularities, matrix factoriza­ tions and LG-models. Czanner, Gabriela, Applications of statis­ Ding, Rui, Multiple response ridge analy­ tics in neuroscience. sis. Sabitova, Maria, Root numbers of Abelian varieties and representations of the Gogtas, Hakan, Improving coverage of Kwanisai, Mike, Estimation in link-tracing Weil-Deligne group. rectangular confidence interval. designs with subsampling. Tripp, ]ames, Contact structures on open ]ia, Gang, Use of simultaneous infer­ Wang, Haiyan, Testing in multifactor 3-manifolds. ence under order restriction, stepdown heteroscedastic anova and repeated testing procedure and stage-wise se­ measures design with large number of Yap, Shirley, Prescribing curvature forms: quential optimal design in clinical dose levels. Solvability and obstruction results. study.

FEBRUARY 2006 NOTICES OF THE AMS 273 Doctoral Degrees Conferred

Sengul, Tulay, The time varying au­ SOUTH CAROLINA Zhong, Ping, Stochastic modeling of HIV toregressive model with covariates to pathogenesis under therapy and vac­ analyze longitudinal data with missing Clemson University (4l cine. values. MATHEMATICAL SCIENCES Sun, Zhuoxin, Repeated measures mix­ University of Tennessee, ture modeling with application to neu­ Hunt, Brian, Multiobjective programming Knoxville (2l roscience. with convex cones: Methodology and applications. MATHEMATICS Limbupasiriporn, ]irapha, Partial permu­ Iskra, John, Decidability in algebraic RHODE ISLAND tation decoding for codes from designs geometry. and finite geometries. Vasi/evska, Violeta, Fibrator properties of PL manifolds. Brown University (15) Limbupasiriporn, Prasit, Hidden sub­ group problem in quantum computing. Vanderbilt University (1l APPLIED MATHEMATICS Roop, John Paul, Variational solution Chen, Shanqin, The heterogeneous multi­ of the fractional advection dispersion MATHEMATICS scale method based on the discon­ equation. Sonkin, Dmitriy, On groups of large tinuous Galerkin and finite volume exponents nand n-periodic products. schemes. Medical University of Chen, Ting-Li, On the statistics of natural South Carolina m TEXAS images. BIOSTATISTICS, BIOINFORMATICS AND Baylor University (3) Curran, John, Adaptive learning among EPIDEMIOLOGY interacting agents: An analysis of the MATHEMATICS many-agent, long-term limit. Yoo, Wonsuk, Bayesian hierarchical change­ point model for longitudinal biomark­ Da Cunha, jeffrey, Lyapunov stability Gao, Yun, Statistical models in neural ers. and Floquet theory for nonautonomous information processing. linear dynamic systems on time scales. Harrison, Matthew, Discovering composi­ University of South Kama, Basant K., Comparison of smallest tional structure. eigenvalues and extremal points. Carolina, Columbia (9) Sirisup, Sirod, Issues in low-dimensional STATISTICAL SCIENCE modeling of unsteady flows: Conver­ EPIDEMIOLOGY AND BIOSTATISTICS Clark, Deeanna Antosh, Statistical issues gence, asymptotic stability and recon­ Moran, Robert, Working and analyzing struction procedures. concerning modeling and evaluating clinical data in a family practice. student achievement and school ac­ Strain, Robert, Some applications of an Shoultz, Gerald, Sprawl, measures of countability. energy method in collisional kinetic sprawl and chronic obstructive pul­ theory. monary disease: A Bayesian spatial Rice University (3) Xu, ]in, High Reynolds number simulation analysis. MATHEMATICS and drag reduction techniques. Sutton, Shae, Modeling of spatially­ Xu, Zhengfu, Anti-diffusive flux correc­ referenced event data in a South Car­ Meng, Zheng, Geometric variational prob­ tions for high order finite difference olina population. lems with cross-sectional constraints. WENO schemes. Trout, Aaron, Spaces with positive com­ MATHEMATICS binatorial curvature. Zhang, Xiao, On large deviations approx­ imations for occupancy models. Kidd, Travis, On the irreducibility of Zhang, ]un, Geometric compactification Laguerre polynomials of Lm(m)(x). of moduli space of cubic surfaces and Kirwan blowup. MATHEMATICS Vatchev, Vesselin, Analysis of the intrinsic Acquista, Karen, A generalization of class mode functions. Texas A&M University (24l field theory using motivic complexes. Zhao, ]ie, Multigrid methods for fourth order problems. MATHEMATICS ]ones, Rafe, Galois martingales and the Feng, Zhaosheng, Some results on the hyperbolic subset of the p-adic Mandel­ STATISTICS wave equation with Van der Pol type brot set. Hare, David, Simultaneous inference for nonlinear boundary condition and the joyce, Michael, Rational points on the £ 6 Burgers-Korteweg-de Vries equation. cubic surface. ratios of linear combinations of general linear model parameters. Hamid, Sami, On the structure of a class Lauzon, Michael, Harmonic analysis for Han, ]un, Parametric latent class model of operators. vector-valued functions with operator for longitudinal markers and recurrent Hoang, Luan, Asymptotic expansions of weights. events. the regular solutions to the 3D Navier­ Wick, Brett, Analytic projections, the ge­ Stokes equations and applications to Stocker, Russell, A general class of para­ the analysis of the helicity. ometry of holomorphic vector bundles metric models for recurrent event data. and applications to the corona problem. Kolev, Tzanio, Dual least-squares meth­ ods for computational electromagnet­ University of Rhode TENNESSEE its. Ryan, john, Global existence of reac­ Island (3l University of Memphis (3) tion diffusion equations over multiple MATHEMATICS domains. MATHEMATICAL SCIENCES Wang, Yanqiu, Preconditioning for the Chatterjee, Esha, Global behavior in ra­ Montagh, Balazs, Unavoidable substruc­ mixed formulation of linear plane elas­ tional difference equations. tures. ticity. Collins, Jarred, Moore-Greig designs. Schroeder, jason, Estimation from re­ Yao, Xudong, A min-max method for find­ Faubert, Glenn, Caterpillar tolerance rep­ sponse-biased incomplete data and ing multiple critical points in Banach resentations of graphs. supplementary information. space.

274 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Doctoral Degrees Conferred

STATISTICS University of Houston (4) University of Texas, Apanasovich, Tatiyana, Testing for spa­ MATHEMATICS Dallas (5) tial correlation and semiparametric spa­ Boiarkine, Oleg, Mixed hybrid finite ele­ MATHEMATICAL SCIENCES tial modeling of binary outcomes with ment methods for diffusion equations application in aberrant crypt foci in on nonmatching meshes. Banks, Troy, Invariant kernels and their orthogonal polynomials. colon carcinogenesis experiments. jacobs, Philip, Symmetric attractors with Bae, Kyounghwa, Bayesian model based non-trivial isotropy. Barakat, Moe, Polynomials in several non­ approaches with MCMC computation to commuting variables and some of their Martynenko, Andrey, Numerical methods asymptotic properties. some bioinformatics problems. for advection-diffusion equations on Costa, Fred, Structured matrix calcula­ Chang, Ilsung, Bayesian inference on locally refined meshes. tions via quaternions. mixture models and their applications. Pepper, Ryan, Binding independence. Navarra-Madsen, ]unalyn, Colorability, Dunlap, Mickey, Using the bootstrap to tangles and quandles. analyze variable stars data. University of North Odushkin, Taras, Mathematical models of Hu, Zonghui, Semiparametric functional Texas (2) atomic scale deformations and spatial data analysis for longitudinal/clustered MATHEMATICS nonuniformities in solid bodies. data: Theory and application. Coiculescu, Ion, Dynamics, thermody­ ]u, Hyunsu, Topics in analyzing longitu­ namic formalism and perturbations of dinal data. transcendental entire functions of finite UTAH ]ung, ]eesun, High resolution linkage and singular type. Brigham Young association study of quantitative trait Ghenciv, Petre, Hamiltonian cycles in loci. subset and subspace graphs. University nl Kim, Hyun Sun, Topics in ordinal logistic University of Texas, MATHEMATICS regression and its applications. Brown, Sarah, A numerical scheme for Ko, Kyungduk, Bayesian wavelet ap­ Arlington (2) Mullins-Sekerka flow in 3-space dimen­ proaches for parameter estimation and MATHEMATICS sions. change point detection in long memory Dimitrov, Dobromir, Nonstandard finite processes. (4) difference methods for dynamical sys­ University of Utah Lee, Ho-]in, Functional data analysis tems with applications in mathematical MATHE!viA TICS classification and regression. biology. Cavaleri, Renzo, A topological quantum Leyk Williams, Malgorzata (Gosia), FLARE Zhu, Xiao Ping, Preliminary test and assay images in colon carcinogenesis. field theory of intersection numbers for shrinkage estimators for the mean of moduli spaces of admissible covers. bivariate normal distribution. Liu, Li-Yu Daisy, Coefficient of intrinsic Folias, Stefanos, Stimulus-induced waves dependence a new measure of associa­ University of Texas, and breathers in synaptically-coupled tion. neural networks. Pokta, Suriani, Bayesian model selection Austin (13) Le, An, Nonlinear eigenvalue problems. using exact and approximated posterior MATHEMATICS Sato, Fumitoshi, Relations in tanto logical probabilities with applications to star rings by localization. data. Baker, Kenneth, Knots on once-punctured torus fibers. Ryu, Duchwan, Bayesian regression anal­ Condon, John, Mahler measure evalua­ VIRGINIA ysis with longitudinal measurements. tions in terms of polylogarithms. Song, ]oon ]in, Bayesian multivariate Fukshansky, Leonid, Algebraic points of Old Dominion spatial models and their applications. small height with additional arithmetic Song, ]uhee, Bootstrapping in a high conditions. University (2) dimensional but very low sample size Kelliher, ]ames, The vanishing viscosity MATHEMATICS AND STATISTICS problem. limit for incompressible fluids in two dimensions. Mav, Deepak, Statistical analysis of longi­ Spinka Holan, Christine, Gene environ­ tudinal and multivariate discrete data. ment interactions in genetic epidemiol­ LaMar, M. Drew, Human acoustics: From ogy. vocal chords to inner ear. Walker, Steven, The straggling Green's function method for ion beam trans­ Lehr, Heather, Analysis of a Darcy-Stokes port. Texas Tech University (5) system modeling fluid flow in vuggy porous media. University of Virginia (6) MATHEMATICS AND STATISTICS Parker, Adam, An elementary construc­ tion of Mo,oOP'r , d). MATHEMATICS Franklin, Scott, A computational three­ field methodology for non-conforming Petersen, Kathleen, One-cusped congru­ Helmstutter, Randall, Quillen equivalent finite elements over partitioned do­ ence subgroups of PSL2(

Guise, Thomas, D-optimal biased coins Chebolu, Sunil, Refinements of chromatic University of Wisconsin, for clinical trials. towers and Krull-Schmidt decomposi­ Madison nol Soukup, Matthew, Evaluating classifica­ tions in stable homotopy categories. tion performance. Hanusa, Christopher, A Gessel-Viennot­ STATISTICS type method for cycle systems with Barrios, Ernesto, Topics on engineering Virginia Polytechnic applications to Aztec pillows. statistics. Institute and State Meyer, Daniel, Melting snowballs. Cheng, Bin, Some hypothesis testing results University (9) Nichifor, Alexandra, Iwasawa theory for for two-way linear models in elliptic curves with cyclic isogenies. clinical trials. MATHEMATICS Skokan, Michael, Regularity of ghosts of Dahl, David, Conjugate Dirichlet pro­ Brunnhofer, Harald, Forced capillary­ geodesic X-ray transform. cess mixture models: Efficient sam­ pling, gene expression and clustering. gravity waves in a 2D rectangular basin. Swanson, jason, Topics in stochastic Chinyoka, Tirivanhu, Numerical simula­ analysis. Hong, Quan, A pseudo empirical likeli­ tion of stratified flows and droplet hood approach to nonignorable nome­ spouse. deformation in 2D shear flow of Newto­ STATISTICS nian and viscoelastic fluids. ]in, Chunfang, Contributions to the de­ Gottardo, Raphael, Robust Bayesian anal­ sign and analysis of quantitative trait Cline, Danny, On the computation of in­ ysis of gene expression microarray loci experiments. variants in non-normal, non-pure cubic data. fields and in their normal closures. Leng, Chenlei, Some problems in model selection. Colon-Reyes, Omar, Monomials dynami­ Washington State cal systems over finite fields. Ma, Shuangge, Penalized M-estimation University (5) for partly linear transformation models Krueger, Denise, Stabilized finite ele­ with current status data. ment methods for feedback control of MATHEMATICS convection diffusion equations. Song, Yang, Two-way latent variable clustering. Pierson, Mark, Theory and application of Edmeade, Dean, Nonlinear stability anal­ a class of abstract differential-algebraic ysis of hexagonal optical pattern for­ Yuan, Ming, Automatic smoothing and equations. mation in an atomic sodium vapor ring variable selection. cavity. Yuan, Zhilong, Designs for phase I cancer Rothstein, Ivan, Semiclassical scattering trials: for two and three body problems. Goff, Matthew, Multivariate discrete phase­ Incorporation of grade informa­ type distributions. tion and multiple risk group studies. Singler, John, Sensitivity analysis of par­ tial differential equations with applica­ Miller, ]ames, Exon and intron detection University of Wisconsin, tions to fluid flow. in human genomic DNA. Milwaukee (2) Vugrin, Kay, On the effects of noise on Nag, Parthasarathi, Energy decay esti­ parameter identification optimization mates for certain class of nonlinear MATHEMATICAL SCIENCES problems. systems arising in models of power systems. Bartl, Michael, On a hyper-Hilbert trans­ form and singular integrals. Sasaki, Takashi, Maxwell's equations WASHINGTON with Yousuf, Muhammad, Smoothing schemes temperature effect. for inhomogenous linear and semilinear parabolic problems with nonsmooth University of data. Washington (15) WEST VIRGINIA APPLIED MATHEMATICS West Virginia WYOMING Farnum, Edward, Stability and dynamics University (2) of solitary waves in nonlinear optical University of Wyoming (4) materials. MATHEMATICS MATHEMATICS Hewitt, Sarah, Dynamics and stability of Martinez-Montejano, Jorge, Results on Christian, justin, Three problems in com­ periodic spatial patterns in the optical hyperspaces. binatorial matrix theory. parametric oscillator. Niu, ]ianbing, Graph minor. Kim, In-]ae, Spectral properties of combi­ Komuro, Rie, Multi-objective evolution­ natorial classes. ary algorithms for ecological process methods. WISCONSIN STATISTICS Medlock; ]an, Integra-differential-equation El-Houbi, Ashraf, Methods for resource models in ecology and epidemiology. Marquette University nl selection studies using correlated data. Pelanti, Marica, Wave propagation algo­ Greenwood, Mark, Functional data analy­ rithms for multicomponent compres­ MATHEMATICS, STATISTICS AND sis for glaciated valley profile analysis. sion flow with applications to volcanic COMPUTER SCIENCE jets. Peters, Matthew, Moist convection and Luo, ]inghui, Construction and analysis the large scale tropical calculation. of airway water clearance models. Williams, David, Solving singular pertur­ bation problems: An amplitude equa­ Medical College of tion approach. Wisconsin (ll

MATHEMATICS BIOSTATISTICS Blair, Matthew, Strichartz estimates for Wong, Hong, Inference for the shared wave equations with coefficients of power variance function frailty model Sobolev regularity. and correlated gamma frailty model.

276 NOTICES OF THE AMS VOLUME 53, NUMBER 2 AMERICAN MATHEMATICAL SOCIETY

THE FISKE SOCIETY The Thomas S. Fiske Society honors individuals who provide for a gift to the American Mathematical Society in their estate plans. They use planned giving to include the AMS in their wills, life insurance policies, or retirement plans.

Such gifts ensure that the AMS will continue to fulfill its mission to promote mathematical research, advance the mathematics profession, support mathematics education at all levels, and foster awareness and appreciation of mathematics well into the future.

Thomas S. Fiske founded the American Mathematical Society in 1888 to foster comradeship and share research through meetings and publications. Fiske Society members hold an honored place in the annals of the Society and in the mathematical community for building on the foundation started by Fiske.

For more information see www.ams.org/giving-to-ams or contact the Development Office, American Mathematical Society, 201 Charles Street, Providence, RI 02904-2294 USA; telephone: 800-321-4267 (U.S. and Canada), 401-455-4000 (worldwide); fax: 401-331-3842; email: [email protected].

www.ams.org From the AMS Secretary

2005 Election Results

In the elections of 2005 the Society elected a president elect, Editorial Boards Committee a vice president, a trustee, five members at large of the Elected as new members of the Editorial Boards Commit­ Council, two members of the Editorial Boards Committee, tee are and three members of the Nominating Committee. Terms Robert L. Bryant from Duke University for these positions are three years beginning on 1 February Stephen Lichtenbaum from Brown University 2006 and ending on 31 January 2009, except for the pres­ ident elect, whose term is for one year (followed by two years Nominating Committee as president and one year as immediate past president), Elected as new members of the Nominating Committee are and for the trustee, whose term is for five years ending on Michael G. Crandall from the University of California 31 January 2011. Members elected to the Nominating at Santa Barbara Committee begin serving immediately, and their terms M. Susan Montgomery from the University of Southern end on 31 December 2008. California Lisa Traynor from Bryn Mawr College President Elect Elected as the new president elect is James G. Glimm from Stony Brook University. Vice President Elected as the new vice president is Ruth M. Charney from Brandeis University. Trustee Reelected as trustee is John B. Conway from the Univer­ sity of Tennessee and the National Science Foundation. Members at Large ofthe Council Elected as new members at large of the Council are William M. Goldman from the University of Maryland Craig L. Huneke from the University of Kansas Judy Anita Kennedy from the University of Delaware Ken Ono from the University of Wisconsin, Madison judy L. Walker from the University of Nebraska

278 N OTICES OF THE AMS VOLUME 53, NUMBER 2 I I 0 ~ Suggestions Your.suggestions are wanted by:

The President, for the following contested seats in the 2006 AMS elections: three members of the Nominating Committee two members of the Editorial Boards Committee

Deadline for suggestions: February 26, 2006

The Editorial Boards Committee, for appointments to various editorial boards of AMS publications

Deadline for suggestions: Can be submitted any time

Send your suggestions for any of the above to: Robert J. Daverman, Secretary American Mathematical Society 312D Ayres Hall University of Tennessee Knoxville, TN 37996-1330 USA email: [email protected]

www. ams.org Nominations by Petition

Vice President or Rules and Procedures Use separate copies of the form for each candidate for vice Member at Large president, member at large, or member of the Nominating One position of vice president and member of the Coun­ and Editorial Boards Committees. cil ex officio for a term of three years is to be filled in the election of 2006. The Council intends to nominate at least 1. To be considered, petitions must be addressed to two candidates, among whom may be candidates nominated Robert]. Daverman, Secretary, American Mathematical by petition as described in the rules and procedures. Society, 312 D Ayres Hall, University of Tennessee, Five positions of member at large of the Council for a Knoxville, TN 37996-1330 USA, and must arrive by term of three years are to be filled in the same election. 25 February 2006. The Council intends to nominate at least ten candidates, 2. The name of the candidate must be given as it appears among whom may be candidates nominated by petition in in the Combined Membership List (www. ams. org/cml ). the manner described in the rules and procedures. If the name does not appear in the list, as in the case of Petitions are presented to the Council, which, accord­ a new member or by error, it must be as it appears in ing to Section 2 of Article VII of the bylaws, makes the nom­ the mailing lists, for example on the mailing label of the inations. The Council of 23 January 1979 stated the intent Notices. If the name of the Council of nominating all persons on whose behalf does not identify the candidate there were valid petitions. uniquely, append the member code, which may be ob­ Prior to presentation to the Council, petitions in support tained from the candidate's mailing label or by the can­ of a candidate for the position of vice president or of mem­ didate contacting the AMS headquarters in Providence ber at large of the Council must have at least fifty valid sig­ ([email protected]). natures and must conform to several rules and opera­ 3. The petition for a single candidate may consist of sev­ tional considerations, which are described below. eral sheets each bearing the statement of the petition, including the name of the position, and signatures. The name of the candidate must be exactly the same on all Editorial Boards Committee sheets. Two places on the Editorial Boards Committee will be filled 4. On the next page is a sample form for petitions. Peti­ by election. There will be four continuing members of the tioners may make and use photocopies or reasonable Editorial Boards Committee. facsimiles. The President will name at least four candidates for these 5. A signature is valid when it is clearly that of the mem­ two places, among whom may be candidates nominated by ber whose petition in the manner described in the rules and procedures. name and address is given in the left-hand The candidate's assent and petitions bearing at least 100 column. valid signatures are required for a name to be placed on 6. The signature may be in the style chosen by the signer. the ballot. In addition, several other rules and operational However, the printed name and address will be checked considerations, described below, should be followed. against the Combined Membership List and the mailing lists. No attempt will be made to match variants of names with the form of name in the CML. A name nei­ Nominating Committee ther in the CML nor on the mailing lists is not that of a Three places on the Nominating Committee will be filled member. (Example: The name Robert]. Daverman is that by election. There will be six continuing members of the of a member. The name R. Daverman appears not to Nominating Committee. be.) The President will name at least six candidates for these 7. When a petition meeting these various requirements ap­ three places, among whom may be candidates nominated pears, the secretary will ask the candidate to indicate by petition in the manner described in the rules and willingness to be included on the ballot. Petitioners can procedures. facilitate the procedure by accompanying the petitions The candidate's assent and petitions bearing at least 100 with a signed statement from the candidate giving valid signatures are required for a name to be placed on consent. the ballot. In addition, several other rules and operational considerations, described below, should be followed.

280 NOTICES OF THE AMS VOLUME 53 NUMBER 2 From the AMS Secretary Nomination Petition for 2006 Election

The undersigned members of the American Mathematical Society propose the name of

as a candidate for the position of (check one): D Vice President D Member at Large of the Council D Member of the Nominating Committee D Member of the Editorial Boards Committee of the American Mathematical Society for a term beginning 1 February, 2007 Return petitions by 25 February 2006 to: Secretary, AMS, 312 D Ayres Hall, University of Tennessee, Knoxville, TN 37996-1330 USA

Name and address (printed or typed)

Signature

Signature

Signature

Signature

Signature

Signature

fEBRUARY 2006 NOTICES OF THE AMS 281 AMERICAN MATHEMATICAL SOCIETY AMS EXEMPLARY PROGRAM PRIZE

At its meeting in January 2004, the AMS Council approved the establishment of a new award called the AMS Award for an Exemplary Program or Achievement in a Mathematics Department. It is to be presented annually to a department that has distinguished itself by undertaking an unusual or particularly effective program of value to the mathematics community, internally or in relation to the rest of society. Examples might include a department that runs a notable minority outreach program, a department that has instituted an unusually effective industrial mathematics intern­ ship program, a department that has promoted mathematics so successfully that a large fraction of its university's undergraduate population majors in mathematics, or a department that has made some form of innovation in its research support to faculty and/or graduate students, or which has created a special and innovative envi­ ronment for some aspect of mathematics research.

The prize amount is $1,200. All departments in North America that offer at least a bachelor's degree in the mathematical sciences are eligible.

The Prize Selection Committee requests nominations for this award, which will be announced at the Joint Mathematics Meetings in New Orleans, Louisiana, in January 2007. Letters of nomina­ tion may be submitted by one or more individuals. Nomination of the writer's own institution is per­ mitted. The letter should describe the specific program( s) for which the department is being nomi­ nated as well as the achievements that make the program( s) an outstanding success, and may include any ancillary documents which support the success of the program(s). The letter should not exceed two pages, with supporting documentation not to exceed an additional three pages.

All nominations should be submitted to the AMS Secretary, Robert J. Daverman, American Mathematical Society, 312D Ayres Hall, University ofTennessee, Knoxville TN 37996-1330. Include a short description of the work that is the basis of the nomination, with complete biblio­ graphic citations when appropriate. The nominations will be forwarded by the Secretary to the Prize Selection Committee, which will make the final decision on the award.

Deadline for nominations is Aprill, 2006. AMERICAN MATHEMATICAL SOCIETY

The selection committee for these prizes requests nominations for con­ sideration for the 2006 awards. Further information about the prizes can be found in the November 2005 Notices, pp. 1251-1255 (also avail­ able at http://www.ams.org/prizes-awards).

Three Leroy P. Steele Prizes are awarded each year in the following cat­ egories: (I) the Steele Prize for Lifetime Achievement: for the cumulative influence of the total mathematical work of the recipient, high level of research over a period of time, particular influence on the development of a field, and influence on mathematics through Ph.D. students; (2) the Steele Prize for Mathematical Exposition: for a book or substantial sur­ vey or expository-research paper; and (3) the Steele Prize for Seminal Contribution to Research: for a paper, whether recent or not, that has proved to be of fundamental or lasting importance in its field, or a model of important research. In 2007 the prize for Seminal Contribution to Research will be awarded for a paper in geometry/topology.

Nominations with supporting information should be submitted to the Secretary, Robert J. Daverman, American Mathematical Society, 312D Ayres Hall, University of Tennessee, Knoxville, TN 37996-1330. Include a short description on the work that is the basis of the nomination, includ­ ing complete bibliographic citations. A curriculum vitae should be included. The nominations will be forwarded by the Secretary to the prize selection committee, which will, as in the past, make final decisions on the awarding of prizes.

Deadline for nominations is March 3 I, 2006. Mathematics Calendar

The most comprehensive and up-to-date Mathematics Calendar information is available one-MATH at http: //www.ams . org/mathcal/.

March 2006 Organizers: Cameron Gordon (Univ. of Texas at Austin), James Howie (Heriot-Watt Univ.), Alan Reid (Univ. of Texas at Austin). * 1 0-12 Recent Developments in Higher Dimensional Algebraic Speakers: Jeffrey Brock (Brown Univ.), David Gabai (Princeton Univ.), Geometry, The Japanese American Mathematics Institute and the Marc Lackenby (Univ. of Oxford), Peter Ozsvath (Columbia Univ.), Johns Hopkins University, Baltimore, Maryland. Peter Shalen (Univ. of Illinois at Chicago), Ian Agol (Univ. of Illinois Topics: Birational geometry and topics related to the minimal model at Chicago), Michel Boileau (Univ. Paul Sabatier, Toulouse), Brian program. Of special interest are new developments concerning Bowditch (Univ. of Southampton), Martin Bridson (Imperial College), derived categories of coherent sheaves, Fano varieties, Mori-Fano Shelly Harvey (Rice Univ.), Craig Hodgson (Univ. of Melbourne), fiber spaces, the explicit geometry of threefolds, minimal log Hyam Rubinstein (Univ. of Melbourne), Zlil Sela (Hebrew Univ.), discrepancies, new points of view on singularities, and rational Richard Weidmann (Univ. of Frankfurt). curves on varieties. Deadline: The meeting is limited in numbers in order to maintain its Organizers: J. Kollar (Princeton University), S. Mori (RIMS- Kyoto), workshop character. Applications are invited now. An application V. Shokurov (Johns Hopkins University), N. Budur (Johns Hopkins form may be found on the website. The application period will University). AdditionalPrincipalJapanese Organizers: S. Ishii (Tokyo close on January 15, 2006. Instiute of Technology), Y. Kawamata (University of Tokyo), and S. Information: http : I /www. icms. org. uk/meetings/2006/ Mukai (RIMS-Kyoto). 3-manifolds/index.html. Invited Speakers: A. Bondal, A. Corti, R. Lazarsfeld, Y. Kawamata, J. McKernan, S. Mukai, M. Mustata, A. Pukhlikov, K. Smith, J. Starr. '' 1 7-19 Transport Properties of Random Schrodinger Operators, Information: http://www.mathematics . jhu.edu/new/jami/ University of Kentucky, Lexington, Kentucky. Jami2006. htm. Organizers: Jean Bellissard, Georgia Institute of Technology, Peter D. Hislop, University of Kentucky. * 1 3-1 7 Workshop on 3-manifolds after Perelman, International Program: This is an intensive, three-day workshop on transport Centre for Mathematical Sciences, Edinburgh, United Kingdom. properties of Schrodinger operators with random potentials and Workshop Summary: The objective of this workshop is the exam­ related problems of transport theory. The focus will be on topics ination of recent developments in 3-dimensional topology in the of recent research including linear response theory and kinetic light of Perelman's probable proof of Thurston's Geometrization equations, noncommutative geometry and the quantum Hall effect, Conjecture, and of other important advances such as the proof of edge and bulk conductivities, the Kubo formula for conductivity, Thurston's Ending Lamination Conjecture, and of Marden's Tame­ classical and quantum diffusion, and other transport phenomena ness Conjecture and the development of Heegaard Floer homology in random media. The workshop consists of hour-long expository theory. The meeting will take stock of the subject and set out talks by leading researchers in random Schrodinger operators and directions for future research. transport theory, short talks by new researchers in the field, a

respect This section contains announcements of meetings and conferences to participation in the meeting, this fact should be noted. All communications of interest to some segment of the mathematical public, including ad 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 specialized topics, as well as announcements of regularly scheduled to notices@ams. org 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 An announcement will be published in the Notices if it contains a call prior to 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 the speakers; a second announcement will be published only if there months prior to the scheduled date of the meeting. The are changes or necessary additional information. Once an announcement complete listing of the Mathematics Calendar will be published only in the September has appeared, the event will be briefly noted in every third issue until issue of the Notices. The March, June/July, and it has been held and a reference will be given in parentheses to the December issues will include, along with new announcements, references to any previously month, year, and page of the issue in which the complete information announced meetings and conferences occurring within the twelve-month appeared. Asterisks ('') mark those announcements containing new or period following the month of those issues. New information revised information. about meetings and conferences that will occur later than the twelve-month In general, announcements of meetings and conferences held in North period will be announced once in full and will not be America carry only the date, title of meeting, place of meeting, names of repeated until the date of the conference or meeting falls within the twelve-month speakers (or sometimes a general statement on the program), deadlines period. The Mathematics Calendar, for abstracts or contributed papers, and as well as Meetings and Conferences of source of further information. the AMS, is Meetings held outside the North American area may carry more detailed now available electronically through the AMS website on the World Wide Web. To access the AMS website, use the URL: information. In any case, if there is any application deadline with http: I /www . ams .erg/.

284 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Mathematics Calendar

poster session, and round table discussions on open problems and material sciences, engineering, mathematics etc. The interest for new directions. operating efficiently HFC is constantly increasing as HFC produce Partially Sponsored by: Institute for Mathematics and its Applica­ free pollution electrical power. This workshop will be focused tions, University of Kentucky, Georgia Institute of Technology. on numerical, computational and mathematical analysis of HFC Confirmed Invited Speakers (as of November 2005):: Michael dynamics. Modeling will be an important face of the workshop. Aizenman (Princeton University), Jean-Michel Combes (Universite de Invited Speakers: Ned Djilali, University of Victoria, Computational Toulon, France), Laszlo Erdos (Ludwig-Maxilmilianssitat Munchen, and modeling fuel cell dynamics; two-phase transport dynamics Germany), Gian Michele Graf (ETH Zurich, Switzerland), Fran~ois in gas diffusive layers; Yalchin Efendiev, Texas A&M University, Germinet (Universite de Cergy-Pontoise, France), Dirk Hundertmark Multiscale analysis and computation of multiphase flows in het­ (University of Illinois, Urbana-Champaign), Abel Klein (University erogeneous porous media; Peter Minev, University of Alberta, Mul­ of California, Irvine), Michael Loss (Georgia Institute of Technol­ tiphase computational fluid dynamics; Keith Promislow, Michigan ogy, Atlanta), Jeff Schenker (ETH Ziirich, Swittzerland,) Hermann State University, Phase change and Hysteresis in Proton Exchange Schulz-Baldes (Friedrich-Alexander-UniversitatErlangen-Niirnberg, Membrane Fuel Cells. Germany,) Gunter Stolz (University of Alabama, Birmingham), Do­ Registration Fee: The registration fee is $100 CAN for all academic minique Spehner (Universite ]Joseph Fourier, Grenoble, Franc). and industrial researchers, $50 CAN dollars for students. The Information and Registration: http : I /www.math. uky. edu/ invited speakers are free of registration fees. -hislop/ima06/. Travel Support: Please note that travel and accommodation support will be available for students. Interested students must contact '' 24-25 Complex Geometry (in honor of Domingo Toledo's 60th Arian Novruzi at novruzi@uottawa. ca. birthday), University of Utah, Salt Lake City, Utah. Information: http: I /www. fields . utoronto. ca/programs/ Organizing Committee: Jim Carlson, Bill Goldman. scientific/05-06/fuelcells/index.html. Speakers: Daniel Allcock (Univ. of Texas), Luis Hernandez (CIMA T), Misha Kapovich (Univ. Calif., Davis), Bruno klingler (Univ. of '' 1 5-1 7 The First International Conference on Mathematical Chicago), Janos Kollar (Princeton Univ.), Yum-Tong Siu (Harvard Sciences, Al-Azhar University, Gaza, The Palestinian Authority. Univ.), Dennis Sullivan (Stony Brook Univ.). Description: The main objective of the conference is to get an Information: http: I /www. math. utah. edu/ complexgeometry or international scientific gathering at our University. We would like to contact Mary Levine, email: mlevine@math. utah. edu, tel: 80 l- overcome the deliberate policy of isolating our people and scientific 581-6841; fax: 801-581-4148. institutions, and to involve the Palestinian researchers in contact with International Researchers in their fields. April 2006 Topics: Pure Mathematics, Applied Mathematics, Mathematical Physics, Theoretical and applied Mechanics, Probability and Statis­ * 1-2 Graduate Student Topology Conference, Indiana University, tics, Biometrics, Computer Sciences. Bloomington, Indiana. Sponsor: Al Azhar University; http: I /www. alazhar-gaza. edu/ Objectives: The goal of the Graduate Student Topology Conference ICMS; email: m. okasha@palnet . com. is to gather graduate students in topology and provide them with the opportunity to give talks, communicate recent advances, and Deadline: February 28, 2006. hear from established researchers in the field. Information: Dr. Mahmoud K. Okasha, Head of the Organizing Plenary Speaker: V. Jones (Berkeley), D. McDuff (Stony Brook). Committee, Al-AzharUniversity, Gaza, P.O. Box 1277, Gaza; email:m. Deadline: February 15, 2006. okasha@alazhar-gaza. edu and m. okasha@palnet . com; tel: +970- Information: To register, to apply to give a talk, or to ask for 599-441133. funding, go to http: I /www . indiana. edu;-gstc/; email: gstc@ '' 1 5-1 7 Workshop on Probabilistic Symmetries and their Appli­ indiana. edu. cations, University of Ottawa, Ottawa, Ontario, Canada. '' 23-May 6 Rigidity and Flexibility (ESI-Program 2006), The Inter­ Introduction: In probability theory, random objects may have in­ national Erwin Schriidinger Institute for Mathematical Physics (ESI), teresting and important symmetry properties: i.e. distributional Vienna, Austria. invariance under a particular family of measurable transformations. Description: This program of the International Erwin Schrodinger The best known symmetries include stationarity, contractability, Institute for Mathematical Physics (ESI) is aimed at the study of exchangeability and rotatability (invariance under shifts, contrac­ various flexible and rigid structures such as flexible polyhedra and tions, permutations and rotations, respectively). Stationarity is a frameworks, polyhedral herissons and virtual polytopes, smooth classical concept which is treated in most standard textbooks, and herissons and smooth surfaces. Within this program the two so the goal of the workshop is to introduce participants to the workshops 1. Flexibility of Polyhedra and Frameworks 2. Herissons remaining three symmetries and their applications. and Virtual Polytopes will be organized in cooperation with the Speakers: Main Speaker: Professor Olav Kallenberg (Auburn Univer­ Institute of Discrete Mathematics and Geometry of the Vienna sity, Alabama). Invited Speakers: Professor Neville Weber (University University of Technology. The organizers of this program invite of Sydney, Australia), Professor Fabio Spizzichino (Universita La persons interested in the above-mentioned topics to take part Sapienza-Rome, Italy), Professor Andre Dabrowski (University of in this program, to share ideas and experiences among different Ottawa). disciplines. Registration Fees: The registration fees for this workshop have Organizers: Victor Alexandrov, Sobolev Institute of Mathematics, been set at $80 per participant ($40 for students). Registration Novosibirsk; Idzhad Kh. Sabitov, Moscow State University; Hellmuth forms should be submitted by April 21, 2006. Stachel, Vienna University of Technology. Information: http: I /www. mathstat. uottawa. car gi vanoff I Information: http : I /www. geometrie. tuwien. ac. at/ esi/. workshop. htm.

May 2006 '' 16-1 8 LMS Workshop on Cluster Algebras and Teichmiiller Theory, University of Leicester, Leicester, United Kingdom. * 1 0-12 Workshop on Numerical, Mathematical and Modeling lnformation:http: I /www . math .le. ac. uk/RESEARCH/LMS/webpage . Analysis Related to Fluid Dynamics in Hydrogen Fuel Cells, html. University of Ottawa, Ottawa, Ontario, Canada. Workshop Description: Hydrogen fuel cells (HFC) are on the * 30-June 2 Geometry and Representation Theory: A conference focus of research of several scientific areas, such as chemistry, in honor of George Lusztig, M.I.T., Cambridge, Massachusetts.

FEBRUARY 2006 NOTICES OF THE AMS 285 Mathematics Calendar

Information: http: I /math. mit. edu/ conferences/lusztig60/ of Chicago, USA), M. Rapoport (Math. Institut, Universitiit Bonn, index. html. Germany), M. Saito (RIMS, Kyoto, Japan), T. Tsuji (Tokyo University, Japan), E. Viehweg (Essen, Germany), C. Voisin (Paris 7, France). june 2006 Deadlines: Support, Housing & Registration: February 1, 2006. Housing & Registration: March 1, 2006. Registration: May 1, 2006. * 4-1 0 Workshop on Commutative Rings, Cortona, Italy. Sponsors: Clay Mathematics Institute (USA), European Research Aim: To bring together researchers in the area of commutative ring Networks, "Arithmetic Algebraic Geometry" and "Algebraic K­ theory. theory, Linear Algebraic Groups & Related Structures", Italian Topics: The main emphasis of the workshop is on factoriza­ Research Network "Geometria sulle Varieta' Algebriche" financed tion and divisibility properties, decomposition of ideals, class by MIUR Universities of Padova, Milano and Venice International groups; multiplicative ideal and module systems, star and semis tar University. operations, Gabriel-Popescu localizing systems; Prufer domains Information: http : I /www .mat . uniroma3. it/GVA/HTVIU/. and their generalizations; Krull and Mori domains; integer val­ ued polynomials; chain conditions and prime spectra; analytically '' 1 9-July 7 Computational Number Theory and Applications to irreducible one-dimensional rings and their value semigroups; Cryptography, University of Wyoming, Laramie, Wyoming. one-dimensional Noetherian rings and algebroid curves. Young Purpose: To bring participants up to speed on the most recent researchers interested in these areas are welcome. developments in computational number theory and mathematical Scientific Committee: Valentina Barucci (Univ. degli Studi "La cryptography. Participants will be introduced to the theory and Sapienza"), Paul-Jean Cahen_(Univ. Paul Cezanne, Aix-Marseille III), applications of computational number theory and its consequences Marco Fontana (Univ. degli Studi "Roma Tre"), Stefania Gabelli (Univ. for cryptography. The conference will take place immediately before degli Studi "Roma Tre"), Evan G. Houston (Univ. of North-Carolina, the Fall 2006 Fields Institute Thematic Program in Cryptography. Charlotte). Speakers: E. Bach (University of Wisconsin-Madison), M. Bauer Organizing Committee: Florida Girolami (Univ. degli Studi "Roma (University of Calgary), M. Jacobson (University of Calgary), E. Gorla Tre"), Giampaolo Picozza (Univ. degli Studi "Roma Tre"), Francesca (University of Zurich), C. Pomerance (Dartmouth College), R. Schei­ Tartarone (Univ. degli Studi "Roma Tre"). dler (University of Calgary), 0. Schirokauer (Oberlin College),].H. Main Sponsor: NdAM (Istituto Nazionale di Alta Matematica). Silverman (Brown University), ]. Sorenson (Butler University),A. Information: http : I /www .mat. uniroma3 . it/users/ cortona/ Stein (University of Wyoming, E. Teske (University of Waterloo), cortona_2006 . html;email: cortona2006©mat. uniroma3. it. N. Theriault (University of Waterloo), H.C. Williams (University of Calgary). '' 1 2-1 5 Journees Peter Shalen, Centre de Recherches Mathema­ tiques, Montreal, Quebec, Canada. Sponsors: Rocky Mountain Mathematics Consortium, The Fields Organizers: Steve Boyer, Dick Canary, Marc Culler, Nathan Dunfield, Institute, Alberta Informatics Circle of Research Excellence (iCORE), Benson Farb. and the University of Wyoming. IMA funding pending. Speakers (''tentative): Ian Agol (Univ. of Illinois at Chicago), Mladen Deadline: For application/call for papers: April1, 2006. Bestvina (Univ. of Utah), Marc Culler (Univ. of Illinois at Chicago), Organizers: M.]. Jacobson, (University of Calgary), A.D. Porter, B.L. Nathan Dunfield (Caltech), Cameron Gordon (Univ. of Texas), ''Alex Shader, A. Stein (University of Wyoming). Lubotzky (Hebrew Univ. of Jerusalem), Yair Minsky (Yale Univ.), Information: Contact: A. Stein, Mathematics Department, University *Maryam Mirzakhani (Princeton Univ./Clay Institute), John Morgan of Wyoming, Laramie, WY 82071; email: astein©uwyo. edu; http: (Columbia Univ.), ''Lenhard Ng (Stanford Univ. I AIM), Peter Ozsvath //math.uwyo.edu/RMMC/2006/rmmc06.html. (Columbia Univ.), Jake Rasmussen (Princeton Univ.), Michah Sageev (Technion). * 20-22 International Conference on Mathematical, Statistical, Information: http: I /www. math. uic. edu/ j ournees. and Computer Methods in HIV/AIDS, Regal Kowloon Hotel, East Kowloon, Hong Kong. '' 12-1 6 EMS mathematical weekend in Pays de Loire, Universite Purpose: To bring together researchers from all over the world to de Nantes, Nantes, France. discuss methods for accurate estimates and future predictions of Topics: With plenary lectures and parallel sessions, the conference HIV I AIDS incidence and prevalence in different parts of the world. will focus on five topics: Inverse problems, chair Roman Novikov; Information: email: aggarwal©math . ucalgary. ca. Large scale stochastics, chair Philippe Carmona; Complex algebraic geometry, chair Christoph Sorger; Global analysis, chair Gilles * 29-July 4 21th International Conference on Operator Theory, Carron; Real algebraic varieties, chair Adam Parusinski. West University, Timisoara, Romania. Organizers: Mathematical Institutes from Angers and Nantes, with Topics: Operator theory, operator algebras and their applications. the support of SMF and SMA!. Steering Committee: W. B. Arveson, K. R. Davidson, N. K. Nikolskii, Information: http : I /www .math. sciences. univ-nantes. fr/ S. Stratila, F.-H. Vasilescu. WEM2006; email: wem2006©math .univ-nantes .fr. Information: http : I /www. imar .rorot.

'' 1 9- 24 Hodge Theory, Venice International University, Venice­ july 2006 Island of San Servolo, Italy. Workshop Topics: This meeting is intended to present the state '' 1 7-2 1 Classification theory for abstract elementary classes, of the art in Hodge Theory covering the full range of its current AIM Research Conference Center, Palo Alto, California. developing topics as well as the interrelation between them: from Topics: This workshop, sponsored by AIM and the NSF, will focus classical transcendental methods and algebraic cycles to mixed, on Shelah's categoricity conjecture for abstract elementary classes. arithmetic, p-adic structures and motives. Thirty years ago Saharan Shelah proposed a far reaching program Organizers: L. Barbieri-Viale (Padova), B. Chiarellotto (Padova), H. of extending first-order classification theory for non-elementary Esnault (Essen), B. Van Geemen (Milano). classes. This workshop will be dedicated to discussing the present Speakers (preliminary list): S. Bloch(University of Chicago, USA) , C. state of Shelah's conjectures as well as the broader program of Breuil (CNRS & IHES, France), G. Faltings (MPI, Bonn, Germany), ].-M. developing a classification theory for abstract elementary classes. Fontaine (Universite de Paris-Sud, Orsay, France), P. Griffiths (lAS, Organizers: Rami Grossberg and Monica VanDieren. Princeton, USA) , U. J annsen (Univ. ofRegensburg, Germany), L. Illusie Deadline: April15, 2006. (Universite de Paris-Sud, Orsay, France), K. Kato (Kyoto University, Information: http:/ /aimath. org/ ARCC/workshops/ Japan), K. S. Kedlaya (MIT, Boston, USA), M. Nori (University categoricity.html.

286 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Mathematics Calendar

'' 1 ?-August 11 Clay Mathematics Institute 2006 Summer School: of Mongolia and the Institute of Mathematics, National University Arithmetic Geometry, Mathematisches Institut, Georg-August­ of Mongolia. Universitat, Gottingen, Germany. Topics: Algebra (ring theory, module theory, commutative algebra Description: Designed for graduate students and mathematicians and etc.), Functional analysis, Applied mathematics and numerical within five years of their Ph.D., the program will introduce the analysis, Probability theory and mathematical statistics, Geometry participants to modern techniques and outstanding conjectures at and topology, Applied Mathematics and Optimization, Mathematical the interface of number theory and algebraic geometry. Education. Topics: This school will offer three core courses (on curves, surfaces, Information: email: mekei@num. edu .mn. and higher-dimensional varieties), supplemented by seminars on computational and algorithmic aspects of arithmetic geometry, August2006 and by mini-courses on more advanced topics. Organizers: Jim Carlson, Henri Damon, David Ellwood, Brendan '' 7- 11 Partial Differential Equations on Noncompact and Singular Hassett and Yuri Tschinkel). Manifolds, University of Potsdam, Potsdam, Germany. Topics Include: Qualitative Theory of PDEs (Regularity, Asymp­ Lecturers: Dan Abramovich, Fedor Bogomolov, Antoine Chambert­ totics), Geometric Analysis on Singular Spaces, K-theoretic Methods, Loir, Ching-Li Chai, Henri Damon, David Harari, Brendan Hassett, Operator Algebra Aspects, Boundary Value Problems, Noncommu­ Andrew Kresch, Yuri Marrin, Frans Oort, Jason Starr, Yuri Tschinkel tative Geometry, Quantization. and others. Organizing Committee: B. Fedosov (Moscow), G. Grubb (Copen­ Deadline: For application is February 28, 2005. For more in­ hagen), T. Krainer (Potsdam), V. Nistor (Penn State), L. Rodino formation and an application form see http: I /www. claymath. (Torino), B.-W. Schulze (Potsdam), N. Tose (Tokyo), M. W. Wong org/ summerschool or contact email: summerschool@claymath . org; (Toronto). telephone: 617-995-2600. Information: PDEs on Noncompact and Singular Manifolds c / o T. Krainer and B.-W. Schulze, Institut fUr Mathematik, Univer­ '' 24-28 2nd SIPTA School on Imprecise Probabilities, Rey Juan sitat Potsdam, Postfach 60 15 53, Carlos University, Madrid, Spain. D-14415 Potsdam, Germany; email:[email protected];http ://pdensm.math.uni­ Organizer: By the International Society for Imprecise Probability: pot sdam. de. Theories and Applications (SIPTA) and by the Group of Statistics and Decision Sciences (GECD) from Rey Juan Carlos University. '' 14-1 8 International Conference on Spectral Theory and Global Information: You can find all the relevant information on http : I I Analysis, Carl von Ossietzky University, Oldenburg, Germany. bayes.escet.urjc.es/-emiranda/sipta. Topics will include: Spectral asymptotics, Scattering theory, Index Theory and Hodge Theory, Spectral Invariants, Analysis on singular '' 24-28 Brazilian Operator Algebras Conference, Florianopolis, and non-compact spaces. Brazil. Organizing Committee: D. Grieser (Oldenburg), T. Krainer (Pots­ Information: http: I /mtm. ufsc. brrexel/oa/. dam), A. Vasy (Stanford). Information: Spectral Theory and Global Analysis, c/ o Prof. Daniel * 24-August 4 Pan-American Advanced Studies Institute (PASI): Grieser, Institut fUr Mathematik, Universitat Oldenburg, D-26111 Analysis and Probability in Quantum Physics, San Joaquin Oldenburg, Germany; email: stga@mathematik. uni -oldenburg. campus, Pontificia Catolica de Chile, Santiago, Chile. de; http ://www.mathematik.uni -oldenburg.de/personen/ Program: The PASI Institute is a two-week program for advanced grieser/stga/. graduate students, post-docs, and assistant professors from the Americas. There will be 6 four-hour minicourses during the first August 2007 week and an international workshop during the second week. Full support is available for Institute students; partial support is '' 3-6 First Announcement ACA'2007: 13th International Confer­ available for workshop participants. ence on Applications of Computer Algebra, Oakland University, Minicourses and their Presenters: Ira W . Herbst, University of Rochester, Michigan. Virginia, The Spectral and Scattering Theory of Quantum Particles Conference Theme: The ACA series of conferences is devoted to in External Fields, Abel Klein, University of California, Irvine, promoting the applications and development of Computer Algebra Random Schrodinger Operators, Jean Bellissard, Georgia Institute and Symbolic Computation. Topics include Computer Algebra and of Technology, Theory of Quantum Transport, Richard Froese, Symbolic Computation in engineering, the sciences, medicine, pure University of British Columbia, Theory of Quantum Resonances, and applied mathematics, education, communication and computer Rafael Benguria, Pontificia Universidad Cat6lica de Chile, Stability science. of Matter and Quantum Field Theory, Laszlo Erdos, Ludwig­ General Chairs: Tony Shaska, Erich Kaltofen, Jaime Gutierrez, Maximilians-Universitiit Munchen, Classical and Quantum Brownian Alexander Hulpke. Motion. Program Chair: Tony Shaska. Workshop: The International Workshop on Analysis and Probability Organizing Committee: Stanly Steinberg, Michael Wester. in Quantum Physics will highlight recent advances in the topics Important Dates: May 15, 2007: Deadline to submit an application discussed during the first week mini-courses. In addition to invited for financial support. June 15, 2007: Notification of decisions for talks by international experts, the PASI students will have the financial support. June 15, 2007: Deadline for early registration. opportunity to present their own research. July 15, 2007: Deadline for regular registration. August 3-6, 2007 Support: PASI is primarily supported by the U.S. National Science Conference Foundation and the Department of Energy. Information: Contact: shaska@oakland. edu;http: I /www . oakl and. Information: Full information, a list of the confirmed Workshop edu/-shaska/aca07 .html. participants, online application forms, etc. available at http: 11 www.ms.uky .edu/-pasi06/.

'' 25-27 International Conference on Mathematics, Institute of Mathematics, National University of Mongolia, Ulaanbaatar, Mon­ golia. Organizer: The Mathematical Society of Mongolia jointly with School of Mathematics and Computer Science, National University

fEBRUARY 2006 NOTICES OF THE AMS 287 New Publications Offered by the AMS

Relatively Algebra and Algebraic ME1Yl9IRS Hyperbolic Geometry AmerlcanMathematlcalSoclety Groups: Intrinsic Relatively Hyperbolic Geometry, Algebraic Groups: Intrinsic Geometry, Properties, and Algebraic Properties, The Theory of and Algorithmic Problems Algorithmic Problems THE THEORY OF Den ts V. Osin GROUP CHARACTERS Group Characters Denis V. Osin AND MATRIX REPRESENTATIONS and Matrix Contents: Introduction; Relative Amorka o Mnthem.tJcol Soct

DUDLEY E. LITTLEWOOD of Groups hyperbolic groups; Algebraic properties; Algorithmic Second Edition problems; Open questions; Appendix. Equivalent definitions of AMS CKJ:U.Sl!A Pt'BLISBD<<; relative hyperbolicity; Bibliography. Dudley E. Littlewood Memoirs of the American Mathematical Society, Volume 179, Number 843 Originally written in 1940, this book remains a classical source on December 2005, 100 pages, Softcover, ISBN 0-8218-3821-0, LC representations and characters of finite and compact groups. 2005053663, 2000 Mathematics Subject Classification: 20F65; The book starts with necessary information about matrices, 20F05, 20F06, 20Fl0, 20F67, 20F69, Individual member algebras, and groups. Then the author proceeds to US$35, List US$ 58, Institutional member US$46, Order code representations of finite groups. Of particular interest in this MEM0/ 179/ 843 part of the book are several chapters devoted to representations and characters of symmetric groups and the closely related theory of symmetric polynmnials. The Analysis concluding chapters present the representation theory of classical compact Lie groups, including a detailed description of representations of the unitary and orthogonal groups. The The Calculus of book, which can be read with minimal prerequisites (an ME1~19IRS undergraduate algebra course), allows the reader to get a good AmcrlcanMnthemntlcalSoclety One-Sided M-ldeals understanding of beautiful classical results about group The Calculus of and Multipliers in representations. One-Sided M-Ideals and Multipliers Operator Spaces This item will also be of interest to those working in discrete in Operator Spaces mathematics and combinatorics. David P. Blecher David P. Blecher and Contents: Matrices; Algebras; Groups; The Frobenius algebra; Vrej Zartklan Vrej Zarikian The symmetric group; Immanants and S-functions; S-functions Contents: of special series; The calculation of the characters of the Introduction; Preliminaries; AmerlennMathemaUealSoclety Spatial symmetric group; Group characters and the structure of action; Examples; Constructions; One-sided groups; Continuous matrix groups and invariant matrices; type decompositions and Groups of unitary matrices; Appendix; Bibliography; Morita equivalence; Central M -structure for operator Supplementary bibliography; Index. spaces; Future directions; Appendix A. Some results from Banach space theory; Appendix B. Infinite matrices AMS Chelsea Publishing over an operator space; Appendix. Bibliography. March 2006, 310 pages, Hardcover, ISBN 0-8218-4067-3, 2000 Memoirs of the American Mathematical Society, Volume 179, Mathematics Subject Classification: 20Cxx, Individual member Number 842 US$41, List US$45, Order code CHEL/357.H December 2005, 85 pages, Softcover, ISBN 0-8218-3823-7, LC 2005053579, 2000 Mathematics Subject Classification: 46L07, 46L89; 46B20, 46B04, Individual member US$35, List US$ 58, Institutional member US$46, Order code MEM0/179/842

288 NOTICES OF THE AMS VOLUME 53, NUMBER 2 New Publications Offered by the AMS

Wave Packet techniques minimal but giving detailed proofs and many CBMS examples and illustrations from physics and celestial Analysis mechanics. After all, the celestial N-body problem is the origin of dynamical systems and gave rise in the past to many Christoph Thiele mathematical developments. Wave Packet Analysis The concept of "wave packet analysis" ]llrgen Moser (1928-1999) was a professor at the Courant originates in Carleson's famous proof Institute, New York, and then at ETH Zurich. He served as Christoph Thiele of almost everywhere convergence of president of the International Mathematical Union and Fourier series of L 2 functions. It was received many honors and prizes, among them the Wolf Prize later used by Lacey and Thiele to in mathematics. Jiirgen Moser is the author of several books, prove bounds on the bilinear Hilbert among them Stable and Random Motions in Dynamical transform. For quite some time, Systems. Eduard Zehnder is a professor at ETH Zurich. He is Carleson's wave packet analysis was coauthor with Helmut Hofer of the book Symplectic Invariants thought to be an important idea, but and Hamiltonian Dynamics. that it had limited applications. But in recent years, it ha.s This item will also be of interest to those working in analysis. become clear that this is an important tool for a number of other applications. This book is an introduction to these tools. Titles in this series are copublished with the Courant Institute of Math­ ematical Sciences at New York University. It emphasizes the classical successes (Carleson's theorem and the Hilbert transform) in the main development. However, the Contents: Transformation theory; Periodic orbits; Integrable book closes with a dedicated chapter on more recent results. Hamiltonian systems; Bibliography. Carleson's original theorem is sometimes cited as one of the Courant Lecture Notes, Volume 12 most important developments of 20th century harmonic January 2006, 256 pages, Softcover, ISBN 0-8218-3577-7, LC analysis. The set of ideas stemming from his proof is now 2005055871, 2000 Mathematics Subject Classification: 37-01, seen as an essential element in modern harmonic analysis. 37Kxx, 53Dxx, 58Exx, 70Fxx, 70H05, All AMS members Indeed, Thiele won the Salem prize jointly with Michael Lacey US$27, List US$34, Order code CLN/12 for work in this area. The book gives a nice survey of important material, such as an overview of the theory of singular integrals and wave packet analysis itself. There is a separate chapter on "further A Geometric I ME¥,,9IRS developments", which gives a broader view on the subject, AmerlcllliMothematlcaiSnciety Mechanism for though it does not exhaust all ongoing developments. A Geometric Mechanism Contents: Introduction; Wavelets and square functions; for Diffusion in Hamiltonian Diffusion in Systems Overcoming the Interpolation of multilinear operators; Paraproducts; Wave Large Gap Problem; Heuristics and Rigorous Hamiltonian Systems packets; Multilinear forms with modulation symmetries; Verifi cation on a Model

Carleson's theorem; The Walsh model; Further applications of Amad ~ : \1 Dd shmns Overcoming the Rarae lrle la Llave wave packet analysis; Bibliography. Large Gap Problem: CBMS Regional Conference Series in Mathematics, Number

105 Am~riean MUh~matiul Society Heuristics and February 2006, 86 pages, Softcover, ISBN 0-8218-3661-7, 2000 Rigorous Verification Mathematics Subject Classification: 42-02; 42A99, 47H60, 42A20, All Individuals US$23, List US$29, Order code on a Model CBMS/105 Amadeu Delshams, Rafael de la Llave, and Tere M. Seara Contents: Introduction; Heuristic discussion of the mechanism; A simple model; Statement of rigorous results; Differential Equations Notation and definitions, resonances; Geometric features of the unperturbed problem; Persistence of the normally hyperbolic invariant manifold and its stable and unstable manifolds; The dynamics in A,; The scattering map; Existence of transition chains; Orbits shadowing the transition chains and proof of Theorem 4.1; Conclusions and remarks; An Notes on Dynamical example; Acknowledgments; Bibliography. Notes on Systems Memoirs of the American Mathematical Society, Volume 179, Dynamical Number 844 Systems Jiirgen Moser and Eduard J. Zehnder December 2005, 141 pages, Softcover, ISBN 0-8218-3824-5, LC 2005053662, 2000 Mathematics Subject Classification: 3 7]40, This book is an introduction to the 37C29, 34C37; 70H08, 37C50, 34C29, Individual member ' " ·····::.:-.-::~::::::::::~~~:: ~6_/vl.~ field of dynamical systems, in US$37, List US$62, Institutional member US$50, Order code particular, to the special class of MEM0/179/ 844 Hamiltonian systems. The authors aimed at keeping the requirements of mathematical

FEBRUARY 2006 NOTICES OF THE AMS 289 New Publications Offered by the AMS

and expositors is intended to capture the essence of the Discrete Mathematics and Coxeter legacy. It is a mixture of surveys, up-to-date information, history, storytelling, and personal memories; and Combinatorics it includes a rich variety of beautiful illustrations. This item will also be of interest to those working in discrete mathematics and combinatorics. A Sharp Threshold Contents: B. Miihlherr, The isomorphism problem for Coxeter MEM9IRS groups; A. V. Borovik, Coxeter theory: The cognitive aspects; AmerlcnnMBthematlca.ISoclety for Random Graphs M. Ronan, From Galois and Lie to Tits buildings; B. Kostant, A Sharp Threshold with a The Coxeter element and the branching law for the finite for Random Graphs with subgroups of SU(2); R. Kellerhals, Hyperbolic Coxeter groups a Monochromatic Triangle Monochromatic in Every Edge Coloring and space forms; P. McMullen and E. Schulte, Regular and

E:hutlFrledgu t chiral polytopes in low dimensions; B. Monson and Voj terh ROdl Triangle in Every Andrt.ej Ruch'oskl A. I. l'rnsmi TetaU Weiss, Polytopes, honeycombs, groups and graphs; Edge Coloring J. M. Wills, Equivelar polyhedra; A. Khovanskii, Combinatorics Ehud Friedgut, Vojtech Rodl, of sections of polytopes and Coxeter groups in Lobachevsky spaces; M. Senechal, Donald and the golden rhombohedra; Andrzej Rucinski, and Prasad B. Griinbaum, Configurations of points and lines; J. Richter­ Tetali Gebert, Meditations on Ceva's theorem; D. Schattschneider, Coxeter and the artists: Two-way inspiration; M. Emmer, The Contents: Introduction; Outline of the proof; Tepees and visual mind: Art, mathematics and cinema; Publications of H. constellations; Regularity; The core section (Proof of Lemma S. M. Coxeter; Index. 2.4); Random graphs; Summaryt, further remarks, glossary; Bibliography. March 2006, 321 pages, Hardcover, ISBN 0-8218-3722-2, 2000 Mathematics Subject Classification: 01A99, 14M25, 20E42, Memoirs of the American Mathematical Society, Volume 179, 20F55, 22E46, 51A20, 51M20, 52B15, 52C23, Number 845 52B70, All AMS members US$ 55, List US$69, Order code COXETER December 2005, 66 pages, Softcover, ISBN 0-8218-3825-3, LC 2005053660, 2000 Mathematics Subject Classification: 05Cl5; 05C55, 05C80, Individual member US$30, List US$ 50, Institutional member US$40, Order code MEM0/ 179/845 Geometry and Topology

General and Translations of Generalized MATHEMATICAL Interdisciplinary MONOGRAPHS Cohomology Akira Kono and Dai Tamaki ~ Generalized Cohomology In the 1950s, Eilenberg and Steenrod The Coxeter Legacy presented their famous Akira Kono characterization of homology theory Reflections and 'Dai Tamaki by seven axioms. Somewhat later, it Projections was found that keeping just the first six of these axioms (all except the Chandler Davis and Erich W. condition on the "homology" of the Ellers, Editors point), one can obtain many other interesting systems of algebraic invariants of topological Donald Coxeter infused enthusiasm, manifolds, such as K-theory, cobordisms, and others. These even passion, for mathematics in theories come under the common name of generalized people of any age, any background, homology (or cohomology) theories. any profession, any walk of life. Enchanted by Euclidean geometry, he The purpose of the book is to give an exposition of was interested in the beauty, the description, and the generalized (co)homology theories that can be read by a wide exploration of the world around us. His involvement in art and group of mathematicians who are not experts in algebraic with artists earned him admiration and friends in the topology. It starts with basic notions of homotopy theory and intellectual community all over the globe. Coxeter's devotion then introduces the axioms of generalized (co)homology to polytopes and his interest in the theory of configurations theory. Then the authors discuss various types of generalized live on in his students and followers. Coxeter groups arise in cohomology theories, such as complex-oriented cohomology various subjects in applied mathematics, and they have a theories and Chern classes, K-theory, complex cobordisms, permanent place in some of the most demanding and and formal group laws. A separate chapter is devoted to fascinating branches of abstract mathematics, such as Lie spectral sequences and their use in generalized cohomology algebras, algebraic groups, Chevalley groups, and Kac-Moody theories. groups. This collection of articles by outstanding researchers

290 NOTICES OF THE AMS VOLUME 53, NUMBER 2 New Publications Offered by the AMS

The book is intended to serve as an introduction to the subject for mathematicians who do not have advanced Number Theory knowledge of algebraic topology. Prerequisites include standard graduate courses in algebra and topology, with some knowledge of ordinary homology theory and homotopy theory. Algebraic Numbers Contents: Preliminaries; Generalized cohomology; and Algebraic Characteristic classes of vector bundles; K-theory; Spectral sequence; Complex cobordism and its applications; Simplicial Functions techniques; Limits; Spectrum; Bibliography; Index. Emil Artin Translations of Mathematical Monographs (Iwanami Series in Famous Norwegian mathematician Modern Mathematics), Volume 230 Niels Henrik Abel advised that one March 2006, approximately 272 pages, Softcover, ISBN 0-8218- should "learn from the masters, not 3514-9 , 2000·Mathematics Subject Classification: 55N20; from the pupils". When the subject is 55N15, 55N22, 55N40, 55T05, 55-02, All AMS members algebraic numbers and algebraic US$39, List US$49, Order code MMON0/230 functions, there is no greater master than Emil Artin. In this classic text, originated from the notes of the course given at Princeton University in 1950-1951 and first published in 1967, one has a beautiful introduction to the subject accompanied by Artin's unique insights and perspectives. The exposition starts with A First Course in the general theory of valuation fields in Part I, proceeds to the local class field theory in Part II, and then to the theory of Topology function fields in one variable (including the Riemann-Roch Continuity and theorem and its applications) in Part III. Dimension Prerequisites for reading the book are a standard first-year graduate course in algebra (including some Galois theory) and John McCleary elementary notions of point set topology. With many examples, this book can be used by graduate students and all How many dimensions does our mathematicians learning number theory and related areas of universe require for a comprehensive algebraic geometry of curves. physical description? In 1905, Poincare argued philosophically about the necessity of the three familiar Contents: General valuation theory: Valuations of a field; dimensions, while recent research is based on 11 dimensions Complete fields; e, f and n; Ramification theory; The different; or even 23 dimensions. The notion of dimension itself Local class field theory: Preparations for local class field presented a basic problem to the pioneers of topology. Cantor theory; The first and second inequalities; The norm residue asked if dimension was a topological feature of Euclidean symbol; The existence theorem; Applications and illustrations; space. To answer this question, some important topological Product formula and function fields in one variable: ideas were introduced by Brouwer, giving shape to a subject Preparations for the global theory; Characterization of fields whose development dominated the twentieth century. by the product formula; Differentials in P F-fields; The Riemann-Roch theorem; Constant field extensions; The basic notions in topology are varied and a comprehensive Applications of the Riemann-Roch theorem; Differentials in grounding in point-set topology, the definition and use of the function fields; Theorems on p-groups and Sylow groups; fundamental group, and the beginnings of homology theory Index of symbols; Subject index. requires considerable time. The goal of this book is a focused introduction through these classical topics, aiming throughout AMS Chelsea Publishing at the classical result of the Invariance of Dimension. January 2006, 349 pages, Hardcover, ISBN 0-8218-4075-4, This text is based on the author's course given at Vassar 2000 Mathematics Subject Classification: 11-01, llRxx, llSxx, College and is intended for advanced undergraduate students. Individual member US$44, List US$49, Order code It is suitable for a semester-long course on topology for CHEL/358.H students who have studied real analysis and linear algebra. It is also a good choice for a capstone course, senior seminar, or independent study. Contents: A little set theory; Metric and topological spaces; Geometric notions; Building new spaces from old; Connectedness; Compactness; Homotopy and the fundamental group; Computations and covering spaces; The Jordan Curve Theorem; Simplicial complexes; Homology; Bibliography. Student Mathematical Library, Volume 31 April 2006, approximately 216 pages, Softcover, ISBN 0-8218- 3884-9, 2000 Mathematics Subject Classification: 54-01, 55-01, 54F45, All AMS members US$28, List US$35, Order code STML/31

FEBRUARY 2006 NOTICES OF THE AMS 291 New Publications Offered by the AMS

Measure Theoretic other countries should be sent to the SMF. Members of the SMF receive MEJY!9IRS a 30% discount from list. tlmencnn~1nthemntka!Soc1 e ty Laws for lim sup Sets Contents: P. Beelen, A. Garcia, and H. Stichtenoth, On towers f volumo \79Numbl:r8-46 of function fields over finite fields; M. Bras-Amor6s, Addition Measure Theoretic Victor Beresnevich, Detta Laws for behavior of a numerical semigroup; 0. Moreno and lim sup Sets Dickinson, and Sanju Velani F. N. Castro, On the calculation and estimation of Waring number for finite fields; G. Frey and T. Lange, Mathematical Victor Beresnevtch Contents: Introduction; Ubiquity and Oetta Dickinson background of Public Key Cryptography; A. Garcia, On curves Sanju Velani conditions on the general setp; The over finite fields; F. Hajir, Tame pro-p Galois groups: A survey statements of the main theorems; Remarks and corollaries to Theorem 1· of recent work; E. W. Howe, K. E. Lauter, and J. Top, Pointless curves of genus three and four; D. Le Brigand, Real quadratic Amer~c a nMathemoiLcalSoc1cly Remarks and corollaries to Theorem 2: The classical results; Hausdorff ' extensions of the rational function field in characteristic two· measures and dimension; Positive and S. R. Louboutin, Explicit upper bounds for the residues at ' full m-measure sets; Proof of s = 1 of the Dedekind zeta functions of some totally real Theorem 1; Proof of Theorem 2: number fields; S. Ballet and R. Rolland, On the bilindar complexity of the multiplication in finite fields; Yu. G. Zarhin, 0 s; G < oo; Proof of Theorem 2: G = oo; Applications; Bibliography. Homomorphisms of abelian varieties. Memoirs of the American Mathematical Society, Volume 179, Serninaires et Congres, Number 11 Number 846 September 2005, 216 pages, Softcover, ISBN 2-85629-175-9, December 2005, 91 pages, Softcover, ISBN 0-8218-3827-X, LC 2000 Mathematics Subject Classification: 14H05, 14G05, 2005053661, 2000 Mathematics Subject Classification: 11]83, 11G20, 20M99, 94B27, 11T06, 11T71, 11R37, 14G1~ 14G15, 11]13, 11K60, 28A78, 28A80, Individual member US$35, List 11R58, 11A55, 11R42, llYxx, 12E20, 14H40, 14K05, US$ 58, Institutional member US$46, Order code Individual member US$53, List US$ 59, Order code SEC0/ 11 MEM0/ 179/ 846

Logic and Foundations

New AMS-Distributed The Continuum Publications A Constructive Approach to Basic Concepts of Real Analysis Rudolf Taschner, Vienna University of Technology, Austria, Editor Geometry and Topology In this small text the basic theory of the continuum, including the elements of metric space theory and continuity, is developed within the system of intuitionistic mathematics in Arithmetic, Geometry and Coding the sense of L.E.}. Brouwer and H. Weyl. The main features are proofs of the famous theorems of Browuer concerning the Theory (AGCT 2003) continuity of all functions that are defined on " whole " intervals, the uniform continuity of all functions that are Yves Aubry and Gilles Lachaud, Institut de defined on compact intervals and the uniform convergence of Mathematiques de Luminy, Marseille, France, all pointwise converging sequences of functions defined on Editors compact intervals. The constructive approach is interesting both in itself and as a contrast to, for example, the formal In May 2003, two events were held in the CIRM (Marseille­ axiomatic one. Luminy) devoted to arithmetic, geometry and their applications in coding theory and cryptography: a European A publication of Vieweg Verlag. The AMS is exclusive distributor in North America. Vieweg Verlag Publications are available worldwide school "Algebraic Geometry and Information Theory" and the from the AMS outside of Germany, Switzerland, Austria, and Japan. 9th international conference "Arithmetic, Geometry and Coding Theory". Some of the courses of the conferences are Contents: Introduction and historical remarks; Real numbers; published in this volume. Topics covered include: Abelian Metric spaces; Continuous functions; Literature; Index. varieties, function fields and curves over finite fields, Galois Vieweg Monographs group of pro-p extensions, Dedekind zeta functions of September 2005, 136 pages, Hardcover, ISBN 3-8348-0040-6, number fields, numerical semigroups, Waring numbers, 2000 Mathematics Subject Classification: 03F55, 26A03, All bilinear complexity of the multiplication in finite fields and AMS members US$43, List US$48, Order code VW / 13 class number problems. A publication of the Societe Mathematique de France, Marseilles (SMF), d1stnbuted by the AMS in the U.S., Canada, and Mexico. Orders from

292 NOTICES OF THE AMS VOLUME 53, NUMBER 2 AMERICAN MATHEMATICAL SOCIETY

Math in the Media is a great way to keep The Feature Column is a series of essays on abreast of math news as reported in news~ various mathematical topics-such as voting, papers and general science magazines. The Penrose tiles, cosmology; and networks­ collection-Tony Phillips' Take on Math in written by David Austin, Bill Casselman, the Media, Math Digest, and Reviews of books, Joe Malkevitch, and Tony Phillips. plays, and films with mathematical themes-is a centralized repository of articles in the media about mathematics.

A in"' t he MEDIA ~OLUMN ''"'''"L '" •'•'"'""''''"'''~ Jlllj A Month/If MaRa;:zw from the Amerwm Mathemalnnl SvucJu "~~·$!'§_ ' , I!!II ITony Phillips' Take on Math in the Penrose Tilings Tied up in Ribbons ~fj_ < ' lfH l l lll~ lDMedia How can we create a tiling by Penrose rh¢11\bs that will cove:: !:.he entire plane

These ,.,..,b c~say'> ::ue. dc siOJned for thosc who havc already While Penrosetllingsarebothmathematical!yintercstingandaesthetically discovered the joys ot m~themlltics pleasing, constructing the5e tilings is a particularly import3ntlssuc since Mathematician Adam as "'ell as for those who may be • Penfi eld NY, a front in "the nationwide math wars ~ t:heyseemtomodel the structure ofquasicrystalsappearing inthcnat\Jral uncomfortable witn mathem~tks . Log<:~n w ins the 2005 world . As we 5aw in this ~ pa ce las t AuoJU 5t. however, constructing Penrose Mathematics is a fast growing and • Glacial climate cycles and the least common multiple tilingsisnoteasyforthefirstapproachthatcomestomindtypicallytails. evolving subject. The domain of World Scrabble ways that mat h emati~s is being • Math on the Millennium Bridge Championship. lro this column, we will first review some of what was discussed in the applied is gro,..ing by leaps and previous column ~nd then describe three methods for constructing Penrose bounds. Examples include CT scans, Penfield 1\l." . a front in "the nationwide m.ath wars" tilings, each of which presents a differentperspe~tive on the tifings. ~udio CD's, facerecognitionsystems, IIII and cell phone technology. Our goal I is to share our eKcitement about Samuel G. Freedman's On Education column in the November 9 2005 New these developments with you. Feature Column York Times reports from Penfield NY, a community which "has become one of the most obvious fronts in the nationwide math wars." These are Recent News the wars "t hat pit progressives against traditionalists, with nothing less ttt ~ : •~~r.!____T~ Ne~·Js from the D.C. than America's educational and economic competitiveness at stake. " Office ltllr.

This Hathematical • Novemb er: The l~at h e m a t i ca l Month • Joe Hoover: "took his daughter, Kathryn, then in sixth grade, to Uncerta·.,,ty Pr inciple • Octob er: Mental C ~ lr;ul<~tion For Journalists lunch at McDonald's and realized she could not compute the correct • Septem ber. Sijlts and Chips • Augu st : Penrose Tiles Talk Press Releases change for their m eal from a $20 bill," Across Mites • Claudia Lioy: spotted her daughter Iris '' plodding t hrough a • June/July: Topology of Venn AHS in the News [)jagrams multiplication pr oblem by counting 23 groups of four apples," • May: Siingshots anCI Space Sh ots Classified Advertisements Positions available, items for sale, services available, and more

degrees and the department is actively in­ Affirmative Action/Equal Opportunity Em­ KENTUCKY volved in teacher preparation. ployer. Western Kentucky University enrolls ap­ 000226 WESTERN KENTUCKY UNIVERSITY proximately 18,000 undergraduate and Department of Mathematics graduate students, including more than Applications are invited for the position of 1,400 minority and 500 international stu­ MARYLAND Head of the Department of Mathematics dents, and has a strong commitment to starting July 1, 2006. achieving diversity among faculty, staff, THE JESS & MILDRED FISHER COLLEGE Applicants must have a doctorate in and administration. The university is in OF SCIENCE& MATHEMATICS mathematics or a mathematical science Bowling Green, between Louisville and Department of Mathematics with appropriate credentials for a tenured Nashville, TN. Assistant Professor, Mathematics appointment at the rank of professor. We Review of applications will begin Janu­ are seeking a dedicated and effective leader ary 16, 2006, and will continue until the Applicants are invited to apply for a who can help promote and strengthen the position is filled. Please send a letter of ap­ tenure-track appointment in applied math­ department's academic, research, and ser­ plication, vita, a statement of administra­ ematics at the rank of Assistant Professor vice programs. Qualified candidates must tive leadership philosophy, and at least beginning Fall 2006. Position is contin­ have an established record of high qual­ three letters of recommendation to: gent on final funding approval for FY 07. ity teaching and research/scholarly activ­ Dr. Keith Andrew, Chair, Preference will be given to candidates that ity and a history of significant professional Mathematics Head Search Committee can support the Department of Mathe­ service. Evidence of additional adminis­ Dept. of Physics and Astronomy matics graduate program in Applied and trative expertise is desired. Qualified can­ Western Kentucky University Industrial Mathematics. The salary is com­ didates must also be committed to recog­ 1906 College Heights Boulevard petitive. Applicants must have an earned nizing and encouraging excellence in #11077 doctorate in mathematics at time of hire. teaching and research/scholarly activity, Bowling Green, KY 42101-1077 Applicants must possess a commitment to and be familiar with current issues in­ teaching, an active research program, email: and volving the mathematics curriculum and the ability to teach a variety of courses, [email protected] at technology. both the undergraduate and graduate lev­ Mathematics is one of nine departments For more information about the Depart­ els. in the College of Science and Engineering. ment of Mathematics at Western Kentucky The Department of Mathematics With 35 full-time positions (23 tenured/ University, visit our web page at http: I I http: I /www. towson. edu/math offers bach­ tenure-track), the department offers bac­ www.wku.edu/math. elor's degree programs in pure mathe­ calaureate and masters programs in math­ All qualified individuals are encouraged matics, applied mathematics, actuarial sci­ ematics. In addition, mathematics is in­ to apply including women, minorities, per­ ence and risk management, and cluded in the university general education sons with disabilities, and disabled veter­ mathematics education. Master's degree requirements for all undergraduate ans. Western Kentucky University is an programs are offered in applied and

Suggested uses for classified advertising are positions available, books issue-February 28, 2006; June/July 2006 issue-April 28, 2006, August 2006 or lecture notes for sale, books being sought, exchange or rental of houses, issue-May 26, 2006; September 2006 issue-June 27, 2006. and typing services. U.S. laws prohibit discrimination in employment on the basis of color, age, The 2006 rate is $100 per inch or fraction thereof on a single column (one­ sex, race, religion, or national origin. "Positions Available" advertisements inch rnirtimum), calculated from top of headline. Any fractional text of 1/ 2 from institutions outside the U.S. cannot be published unless they are inch or more will be charged at the next inch rate. No discounts for multi­ accompanied by a statement that the institution does not discriminate on ple ads or the same ad in consecutive issues. For an additional $10 charge, these grounds whether or not it is subject to U.S. laws. Details and spe­ announcements can be placed anonymously. Correspondence will be cific wording may be found on page 1373 (vol. 44). forwarded. Situations wanted advertisements from involuntarily unemployed math­ Advertisements in the "Positions Available" classified section will be set ematicians are accepted under certain conditions for free publication. Call with a rnirtimurn one-line headline, consisting of the institution name above toll-free 800-321-4AMS (321-4267) in the U.S. and Canada or 401-455-4084 body copy, unless additional headline copy is specified by the advertiser. worldwide for further information. Headlines will be centered in boldface at no extra charge. Ads will appear Submission: Promotions Department, AMS, P.O. Box 6248, Providence, in the language in which they are submitted. Rhode Island 02940; or via fax: 401-331-3842; or send email to There are no member discounts for classified ads. Dictation over the cl assads@ams . or g. AMS location for express delivery packages is telephone will not be accepted for classified ads. 201 Charles Street, Providence, Rhode Island 20904. Advertisers will be Upcoming deadlines for classified advertising are as follows: March 2006 billed upon publication. issue-December 30, 2005; April 2006 issue-January 31, 2006; May 2006

294 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Classified Advertisements industrial mathematics, and mathematics students. Candidates with a recent Ph.D. education. and with outstanding research potential SWITZERLAND Applicants should submit a letter of ap­ will be given higher priority. plication, a resume, a description of re­ Please apply to Human Re sources, The UNIVERSITY OF FRIBOURG search, a statement of teaching experience Cooper Union, 30 Cooper Square, NYC Department of Mathematics and philosophy, and copies of all gradu­ 10003 or [email protected]. The Cooper The Department for Mathematics at the ate transcripts. Additionally, three letters Union is an AA/EOE employer. of recommendation, addressing both University of Fribourg (Switzerland) in­ teaching and research should be sent to: 000203 vites applications for the following posi­ tions: Dr. Raouf Boules, Chairperson, Search Committee l. Senior Assistant in Analysis and its Department of Mathematics RHODE ISLAND Applications: Towson University It is part of the duties of the senior as­ 8000 York Road ROGER WILLIAMS UNIVERSITY sistant to teach 4 to 6 hours a week on all Towson, MD 21252-0001 levels, mainly in analysis. An intensive re­ Math Faculty Positions search activity is expected. She or he will Applications or material sent by email or Bristol, Rl supervise master theses, coach seminars, facsimile will not be considered. Priority and participate in administrative tasks of will be given to applications received on The Mathematics Department of the Fein­ the department. The successful candidate or before February 15, 2006. stein College of Arts and Sciences invites will have earned a Ph.D. in mathematics, Towson University is an Equal Oppor­ applications for two tenure-track posi­ show strong promise of excellence in tunityI Affirmative Action Employer and tions, both at the rank of Assistant Pro­ teaching, and have a strong research has a strong institutional commitment to fessor, to begin in Fall 2006. Candidates record. The position starts October 1, 2006. diversity. Women, minorities, persons with for the first position should specialize in 2. Doctor assistant in Applied Mathe­ disabilities, and veterans are encouraged some area of analysis, while the second po­ matics: to apply. sition is open to candidates in any area of This is a postdoc position with teaching 000228 specialization. The primary emphasis of ei­ duties. Preference will be given to candi­ ther position is teaching both majors and dates in the field of numerical analysis/sta­ non-majors in an undergraduate setting, tistics. Good knowledge of scientific com­ MASSACHUSETTS but an ongoing program of publishable puting and willingness to participate in research and a commitment to depart­ statistical consulting is expected. The po­ WILLIAMS COLLEGE mental and university-wide service are also sition starts September l, 2006. Department of Mathematics expected. A Ph.D. in mathematics at the Both positions are limited to 5 years. and Statistics time of appointment is required. Success The candidates are supposed to master in obtaining grants and at least three years French or German and to understand the Williams College Department of Mathe­ other language. Send letter of application, matics and Statistics invites applications of full-time teaching experience are highly current vita, references and research plan for a newly authorized visiting position in desirable. to the address below before March l, 2006. mathematics for the 2006-2007 year, prob­ For a full job description please visit For additional information, please con­ ably at the rank of assistant professor, http://www. rwu.edu. tact: however, in exceptional cases, a more ad­ To apply send resume to: Roger Williams Prof. Dr. Norbert Hungerbuhler vanced appointment might be considered. University, Office of Human Resources, Department of Mathematics A Ph.D. is required. Send a vita and three One Old Ferry Road, Bristol, RI 02809 or University of Freiburg, Perolles letters of recommendation on teaching email: human_resources@rwu. edu. Appli­ CH -1700 Freiburg and research to: Visitor Hiring Committee, cations will be considered starting Janu­ http://www.unifr.ch/math Department of Mathematics and Statis­ ary 15,2006. Equal Opportunity/Affirma­ email: tics, Williams College, Williamstown, MA tive Action/ Americans with Disabilities [email protected] 01267. Consideration of applications will Act Employer with a strong commitment 000229 begin on November 15th and continue until the position is filled. Williams College to diversity. is dedicated to providing a welcoming in­ 000227 tellectual environment for all of its faculty, staff and students; as an AA/EOE em­ ployer, Williams especially welcomes ap­ GUAM plications from women and minority can­ didates. UNIVERSITY OF GUAM 000102 Department of Mathematics Asst/As soc Prof. Math vacancy at UOG. NEW YORK Ph.D. (req.) in Math Sci (prefer Pure/Ap­ plied, Math Stat). Send CV, 3 ref. letters, THE COOPER UNION copies of grad transcripts, GovGuam ap­ for the Advancement of Science & Art plication to Chair, Math Search, HRO, UOG, Department of Mathematics Mangilao, GU 96923. Visit http: I /www. uog. edu or email crmtai ta@uog9. uog. edu. The Department of Mathematics in the No email app. accepted. EEO/ AA Emp. School of Engineering invites applications 000206 for a full-time tenure-track faculty position to commence September 2006. Applicants must have a Ph.D. in mathematics and a strong ability to teach mathematics to ex­ ceptionally qualified undergraduate fEBRUARY 2006 NOTICES OF THE AMS 295 General Information Regarding Meetings &Conferences of the AMS

Speakers and Organizers: The Council has decreed that no on orgamzmg a Special Session, see www. ams. o rg/ paper, whether invited or contributed, may be listed in the pro­ meetings/ specialsessionmanual.html. gram of a meeting of the Society unless an abstract of the paper Contributed Papers: The Society also accepts abstracts has been received in Providence prior to the deadline. for ten-minute contributed papers. These abstracts will be Although an individual may present only one ten-minute grouped by related Mathematical Reviews subject classifica­ contributed paper at a meeting, any combination of joint au­ tions into sessions to the extent possible. The title and thorship may be accepted, provided no individual speaks author of each paper accepted and the time of presentation more than once. An author can speak by invitation in more will be listed in the program of the meeting. than one Special Session at the same meeting. Other Sessions: In accordance with policy established by Special Sessions: The number of Special Sessions at an An­ the AMS Committee on Meetings and Conferences, mathe­ nual Meeting is limited. Special Sessions at annual meetings maticians interested in organizing a session at an annual or are held under the supervision of the Program Committee for sectional meeting on employment opportunities inside or National Meetings and, for sectional meetings, under the outside academia for young mathematicians should contact supervision of each Section Program Committee. They are the associate secretary for the meeting with a proposal by administered by the associate secretary in charge of that the stated deadline. Also, potential organizers for poster meeting with staff assistance from the Meetings and Confer­ sessions on a topic of choice should contact the associate ences Department in Providence. (See the list of associate secretary before the deadline. secretaries on page 311 of this issue.) Abstracts: Abstracts for all papers must be received by the Each person selected to give an Invited Address is also in­ meeting coordinator in Providence by the stated deadline. vited to generate a Special Session, either by personally or­ Unfortunately, late papers cannot be accommodated. ganizing one or by having it organized by others. Proposals Submission Procedures: Visit the Meetings and Confer­ to organize a Special Session are sometimes solicited either ences homepage on the Web at http: I jwww. ams. org/ meet­ by a program committee or by the associate secretary. Other ings and select "Submit an abstract". proposals should be submitted to the associate secretary in See the inside front cover of Abstracts ofPapers Presented to charge of that meeting (who is an ex officio member of the pro­ the American Mathematical Society for information on abstracts gram committee) at the address listed below. These propos­ published by title and not presented at a meeting. als must be in the hands of the associate secretary at least seven Site Selection for Sectional Meetings months (for sectional meetings) or nine months (for national Sectional meeting sites are recommended by the associate meetings) prior to the meeting at which the Special Session is secretary for the section and approved by the Secretariat. to be held in order that the committee may consider all the Recommendations are usually made eighteen to twenty-four proposals for Special Sessions simultaneously. Special Sessions months in advance. Host departments supply local informa­ must be announced in the Notices in a timely fashion so that tion, ten to fifteen rooms with overhead projectors for con­ any Society member who so wishes may submit an abstract tributed paper sessions and Special Sessions, an auditorium for consideration for presentation in the Special Session. with twin overhead projectors for Invited Addresses, space for Talks in Special Sessions are usually limited to twenty min­ registration activities and an AMS book exhibit, and registra­ utes; however, organizers who wish to allocate more time to tion clerks. The Society partially reimburses for the rental of individual speakers may do so within certain limits. A great facilities and equipment and for staffing the registration desk. many of the papers presented in Special Sessions at meetings Most host departments volunteer; to do so, or for more in­ of the Society are invited papers, but any member of the So­ formation, contact the associate secretary for the section. ciety who wishes to do so may submit an abstract for con­ sideration for presentation in a Special Session, provided it is submitted to the AMS prior to the special early deadline for consideration. Contributors should know that there is a limit to the size of a single Special Session, so sometimes all places are filled by invitation. Papers submitted for consideration for inclusion in Special Sessions but not accepted will receive con­ sideration for a contributed paper session, unless specific instructions to the contrary are given. The Society reserves the right of first refusal for the pub­ lication of proceedings of any Special Session. If published by the AMS, these proceedings appear in the book series Contemporary Mathematics. For more detailed information

296 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Meetings & Conferences oftheAMS

IMPORT ANT INFORMATION REGARDING MEETINGS PROGRAMS: AMS Sectional Meeting programs do not appear in the print version of the Notices. However, comprehensive and continually updated meeting and program information with links to the abstract for each talk can be found on the AMS website. See http: I jwww. ams. org/meeti ngs/. Final programs for Sectional Meetings will be archived on the AMS website accessible from the stated URL and in an electronic issue of the Notices as noted below for each meeting.

Karen V. H. Parshall, University of Virginia, The British de­ Miami, Florida velopment of the theory of invariants, 1841-1895. Florida International University Michael S. Vogelius, Rutgers University, Electromagnetic imaging- An applied analyst's perspective. April1-2, 2006 Special Sessions Saturday - Sunday Approximation Theory and Orthogonal Polynomials (Code: Meeting #1 015 SS SA), Doron S. Lubinsky, Georgia Institute of Technol­ Southeastern Section ogy, and Edward B. Saff, Vanderbilt University. Associate secretary: Matthew Miller Commutative Algebra and Algebraic Geometry (Code: SS Announcement issue of Notices: January 2006 lA), Laura Ghezzi, Florida International University, Huy Program first available on AMS website: February 16, 2006 Tai Ha, Tulane University, and Aron Simis, University Fed­ Program issue of electronic Notices: April 2006 eral de Pernambuco. Issue of Abstracts: Volume 27, Issue 2 Composition Operators and Complex Dynamical systems Deadlines (Code: SS 16A), Brian P. Kelly, University of Louisiana, Monroe, and Christopher N. B. Hammond, Connecticut For organizers: Expired College. For consideration: of contributed papers in Special Sessions: Expired Financial Mathematics (Code: SS 17A), Alec N. Kercheval For abstracts: February 7, 2006 and Craig A. Nolder, Florida State University. Geometry of Banach Spaces and Connections with Other The scientific information listed below may be dated. For Areas (Code: SS llA), Edward W. Odell, University of the latest information, see www. ams. o rg/ amsmtgs/ Texas at Austin, Thomas B. Schlumprecht, Texas A&M Uni­ sectional.html. versity, and Stephen Dilworth, University of South Carolina. Geometry of Riemannian Manifolds with Additional Struc­ Invited Addresses tures (Code: SS 2A), Tedi C. Draghici, Gueo V. Grantcharov, Andrea R. Nahmod, University of Massachusetts, Amherst, and Philippe Rukimbira, Florida International University. Bilinear operators in analysis and PDEs. Harmonic Analysis and Partial Differential Equations (Code: Edward Odell, University of Texas at Austin, Embeddings SS lOA), Mario Milman, Florida Atlantic University, and in Banach space theory. Marius Mitrea, University of Missouri.

FEBRUARY 2006 NOTICES OF THE AMS 297 Meetings & Conferences

History of Mathematics (Code: SS 18A), Karen H. Parshall, Program issue of electronic Notices: April 2006 University of Virginia. Issue of Abstracts: Volume 27, Issue 2 Imaging, Homogenization, and Shape Optimization (Code: Deadlines SS 14A), MichaelS. Vogelius, Rutgers University, and Shari Moskow, University of Florida. For organizers: Expired For consideration of contributed papers in Special Sessions: Interpolation Theory and Applications (Code: SS 15A), Expired Michael Cwikel, Technion, Laura De Carli, Florida Inter­ For abstracts: February 14, 2006 national University, and Mario Milman, Florida Atlantic University. The scientific information listed below may be dated. For Invariants of Low-Dimensional Manifolds (Code: SS 9A), the latest information, see www.ams.org/amsmtgs/ Thomas G. Lennes, Florida International University, and sectional.html. Nikolai N. Saveliev, University of Miami, Coral Gables. Mathematical Models in Image and High-Dimensional Data Invited Addresses Analysis (Code: SS 13A), Hanna E. Makaruk and Robert M. Douglas N. Arnold, Institute for Math and Applications, Owczarek, Los Alamos National Laboratory, and Nikita University of Minnesota, Title to be announced. Sakhaneko, University of New Mexico and Los Alamos National Laboratory. Bela Bollobas, University of Memphis and Cambridge Uni­ versity, Inhomogeneous random graphs (Erdos Memorial Monomials and Resolutions (Code: SS 3A), Joseph P. Bren­ Lecture). nan, North Dakota State University, and Heath M. Martin, University of Central Florida. Steven C. Hofmann, University of Missouri, Title to be announced. Nonlinear Waves (Code: SS 19A), Andrea R. Nahmod, Uni­ versity of Massachusetts, Amherst, and Sijue Wu, Univer­ Michael Larsen, University of Indiana, Title to be sity of Michigan at Ann Arbor. announced. Partial Differential Equations and Several Complex Variables Christopher M. Skinner, University of Michigan, Title to (Code: SS 6A), Shiferaw Berhanu, Temple University, and be announced. Hamid Meziani, Florida International University. Special Sessions Qualitative Analysis ofPartial Differential Equations (Code: SS 4A), Congming Li, University of Colorado. Algebraic Structures of Exactly Solvable Models (Code: SS 9A), Michael Gekhtman, University of Notre Dame, Mikhail Recent Developments on Fluid and Geophysical Fluid Dy­ Shapiro, Michigan State University, and Alexander Stolin, namics (Code: SS 12A), C. Cao and T. Tachim Medjo, University of Gothenburg. Florida International University, and X. Wang, Florida State University. Analysis and Geometry ofNon-linear Evolution and Equations (Code: SS 19A), Alexandrou A. Himonas and Gerard K. Singular Integrals, Geometric Analysis, and Free Boundary Misiolek, University of Notre Dame. Problems (Code: SS 8A), Marianne Korten and Charles N. Moore, Kansas State University. Combinatorial Algebraic Geometry (Code: SS 2A), Juan C. Migliore, University of Notre Dame, and Uwe R. Nagel, Uni­ Spectral Geometry ofManifolds with Boundary and Singular versity of Kentucky. Spaces (Code: SS 20A), Juan B. Gil, Pennsylvania State Uni­ versity, Altoona, and Patrick T. McDonald, New College, Commutative Algebra and Algebraic Geometry (Code: SS University of South Florida. lA), Alberto Corso, University of Kentucky, Claudia Polini, University of Notre Dame, and Bernd Ulrich, Purdue Uni­ Structure ofFunction Spaces and Applications (Code: SS 7A), versity. Jan Lang, The Ohio State University, and Osvaldo Mendez, University of Texas at El Paso. Developments and Applications in Differential Geometry (Code: SS 4A), Jianguo Cao, Xiaobo Liu, and Brian Smyth, University of Notre Dame. Notre Dame, Indiana Dynamical Systems (Code: SS lOA), Francois Ledrappier, University of Notre Dame, and Arnie Wilkinson, North­ University of Notre Dame western University. April8-9, 2006 Harmonic Analysis, PDE and Geometric Function Theory (Code: SS 14A), John L. Lewis, University of Kentucky, and Saturday - Sunday Steve C. Hofmann, University of Missouri. Meeting #1 016 Holomorphic Methods and Heat Kernels in Harmonic Analy­ Central Section sis and Quantization Theory (Code: SS 16A), Brian Hall and Associate secretary: Susan]. Friedlander William Kirwin, University of Notre Dame. Announcement issue of Notices: January 2006 Mathematical Biology (Code: SS llA), Mark Alber and Bei Program first available on AMS website: February 23, 2006 Hu, University of Notre Dame.

298 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Meetings & Conferences

Model Theory and Computability (Code: SS 8A), Steven The scientific information listed below may be dated. For Allen Buechler, Julia Knight, and Sergei Starchenkoa, the latest information, see www. ams. org/amsmtgs/ University of Notre Dame, and Steffen Lempp, University sectional . html. of Wisconsin. New Developments in Optimization (Code: SS lSA), Leonid Invited Addresses Faybusovich, University of Notre Dame. Ailana M. Fraser, University of British Columbia, Title to Nonlinear Waves (Code: SS 13A), MarkS. Alber and Pavel be announced. Lushnikov, University of Notre Dame, and Ildar Gabotiv Dmitri Nikshych, University of New Hampshire, Algebraic and Vladimir E. Zakharov, University of Arizona. theory of tensor categories. Number Theory (Code: SS 21A), Scott T. Parsell and Florian Pop, University of Pennsylvania, Title to be an­ Jonathan P. Sorenson, Butler University. nounced. Numerical Solution of Polynomial Systems (Code: SS 7A), Konstantina Trivisa, University of Maryland, College Park, Christopher S. Peterson, Colorado State University, and Title to be announced. Andrew J. Sommese, University of Notre Dame. PDEs and Geometric Analysis (Code: SS 22A), Matt Gursky Special Sessions and Qing Han, University of Notre Dame. Algebraic Groups (Code: SS SA), George J. McNinch, Tufts Several Complex Variables (Code: SS 6A), Nancy K. Stan­ University, and Eric Sommers, University of Massachusetts­ ton and jeffrey A. Diller, University of Notre Dame. Amherst. Special Functions and Orthogonal Polynomials (Code: SS SA), Arithmetic Geometry and Modular Forms (Code: SS 6A), Diego Dominici, State University of New York at New Paul E. Gunnells and Farshid Hajir, University of Massa­ Paltz. chusetts, Amherst. Topics in Representation Theory (Code: SS 17A), Sam Evens, Arrangements and Configuration Spaces (Code: SS lOA), University of Notre Dame, and Jiu-Kang Yu, Purdue Uni­ Graham C. Denham, University of Western Ontario, and versity. Alexander I. Suciu, Northeastern University. Topology and Physics (Code: SS 18A), Stephan A. Stolz and Banach Lattices, Regular Operators, and Applications (Code: Bruce Williams, University of Notre Dame. SS 3A), A. K. Kitover, Community College of Philadelphia, Undergraduate Mathematical Research (Code: SS 20A), M. Orhon, University of New Hampshire, and A. W. Wick­ Francis X. Connolly, University of Notre Dame, and stead, Queen's University of Belfast. Zsuzsanna Szaniszlo, Valparaiso University. Banach Spaces ofAnalytic Functions (Code: SS 2A), Rita A. Water Waves (Code: SS 12A), David Nicholls, University of Hibschweiler, University of New Hampshire, and Illinois at Chicago. Thomas H. MacGregor, SUNY Albany and Bowdoin College. Discrete and Convex Geometry (Code: SS lA), Daniel A. Klain, University of Massachusetts (Lowell), Barry R. Mon­ Durham, New son, University of New Brunswick, and Egon Schulte, Hampshire Northeastern University. Galois Theory in Arithmetic and Geometry (Code: SS 8A), University of New Hampshire Florian Pop and David Harbater, University of Pennsyl­ vania, and Rachel J. Pries, Colorado State University. April22-23, 2006 Geometric Methods in Group Theory and Topology (Code: Saturday - Sunday SS 9A), Kim Ruane, Tufts University, jennifer Taback, Meeting #l 01 7 Bowdoin College, and Peter N. Wong, Bates College. Eastern Section Global Perspectives on the Geometry of Riemann Surfaces Associate secretary: Lesley M. Sibner (Code: SS 14A), Eran Makover and Jeffrey K. McGowan, Announcement issue of Notices: February 2006 Central Connecticut State University. Program first available on AMS website: March 9, 2006 Hopf Algebras and Galois Module Theory(Code: SS 4A), Tim­ Program issue of electronic Notices: April 2006 othy Kohl, Boston University, and Robert G. Underwood, Issue of Abstracts: Volume 27, Issue 2 Auburn University Montgomery. Deadlines Mathematical Challenges in Physical and Engineering Sci­ For organizers: Expired ences (Code: SS 13A), Marianna A. Shubov, University of For consideration of contributed papers in Special Sessions: New Hampshire. Expired Quantum Invariants ofKnots and 3-Manifolds (Code: SS llA), For abstracts: February 21, 2006 NOTE: This date is ear­ Charles D. Frohman, University of Iowa, and Razvan Gelca, lier than previously published. Texas Tech University.

FEBRUARY 2006 NOTICES OF THE AMS 299 Meetings & Conferences

Symplectic and Contact Topology (Code: SS 7A), Weimin Local Information Chen, Michael G. Sullivan, and Hao Wu, University of The university's website is www. unh. edu; the department Massachusetts, Amherst. of mathematics is at www. math. unh. edu. Campus infor­ Topological Algebras and Applications (Code: SS 12A), mation for visitors, including a map and directions, is at Alexander A. Katz, St. John's University, and Genady Y. www.unh.edu/welcome/visitingunh.html. Grabarnik, IBM T. ]. Watson Research Center. Other Activities Accommodations Book Sales: Examine the newest titles from the AMS! Many Participants should make their own arrangements directly of the AMS books will be available at special discounts avail­ with a hotel of their choice as early as possible. Special able only at the meeting. Complimentary coffee will be rates have been negotiated with the hotels listed below. served courtesy of AMS Membership Services. Rates quoted do not include the hotel tax of 8%. The AMS is AMS Editorial Activity: An acquisitions editor from not responsible for rate changes or for the quality of the the AMS book program will be present to speak with accommodations. When making a reservation, participants prospective authors. If you have a book project that you should state that they are with the American Mathematical would like to discuss with the AMS, please stop by the book Society (AMS) Meeting at the University of New exhibit. Hampshire group. Cancellation and early checkout policies vary; be sure to check when you make your reservation. Parking The Hotel New Hampshire, 2 Main Street, Durham, NH Parking information will be available at a later date. Watch 03824, 603-868-1234 or i nfo@hotel newhampshi re. net, the meeting website at www. ams. o rg/ amsmtgs/ located next to Durham's historic district and within a secti anal . html for the most up-to-date details. 5- to 15-minute walking distance of campus; US$99/ Registration and Meeting Information single or double, refrigerators in rooms, complimentary The meeting is on the campus of the University of New continental breakfast; free Internet access. Deadline for Hampshire (UNH), Durham, NH. reservations is March 21, 2006. Be sure to check cancel­ The registration desk lation and early checkout policies. will be open Saturday, April 22, 7:30a.m. to 4:00p.m., and Sunday, April 23, 8:00a.m. to The New England Center, 15 Stratford Rd., Durham, NH 03824,800-590-4334 or 603-862-2801, (international par­ noon. Fees are US$40 for AMS or CMS members, US$60 for ticipants may send email for reservations to shelley. nonmembers; and US$5 for students, unemployed math­ burch@unh. edu); located on campus and within walking ematicians, and emeritus members. Fees are payable on distance of the train station; US$99/ single/ double. Ameni­ site by cash, check, or credit card. Locations for the reg­ ties include a full service restaurant and lounge on the istration desk, Invited Addresses and Special Sessions will premises, complimentary access to the university's Hamel be announced at a later date. Please watch the meeting web­ Recreation Center, and complimentary Internet access (in­ site at www. ams. org/amsmtgs/secti anal . html for the cluding wireless) throughout the hotel. The number of most up-to-date details. rooms available is limited! Please make your reservations Travel and Campus Map early because of an anticipated sell out. Be sure to check cancellation and early checkout policies. Boston's Logan International Airport (BOS) is approxi­ Also very close to campus is the Pines Guest mately 60 miles from Durham. Some participants may House, 47 Dover Rd., Durham, 603-868-3361, www. find it less expensive to fly into Manchester Airport (MHT), thepi nesguesthouse. com, rates are US$ 79-129. approximately 40 miles from Durham, however, bus ser­ The Hickory Pond Inn, 1 Stagecoach Rd., Durham, 800- vice is not available from Manchester to Durham. 658-0065 or 603-659-2227, www. hi ckorypondi nn. com, Rail service is available from Boston's North Station is about three miles from campus; rates start at about on Amtrak directly to the UNH campus. See www. US$89 depending upon season. thedowneaster. com. The fare is US$14 each way. Service Other hotels in Dover, NH (about four to five miles from Logan Airport to North Station is provided by sub­ north) or Portsmouth, NH (about eight to nine miles south) way or taxi. can be found using your favorite Internet hotel search C & J Trailways (800-258-7111 or www. cjtrai lways. engine, e.g., Orbi tz. com or Expedi a. com, many of which com) offers very limited bus service (US$13 each way) be­ feature discounted rates. Be careful to read the terms tween Boston and Durham (leaves North Station (Amtrak) thoroughly; some hotels may require full payment when once daily at 3:15 p.m. and returns from Durham once daily making the reservation and cancellation penalties vary. at 1:00 p.m.). Other options are to take the bus to Portsmouth (10 miles from Durham) or Dover (five miles Food Service from Durham), New Hampshire, and then a taxi or Wild­ Holloway Commons is the campus dining hall offering cat shuttle (www. unh. edu/transportati on/wildcat/ great buffet-style food. The costs and times are-break­ index. htm) for service to Durham. fast: 7:15 a.m.-11:00 a.m., US$6.50; lunch: 11:00 a.m.-4:30 The official airline for the meeting is Delta Airlines. Take p.m., US$8.75; and dinner: 4:30 p.m.-9:30p.m., US$11.00. advantage of Delta's new SimpliFares™ and enjoy the Information on local dining near the campus will be avail­ following benefits: able on site. • No Saturday night stay required-more flexibility

300 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Meetings & Conferences

• Always affordable- realize up to 50% savings on residence abroad. This may include documentation of the everyday fares in the contiguous 48 states following: • Lower change fees-reduced from US$100 to US$ 50 - family ties in home country or country of legal to change travel plans permanent residence • Just eight fares- less guessing and easier planning - property ownership To make immediate reservations call Delta Air Lines at - bank accounts 800-221-1212. Be sure to reference US738367060 or visit www. delta. com and enter SkyBonus account number - employment contract or statement from employer US738367060 in your passenger information screen to be stating that the position will continue when the employee recognized as a participant. Your benefits include: returns; • No service fees • Visa applications are more likely to be successful if • 1,000 sky miles for Delta members done in a visitor's home country than in a third country; • Skip the airport lines; check in online • Applicants should present their entire trip itinerary, including travel to any countries other than the United Car Rental States, at the time of their visa application; Avis is the official car rental company for the sectional • Include a letter of invitation from the meeting orga­ meeting in Durham, New Hampshire. All rates include un­ nizer or the U.S. host, specifying the subject, location and limited free mileage. Weekend daily rates are available dates of the activity, and how travel and local expenses will from noon Thursday to Monday at 11:59 P.M. Rates for this meeting are effective April15, 2006 to April30, 2006, and be covered; begin at US$35.99/ day (weekend rate). Should a lower • If travel plans will depend on early approval of the qualifying rate become available at the time of booking, visa application, specify this at the time of the application; Avis is pleased to offer a 5% discount off the lower qual­ • Provide proof of professional scientific and/or edu­ ifying rate or the meeting rate, whichever is lowest. Rates cational status (students should provide a university tran­ do not include any state or local surcharges, tax, optional script). coverages or gas refueling charges. Renters must meet This list is not to be considered complete. Please visit Avis's age, driver, and credit requirements. Reservations the websites above for the most up-to-date information. can be made by calling 800-331-1600 or online at www. Reminder: Machine-Readable Passports Required by avis. com. Avis's Discount Number is B159266. June 26, 2005. Getting to the University by Car: From the south, in­ The Department of Homeland Security reminds travel­ cluding Logan International Airport in Boston, MA: Take I-95 North to Exit 4 (N.H. Lakes and Mountains, Spaulding ers from the 27 Visa Waiver Program (VWP) countries that Turnpike). Continue North to Exit 6W and follow Route 4 as of June 26, 2005, they must have a machine-readable West. Exit at Route 155A and turn east toward Durham. passport to enter the United States without a visa. Begin­ Follow 15 SA through a short stretch of fields. Take a left ning June 26, 2005, transportation carriers will be fined onto Loop Road, bearing right and driving a short distance US$ 3 ,300, per violation, for transporting any VWP traveler until you reach the UNH Visitor Center, a small white clap­ to the United States without a machine-readable passport. board building on your left. Metered parking is available Similarly, VWP travelers arriving in the United States on at the lot adjacent to the Visitor Center. Special parking that date without a machine-readable passport should not arrangements for meeting participants will be announced anticipate being granted one-time entry into the country. at a later date. As an alternative for persons with immediate travel plans Information for International Participants who are unable to obtain a machine-readable passport in Visa regulations are continually changing for travel to time, the individual may apply for a U.S. visa at a U.S. Con­ the United States. Visa applications may take from sulate or Embassy abroad. three to four months to process and require a personal interview, as well as specific personal information. Inter­ Weather national participants should view the important informa­ Mark Twain once said that if you don't like the weather in tion about traveling to the U.S. found at http: I jwww7. New England, just wait a minute. Conditions in Durham nationalacademies.org/visas/Traveling_to_US. during late April can be unpredictable so layered clothing html and http: I /travel. state. gov /visa/index. html. is advisable. Rainfall averages 4" in April, and snow is If you need a preliminary conference invitation in order possible. Temperatures can range from about 3 5° Fahren­ to secure a visa, please send your request to dl s@ams. o rg. heit at night to 60° Fahrenheit during the day. If you discover you do need a visa, the National Acad­ emies website (see above) provides these tips for suc­ cessful visa applications: • Visa applicants are expected to provide evidence that they are intending to return to their country of residence. Therefore, applicants should provide proof of "binding" or sufficient ties to their home country or permanent

FEBRUARY 2006 NOTICES OF THE AMS 301 Meetings & Conferences

Geometric Dynamics and Ergodic Theory (Code: SS llA), San Francisco, Yitwah Cheung and Arek Goetz, San Francisco State Uni­ versity, and Slobodan Simic, San Jose State University. California Geometry of Grabner Bases (Code: SS 2A), Bernd Sturmfels, University of California Berkeley, and Alexander Yong, San Francisco State University University of Minnesota and Fields Institute. Hilbert Functions and Resolutions (Code: SS 12A), Benjamin April29-30, 2006 Richert, California Polytechnic State University, and Sean Saturday - Sunday Sather-Wagstaff, California State University, Dominguez Hills. Meeting #1 018 History and Philosophy of Mathematics (Code: SS lA), Western Section Shawnee L. McMurran, California State University, San Associate secretary: Michel L. Lapidus Bernardino, and James J. Tattersall, Providence College. Announcement issue of Notices: February 2006 Program first available on AMS website: March 16, 2006 Homological and K-theoretical Trends in Algebraic Com­ Program issue of electronic Notices: April 2006 binatorics (Code: SS 6A), Joseph Gubeladze and Serkan Hosten, San Francisco State University. Issue of Abstracts: Volume 27, Issue 2 Liapunov Exponents and Nonuniform Hyperbolicity (Code: Deadlines SS 7A), Anton Gorodetski and Vadim Kaloshin, Califor­ Fororganizers: Expired nia Institute of Technology. For consideration of contributed papers in Special Sessions: Lie Algebras and Applications (Code: SS 9A), Dimitar Expired Grantcharov, San Jose State University, Vera Serganova, For abstracts: March 7, 2006 University of California Berkeley, and Arturo Pianzola, University of Alberta. The scientific information listed below may be dated. For Partial Differential Equations and Their Applications (Code: the latest information, see www. ams. org/amsmtgs/ SS 14A), Steve Shkoller, University of California Davis. sectional . html. Probability and Statistical Physics (Code: SS SA), Marek Biskup, University of California Los Angeles, Noam Berger, Invited Addresses California Institute of Technology and University of Cali­ lincoln Chayes, University of California Los Angeles, Title fornia Los Angeles, and Balint Virag, University of Toronto. to be announced. Q-series and Partitions (Code: SS 8A), Neville Robbins, San C. Robin Graham, University of Washington, Title to be Francisco State University. announced. Accommodations Vadim Kaloshin, California Institute of Technology, Title Participants should make their own arrangements directly to be announced. with a hotel of their choice. Rates quoted do not include Benoit B. Mandelbrot, Yale University, The Nature of sales tax. The AMS is not responsible for rate changes or Roughness in Mathematics, Science, and Art (Einstein for the quality of the accommodations. When making a Public Lecture in Mathematics). reservation, participants should state they are with the Yuval Peres, University of California Berkeley, Title to be American Mathematical Society group (AMS Meeting). None announced. of the hotels listed are within walking distance of the meeting. Cancellation and early checkout policies vary; be Special Sessions sure to check when you make your reservation. The Great Highway Inn, 12 34 Great Highway, San Fran­ Computational Arithmetic Geometry (Code: SS 13A), cisco, CA, 94112; 800-624-6644, 415-731-6644, fax: 415- Kenneth A. Ribet, University of California Berkeley, and 731-5309. Rates are US$110/single and US$125/double. Kristin Estrella Lauter, Microsoft Corporation. Cancellation policy requires a 72-hour notice. Cancellation Elliptic Methods in Geometry (Code: SS 3A), C. Robin and early checkout policies vary; be sure to check when Graham, University of Washington, and Rafe Mazzeo, you make your reservation. Stanford University. Hampton Inn, 2700 Junipero Serra Blvd., Daly City, CA; Enumerative Aspects of Polytopes (Code: SS lOA), Federico 650-755-7500 or 866-519-4851. Rates are US$109 a night, based upon single or double occupancy, plus 10% tax. All Ardila and Matthias Beck, San Francisco State University. terms and conditions are subject to availability. Recently Fractal Geometry: Connections to Dynamics, Geometric built, the Hampton Inn is located on Junipero Serra Blvd. Measure Theory, Mathematical Physics and Number ,just two miles South of the campus. All rooms include Theory (Code: SS 4A), MichelL. Lapidus and Erin P. Pearse, telephone with complimentary local calls, data ports, cable University of California Riverside, and Machiel van television, and hairdryers. Free parking on property, hot Frankenhuijsen, Utah Valley State College. breakfast, and heated pool are also included. Deadline for

302 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Meetings & Conferences reservations is March 31, 2006. Cancellation and early Parking checkout policies vary; be sure to check when you make Parking is available in the university parking structure your reservation. located on South State Street. For more information Sheraton Gateway Hotel-San Francisco Airport, 600 Air­ regarding parking please visit http: I jwww. sfsu. edu/ port Blvd., Burlingame, CA, 94010; 650-340-8500, http: I I %7Eparking/text/tocampus.html. www. sheratonsfo. com. Rates are US$100 single/double. There is an additional $15 fee per person for triple or quad Registration and Meeting Information occupancy. Deadline for reservations is April 7, 2006. Can­ The registration desk will be located on the third (main) cellation and early checkout policies vary; be sure to check floor of Thornton Hall, and will be open from 7:30a.m. to when you make your reservation. 4:00 p.m. on Saturday, and 8:00 a.m. to noon on Sunday. Talks will take place in the Science Building and Thornton Food Service Hall. A list of restaurants will be available at the registration Registration fees are US$40 for AMS or CMS members, desk. US$60 for nonmembers; and US$5 for students, unem­ ployed mathematicians, and emeritus members. Fees are Local Information payable on site by cash, check, or credit card. Please visit the websites maintained by San Francisco State University at http: I /www. sfsu. edu, the Department of Travel Information and Campus Map Mathematics at http: I /math. sfsu. edu, and the site San Francisco Airport (SFO): From the departure area maintained by the San Francisco Convention and Visitors take the 1-280 North entrance. Take I-280 North, exit at 19th Bureau at http: I /www. sfvi si tor. org. Avenue. Take Junipero Serra Boulevard to Holloway Avenue; turn left on Holloway Avenue to campus at 19th Avenue. Other Activities To get to the parking garage, continue on Holloway AMS Editorial Activity: An acquisitions editor from the Ave. to Font Blvd. Turn right onto Font Blvd. and continue AMS book program will be present to speak with prospec­ to Lake Merced Blvd. Turn right onto Lake Merced Blvd., tive authors. If you have a book project that you would like then take an immediate right onto State Drive which is the to discuss with the AMS, please stop by the book exhibit. entrance to the parking garage. Book Sales: Examine the newest titles from the AMS! By Public Transportation: BART: Exit the Daly City Many of the AMS books will be available at a special dis­ BART Station then take the SFSU shuttle or the MUNI 28 count available only at the meeting. Complimentary cof­ bus. SuperShuttle: Call 800-258-3826 for reservations or fee will be served courtesy of AMS Membership Services. find supershuttle vans outside of Departures. By Car: From the North: Take Highway 101 South, cross Special Presentation the Golden Gate Bridge. Take 19th Avenue/Highway 1 exit. The American Mathematical Society sponsors a series of Follow 19th Avenue to campus at Holloway Avenue. public lectures in mathematics entitled The AMS Einstein To get to the parking garage, turn right onto Holloway Public Lecture in Mathematics. The lectures began in Ave. and continue to Font Blvd. Turn right onto Font Blvd. 2005, to celebrate the one-hundredth anniversary of and continue to Lake Merced Blvd. Turn right onto Lake Einstein's annus mirabilis. They are to be given annually Merced Blvd., then take an immediate right onto State at one of the Society's eight sectional meetings. The De­ Drive which is the entrance to the parking garage. partment of Mathematics at San Francisco State University From the South: Take 1-280 North, exit at 19th Avenue. is honored that the AMS has chosen the San Francisco Take Junipero Serra Boulevard to Holloway Avenue, turn meeting for its second public lecture and that Wolf Prize left on Holloway Avenue to campus at 19th Avenue. winner Benoit Mandelbrot, Yale University, will be the To get to the parking garage, continue on Holloway speaker. He will speak on "The Nature of Roughness in Ave. to Font Blvd. Turn right onto Font Blvd. and continue Mathematics, Science, and Art", Saturday, April29, in Jack to Lake Merced Blvd. Turn right onto Lake Merced Blvd., Adams Hall at 8:00 p.m. then take an immediate right onto State Drive which is the Dinner Buffet: Saturday, April 29, 6:00-8:00 p.m. Din­ entrance to the parking garage. ner Buffet at the Seven Hills Conference Center on the From the East: Take 1-80 West across the Bay Bridge to San Francisco State University campus. There will be a Highway 101 South. Take 101 South to 1-280 toward Daly wide selection of salads, entrees, and desserts, including City. Take the San Jose Avenue/Mission St. exit (immedi­ vegetarian entrees. Cost is $25 .00 per person, which must ately after the Ocean Avenue exit), bearing right onto be prepaid by sending a check or money order to: Sagamore Street to Brotherhood Way to Junipero Serra AMS Dinner Buffet Boulevard North. Take junipero Serra Boulevard to Hol­ Department of Mathematics loway Avenue, turn left on Holloway Avenue to campus San Francisco State University at 19th Avenue. 1600 Holloway Avenue To get directly to the parking garage stay on Brother­ San Francisco, CA 94132 hood Way and turn right onto Lake Merced Blvd. Turn right Make the check or money order payable to Math. Dept. onto State Drive which is the third light after turning onto SFSU. The deadline for reservations is April15. Lake Merced Blvd. and immediately after Font Blvd.

FEBRUARY 2006 NOTICES OF THE AMS 303 Meetings & Conferences

Car Rental: Avis is the official car rental company for The Department of Homeland Security reminds travel­ the sectional meeting in San Francisco, California. All rates ers from the 27 Visa Waiver Program (VWP) countries that include unlimited free mileage. Weekend daily rates are as of June 26, 2005, they must have a machine-readable available from noon Thursday to Monday at 11:5 9 P.M. Rates passport to enter the United States without a visa. Begin­ for this meeting are effective April22, 2006 to May 7, 2006, ning June 26, 2005, transportation carriers will be fined and begin at US$24.99/ day (weekend rate). Should a lower US$3,300, per violation, for transporting any VWP traveler qualifying rate become available at the time of booking, to the United States without a machine-readable passport. Avis is pleased to offer a 5% discount off the lower qualify­ Similarly, VWP travelers arriving in the United States on ing rate or the meeting rate, whichever is lowest. Rates do not that date without a machine-readable passport should not include any state or local surcharges, tax, optional cover­ ages or gas refueling charges. Renters must meet Avis's age, anticipate being granted one-time entry into the country. driver, and credit requirements. Reservations can be made As an alternative for persons with immediate travel plans by calling 800-331-1600 or online at http: I /wvwv. avis. com. who are unable to obtain a machine-readable passport The Avis Discount Number for this meeting is B159266. in time, the individual may apply for a U.S. visa at a U.S. Consulate or Embassy abroad. Special Travel Information for International Participants Weather Visa regulations are continually changing for travel to the The weather in April is variable, with temperatures from United States. Visa applications may take from three to four 70° Fahrenheit to 85° Fahrenheit. The weather can turn cold, months to process and require a personal interview, as well overcast, and windy due to the close proximity of the San as specific personal information. International participants Francisco State University campus to the ocean. should view the important information about traveling to the U.S. found at http: I /www7. national academies. o rg/ visas/Traveling_to_US.html and http://travel. state. gov /visa/index. html. If you need a preliminary Salt Lake City, Utah conference invitation in order to secure a visa, please send University of Utah your request to wsd@ams. org. If you discover you do need a visa, the National Academies website (see above) provides October 7-8,2006 these tips for successful visa applications: Saturday - Sunday • Visa applicants are expected to provide evidence that they are intending to return to their country of residence. Meeting #1 019 Therefore, applicants should provide proof of "binding" or sufficient ties to their home country or permanent Western Section residence abroad. This may include documentation of the Associate secretary: Michel L. Lapidus following: Announcement issue of Notices: August 2006 - family ties in home country or country of legal Program first available on AMS website: August 24, 2006 permanent residence Program issue of electronic Notices: October 2006 - property ownership Issue of Abstracts: Volume 27, Issue 3 - bank accounts - employment contract or statement from employer Deadlines stating that the position will continue when the employee For organizers: March 7, 2006 returns; For consideration of contributed papers in Special Sessions: • Visa applications are more likely to be successful if June 20, 2006 done in a visitor's home country than in a third country; For abstracts: August 15, 2006 • Applicants should present their entire trip itinerary, including travel to any countries other than the United The scientific information listed below may be dated. For States, at the time of their visa application; the latest information, see www.ams.org/amsmtgs/ • Include a letter of invitation from the meeting orga­ sectional . htm l. nizer or the U.S. host, specifying the subject, location and dates of the activity, and how travel and local expenses will Invited Addresses be covered; • If travel plans will depend on early approval of the William Arveson, University of California Berkeley, Title visa application, specify this at the time of the application; to be announced. • Provide proof of professional scientific and/or educa­ Alexei Borodin, California Institute of Technology, Title tional status (students should provide a university tran­ to be announced. script). This list is not to be considered complete. Please visit Izabella Joanna Laba, University of British Columbia, Title the websites above for the most up-to-date information. to be announced. Reminder: Machine-Readable Passports Required by Darren Long, University of California Santa Barbara, Title June 26, 2005. to be announced.

304 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Meetings & Conferences

Special Sessions Ergodic Theory (Code: SS 1A), Nikos Frantzikinakis, Harmonic Analysis: Trends and Perspectives (Code: SS 1A), Pennsylvania State University, Bryna R. Kra, Northwestern Alex Iosevich, University of Missouri, and Michael T. University, and Mate Wierdl, University of Memphis. Lacey, Georgia Institute of Technology. Nonlinear Differential Equations: Methods and Applica­ tions (Code: SS 2A), David G. Costa, University of Nevada, Storrs, Connecticut and Zhi-Qiang Wang. University of Connecticut

October 28-29, 2006 Cincinnati, Ohio Saturday - Sunday University of Cincinnati Meeting #1 021 October 21-22, 2006 Eastern Section Saturday - Sunday Associate secretary: Lesley M. Sibner Announcement issue of Notices: August 2006 Meeting #1 020 Program first available on AMS website: September 14, Central Section 2006 Associate secretary: Susan]. Friedlander Program issue of electronic Notices: October 2006 Announcement issue of Notices: August 2006 Program first available on AMS website: September 7, 2006 Issue of Abstracts: Volume 27, Issue 4 Program issue of electronic Notices: October 2006 Deadlines Issue of Abstracts: Volume 27, Issue 3 For organizers: March 28, 2006 Deadlines For consideration of contributed papers in Special Sessions: For organizers: March 21, 2006 july 11, 2006 For consideration of contributed papers in Special Sessions: For abstracts: September 6, 2006 July 5, 2006 For abstracts: August 29, 2006 The scientific information listed below may be dated. For the latest information, see www. ams. o rg/ amsmtgs/ The scientific information listed below may be dated. For sectional . html. the latest information, see www.ams.org/amsmtgs/ sectional . html. Invited Addresses Invited Addresses Changfeng Gui, University of Connecticut, Storrs, Title to Suncica Canic, University of Houston, Title to be be announced. announced. Katrin Wehrheim, Institute for Advanced Study, Title to Bryna R. Kra, Northwestern University, Title to be be announced. announced. Ezra N. Miller, University of Minnesota, Title to be Special Sessions announced. Combinatorial Methods in Equivariant Topology (Code: SS Jon G. Wolfson, Michigan State University, Title to be 1A), Tara Holm, University of Connecticut, Storrs, and announced. Tom C. Braden, University of Massachusetts, Amherst.

Special Sessions Number Theory (Code: SS 2A), Keith Conrad, University of Connecticut, Storrs, David Pollack, Wesleyan University, Analysis and Potential Theory on Metric Spaces (Code: SS and Thomas A. Weston, University of Massachusetts, 4A), Thomas Bieske, University of South Florida, and Zair Amherst. Ibragimov and Nageswari Shanmugalingam, University of Cincinnati. Applied Algebraic Geometry and Cryptography (Code: SS 3A), Jintai Ding, Jason Eric Gower, and Timothy J. Hodges, University of Cincinnati, Lei Hu, Chinese Academy of Sci­ ences, and Dieter S. Schmidt, University of Cincinnati. Birational Geometry(Code: SS 2A), Mirel Constantin Caibar and Gary P. Kennedy, Ohio State University.

FEBRUARY 2006 NOTICES OF THE AMS 305 Meetings & Conferences

matical Association of America (MAA), annual meetings of Fayetteville, the Association for Women in Mathematics (A VVM) and the National Association of Mathematicians (NAM), and the winter meeting of the Association for Symbolic Logic (ASL), Arkansas with sessions contributed by the Society for Industrial and University of Arkansas Applied Mathematics (SIAM). Associate secretary: Susan]. Friedlander November 3-4, 2006 Announcement issue of Notices: October 2006 Friday - Saturday Program first available onAMS website: November 1, 2006 Program issue of electronic Notices: January 2007 Meeting #1 022 Issue of Abstracts: Volume 28, Issue 1 Southeastern Section Associate secretary: Matthew Miller Deadlines Announcement issue of Notices: September 2006 For organizers: April1, 2006 Program first available on AMS website: September 21, For consideration of contributed papers in Special Sessions: 2006 To be announced Program issue of electronic Notices: November 2006 For abstracts: To be announced Issue of Abstracts: Volume 27, Issue 4 Deadlines Davidson, North For organizers: April 3, 2006 For consideration of contributed papers in Special Sessions: July 18, 2006 Carolina For abstracts: September 12, 2006 Davidson College

The scientific information listed below may be dated. For March 3-4, 2007 the latest information, see www. ams. org/amsmtgs/ Saturday - Sunday sectional . html. Southeastern Section Associate secretary: Matthew Miller Invited Addresses Announcement issue of Notices: To be announced Richard P. Anstee, University of British Columbia, Title to Program first available on AMS website: To be announced be announced. Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Arun Ram, University of Wisconsin, Title to be announced. Donald G. Saari, University of California Irvine, Title to be Deadlines announced. For organizers: August 3, 2006 Andras Vasy, Massachusetts Institute of Technology, Title For consideration of contributed papers in Special Sessions: to be announced. To be announced For abstracts: To be announced Special Sessions Dirac Operators in Analysis and Geometry (Code: SS 1A), John Ryan, University of Arkansas, Marius Mitrea, Uni­ Oxford, Ohio versity of Missouri, and Mircea Martin, Baker University. Miami University March 16-1 7, 2007 New Orleans, Friday - Saturday Central Section Louisiana Associate secretary: Susan]. Friedlander Announcement issue of Notices: To be announced New Orleans Marriott and Sheraton New Program first available on AMS website: To be announced Orleans Hotel Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced January 4-7,2007 Thursday - Sunday Deadlines For organizers: To be announced Meeting #1 023 For consideration of contributed papers in Special Sessions: ]oint Mathematics Meetings, including the 113th Annual To be announced Meeting of the AMS, 90th Annual Meeting of the Mathe- For abstracts: To be announced

306 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Meetings & Conferences

Special Sessions Finite Geometry and Combinatorics (Code: SS 3A), Mark A. Albuquerque, New Miller, Marietta College. Mexico Geometric Topology (Code: SS 2A), Jean-Francois LaFont, SUNY Binghamton and Ohio State University, and Ivonne J. University of New Mexico Ortiz, Miami University. October 13-14,2007 Large Cardinals in Set Theory (Code: SS 1A), Paul B. Saturday - Sunday Larson, Miami University, Justin Tatch Moore, Boise State Western Section University, and Ernest Schimmerling, Carnegie Mellon Associate secretary: Michel L. Lapidus University. Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced Hoboken, New Jersey Issue of Abstracts: To be announced Stevens Institute of Technology Deadlines For organizers: To be announced April14-1 5, 2007 For consideration of contributed papers in Special Sessions: Saturday - Sunday To be announced For abstracts: To be announced Eastern Section Associate secretary: Lesley M. Sibner Announcement issue of Notices: To be announced Program first available on AMS website: To be announced San Diego, California Program issue of electronic Notices: To be announced San Diego Convention Center Issue of Abstracts: To be announced January 6-9, 2008 Deadlines Sunday - Wednesday For organizers: September 14, 2006 ]oint Mathematics Meetings, including the 114th Annual Meeting of the AMS, 9lst Annual Meeting of the Mathe­ For consideration of contributed papers in Special Sessions: matical Association of America (MAA), annual meetings of To be announced the Association for Women in Mathematics (A WM) and the For abstracts: To be announced National Association of Mathematicians (NAM), and the winter meeting of the Association for Symbolic Logic (ASL), with sessions contributed by the Society for Industrial and Tucson, Arizona Applied Mathematics (SIAM). Associate secretary: Michel L. Lapidus University of Arizona Announcement issue of Notices: October 2007 Program first available onAMS website: November 1, 2007 April21 :..22, 2007 Program issue of electronic Notices: January 2008 Saturday - Sunday Issue of Abstracts: Volume 29, Issue 1 Western Section Deadlines Associate secretary: Michel L. Lapidus Announcement issue of Notices: To be announced For organizers: April1, 2007 For consideration of contributed papers in Special Sessions: Program first available on AMS website: To be announced To be announced Program issue of electronic Notices: To be announced For abstracts: To be announced Issue of Abstracts: To be announced Deadlines Bloomington, Indiana For organizers: September 21, 2006 For consideration of contributed papers in Special Sessions: Indiana University To be announced April4-6, 2008 For abstracts: To be announced Friday - Sunday Central Section Associate secretary: Susan]. Friedlander Announcement issue of Notices: To be announced

FEBRUARY 2006 NOTICES OF THE AMS 307 Meetings & Conferences

Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced Shanghai, People's Issue of Abstracts: To be announced Republic of China Deadlines For organizers: September 4, 2007 Fudan University For consideration of contributed papers in Special Sessions: To be announced December 17-21,2008 For abstracts: To be announced Wednesday - Sunday First ]oint Interntional Meeting Between the AMS and the Shanghai Mathematical Society Rio de Janeiro, Brazil Associate secretary: Susan ]. Friedlander Announcement issue of Notices: To be announced Instituto Nacional de Matematica Pura e Program first available on AMS website: To be announced Aplicada (IMPA) Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced June 4-7,2008 Wednesday - Saturday Deadlines First ]oint International Meeting with the Sociedade For organizers: To be announced Brasileira de Matematica. For consideration of contributed papers in Special Sessions: Associate secretary: Lesley M. Sibner To be announced Announcement issue of Notices: To be announced For abstracts: To be announced Program first available on AMS website: Not applicable Program issue of electronic Notices: Not applicable Issue of Abstracts: Not applicable Washington, District Deadlines of Columbia For organizers: To be announced For consideration of contributed papers in Special Sessions: Marriott Wardman Park Hotel and Omni To be announced Shoreham Hotel For abstracts: To be announced January 7-1 0, 2009 Wednesday - Saturday Vancouver, Canada ]oint Mathematics Meetings, including the 115th Annual Meeting of the AMS, 92nd Annual Meeting of the Mathe­ University of British Columbia matical Association of America (MAA), annual meetings of the Association for Women in Mathematics (A W'M) and the October 4-5, 2008 National Association of Mathematicians (NAM), and the Saturday - Sunday winter meeting of the Association for Symbolic Logic (ASL), Western Section with sessions contributed by the Society for Industrial and Associate secretary: Michel L. Lapidus Applied Mathematics (SIAM). Announcement issue of Notices: To be announced Associate secretary: Lesley M. Sibner Program first available on AMS website: To be announced Announcement issue of Notices: October 2008 Program issue of electronic Notices: To be announced Program first available on AMS website: November 1, 2008 Issue of Abstracts: To be announced Program issue of electronic Notices: January 2009 Issue of Abstracts: Volume 30, Issue 1 Deadlines For organizers: March 9, 2008 Deadlines For consideration of contributed papers in Special Sessions: For organizers: April1, 2008 To be announced For consideration of contributed papers in Special Sessions: For abstracts: To be announced To be announced For abstracts: To be announced

308 NOTICES OF THE AMS VOLUME 53, NUMBER 2 Meetings & Conferences San Francisco, Boston, California Massachusetts Moscone Center West and the San john B. Hynes Veterans Memorial Francisco Marriott Convention Center, Boston Marriott Hotel, January 6-9, 201 0 and Boston Sheraton Hotel Wednesday - Saturday January 4-7, 2012 ]oint Mathematics Meetings, including the 116th Annual Wednesday - Saturday Meeting of the AMS, 93rd Annual Meeting of the Mathe­ ]oint Mathematics Meetings, including the 118th Annual matical Association of America (MAA), annual meetings of Meeting of the AMS, 95th Annual Meeting of the Mathe­ the Association for Women in Mathematics (A WM) and the matical Association of America, annual meetings of the National Association of Mathematicians (NAM), and the Association for Women in Mathematics (A WM) and the winter meeting of the Association for Symbolic Logic (ASL), National Association of Mathematicians (NAM), and the with sessions contributed by the Society of Industrial and winter meeting of the Association for Symbolic Logic (ASL), Applied Mathematics (SIAM). Associate secretary: Matthew Miller with sessions contributed by the Society for Industrial and Applied Mathematics (SIAM). Announcement issue of Notices: October 2009 Program first available on AMS website: November 1, 2009 Associate secretary: Michel L. Lapidus Program issue of electronic Notices: January 2010 Announcement issue of Notices: October 2011 Issue of Abstracts: Volume 31, Issue 1 Program first available on AMS website: November 1, 2011 Program issue of electronic Notices: January 2012 Deadlines Issue of Abstracts: Volume 33, Issue 1 For organizers: April1, 2009 Deadlines For consideration of contributed papers in Special Sessions: To be announced For organizers: April1, 2011 For abstracts: To be announced For consideration of contributed papers in Special Sessions: To be announced New Orleans, For abstracts: To be announced Louisiana San Diego, California New Orleans Marriott and Sheraton New San Diego Convention Center and San Orleans Hotel Diego Marriott Hotel and Marina January 5-8,2011 January 9-12,2013 Wednesday - Saturday Wednesday - Saturday ]oint Mathematics Meetings, including the 117th Annual ]oint Mathematics Meetings, including the 119th Annual Meeting of the AMS, 94th Annual Meeting of the Mathe­ Meeting of the AMS, 96th Annual meeting of the Mathe­ matical Association ofAmerica, annual meetings of the As­ matical Association of America, annual meetings of the sociation for Women in Mathematics (A WM) and the National Association for Women in Mathematics (A WM) and the Association ofMathematicians (NAM), and the winter meet­ National Association of Mathematicians (NAM), and the ing of the Association for Symbolic Logic (ASL), with sessions winter meeting of the Association for Symbolic Logic (ASL), contributed by the Society for Industrial and Applied Math­ with sessions contributed by the Society for Industrial and ematics (SIAM). Applied Mathematics (SIAM). Associate secretary: Susan J Friedlander Associate secretary: Lesley M. Sibner Announcement issue of Notices: October 2010 Announcement issue of Notices: To be announced Program first available on AMS website: November 1, 2010 Program first available on AMS website: To be announced Program issue of electronic Notices: january 2011 Program issue of electronic Notices: To be announced Issue of Abstracts: Volume 32, Issue 1 Issue of Abstracts: To be announced Deadlines Deadlines For organizers: April1, 2010 For organizers: April1, 2012 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

FEBRUARY 2006 NOTICES OF THE AMS 309 John Howard Van Amringe John Emory McClintock George William Hill Simon Newcomb Robert Simpson Woodward AMS Eliakim Hastings Moore Thomas Scott Fiske William Fogg Osgood Henry Seely White Maxi me B6cher PRESIDENTS Henry Burchard Fine Edward Burr Van Vleck Ernest William Brown Leonard Eugene Dickson A TIMELINE Frank Morley Gilbert Ames Bliss Oswald Veblen George David Birkhoff Virgil Snyder AMS presidents Earle Raymond Hedrick Luther Pfahler Eisenhart Arthur Byron Coble play a key role in Solomon Lefschetz Robert Lee Moore Griffith Conrad Evans leading the Society Harold Calvin Marston Morse Marshall Harvey Stone Theophil Henry Hildebrandt and representing the Einar Hille Joseph Leonard Walsh John von Neumann profession. Browse Gordon Thomas Whyburn Raymond Louis Wilder Richard Dagobert Brauer through the timeline to see each Edward James McShane Deane Montgomery Joseph Leo Doob AMS president's page, which Abraham Adrian Albert Charles Bradfield Morrey Jr. Oscar Zariski includes the institution and date Nathan Jacobson Saunders Mac Lane Lipman Bers of his/her doctoral degree, a brief R H Bing Peter_ David Lax note about his/her academic Andrew Mattei Gleason Julia Bowman Robinson Irving Kaplansky career and honors, and links to George Daniel Mostow William Browder Michael Artin more extensive biographical Ronald L. Graham Cathleen Synge Morawetz . Arthur M. Jaffe information. Felix E. Browder Hyman Bass David Eisenbud James G. Arthur www.ams.org/ams/amspresidents.html @. AMERICAN MATHEMATICAL SOCIETY 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: 951- e-mail: lsi bner@duke. poly. edu; telephone: 718-260-3505 . 827-5910. Southeastern Section: Matthew Miller, Department of Math­ Central Section: Susanj. Friedlander, Department of Math­ ematics, University of South Carolina, Columbia, SC 29208- ematics, University of Illinois at Chicago, 851 S. Morgan (M/C 0001, e-mail: mill er@math. sc. edu; telephone: 803-777-3690. 249), Chicago, lL 60607-7045; e-mail: susan@math. nwu. edu; tele­ phone: 312-996-3041.

The Meetings and Conferences section of the Notices December 17-21 Shanghai, People's gives information on all AMS meetings and conferences Republic of China p. 308 approved by press time for this issue. Please refer to the page 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 . 308 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. 308 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. o rglmeeti ngsl. January 5-8 New Orleans, Louisiana p. 309 Annual Meeting Meetings: 2012 2006 January 4-6 Boston, Massachusetts p. 309 Aprill-2 Miami, Florida p. 297 Annual Meeting April8-9 Notre Dame, Indiana p.298 2013 April 22-23 Durham, New Hampshire p. 299 January 4-6 San Diego, California p . 309 April29-30 San Francisco, California p. 302 Annual Meeting October 7-8 Salt Lake City, Utah p. 304 October 21-22 Cincinnati, Ohio p. 305 Important Information Regarding AMS Meetings October 28-29 Storrs, Connecticut p. 305 Potential organizers, speakers, and hosts should refer to November 3-4 Fayetteville, Arkansas p. 305 page 296 in the February 2006 issue of the Notices for gen­ eral information regarding participation in AMS meetings and conferences. 2007 January 4-7 New Orleans, Louisiana p . 306 Abstracts Annual Meeting Speakers should submit abstracts on the easy-to-use interactive March 3-4 Davidson, North Carolina p. 306 Web form. No knowledge of LATEX is necessary to submit an March 16-17 Oxford, Ohio p. 306 electronic form, although those who use LAfJ:X may submit April14-15 Hoboken, New Jersey p. 307 abstracts with such coding, and all math displays and simi­ April21-22 Tuscan, Arizona p.307 larily coded material (such as accent marks in text) must October 13-14 Albuquerque, New Mexico p. 307 be typeset in INJ:X. Visit http: I lwww. ams. orglcgi -bi nl abstractslabstract.pl. Questions about abstracts and requests for paper forms 2008 may be sent to abs-i nfo@ams. org. January 6-9 San Diego, California p. 307 Close attention should be paid to specified deadlines in this Annual Meeting issue. Unfortunately, late abstracts cannot be accommodated. April4-6 Bloomington, Indiana p. 307 June 4-7 Rio de Janeiro, Brazil p. 308 October 4-5 Vancouver, Canada p. 308

Conferences: (see http: I lwww. ams. o rglmeeti ngsl for the most up-to-date information on these conferences.) June 4-June 29, 2006: Joint Summer Research Conferences in the Mathematical Sciences, Snowbird, Utah (see November 2005 Notices, page 1296). Co-sponsored conference: 22nd Annual Workshop on Mathematical Problems in Industry, june 12-16, 2006, Olin College, Needham, MA. For details see http: I lproj ects. olin. edulmpi 2006/.

fEBRUARY 2006 NOTICES OF THE AMS 311 I CAMBRIDGE I I I OUTSTANDING SCHOLARSHIP

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