AMERICAN MATHEMATICAL SOCIETY

" "' ' " ~ ~ \~ ~"' "' ~ "" "' ~ ~ - '-' '~- New and Noteworthy from the American Mathematical Society

Real Analysis Frank Morgan, Williams College, Williamstown, MA Written by award-winning author and professor, Frank Morgan, this text­

FRANK MORGAN book offers a simple, yet sophisticated point of view for undergraduates studying real analysis.

The book builds the theory behind calculus directly from the basic concepts of real numbers, limits, and open and closed sets in ffi. n. Morgan provides efficient proofs and shows how to derive them. There are excellent exercises accompanied by some solutions.

Professor Morgan received the first national Haimo teaching award from the Mathematical Association of America. He has also garnered top teaching awards from Rice University and MIT.

2005; 151 pages; Hardcover; ISBN 0-8218-3670-6; List US$39;AII AMS members US$31 ; Order code REAL

The Wild Change is Mathematical World of Possible Publishing 4-Manifolds Stories of Women and A Guidebook Minorities in AJexandruScorpan, Mathematics Steven G. Krantz, University of Florida, Patricia Kenschaft Washington University, Gainesville, FL Montclair State St. Louis, MO University, Upper Montclair, N] For a complete description, go to For a complete description, go to www.ams.org/bookstore-getitem/item=fourman For a complete description, go to www.ams.org/bookstore-getitem/item=matpub 2005; 609 pages; Hardcover; ISBN 0-8218-3749-4; List www.ams.org/bookstore-getitem/item=change 2005; approximately 320 pages; Softcover; ISBN · 1 US$69; All AMS members US$55; Order code 2005; approximately 200 pages; Softcover; ISBN 0-8218-3699-4; List US$29;AII AMS members US$2.3; FOURMAN 0-8218-3748-6; List US$29;AII AMS members US$23; Order code MATPUB Order code CHANGE

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Cornerstones Series Geometric Function Theory Complex This new series contains textbooks foc using on "what Explorations in Complex Analysis Numbers st udents need to know" and "what faculty should STEVEN G. KRANTZ, Washington University, St. Louis, MO teach" in various selected topics in pure mathematics from A to ••• Z and related subj ects. Presented from a geometric analytical viewpoint, this TITU ANDREESCU, University of work add resses advanced topics in complex analysis Texas, Dallas, TX; DORIN ANDRICA, Series Editors: that ve rge on modern areas of research, including "Babes-Bolyai" University, Cluj-Napoca, CHARLES L. EPSTEIN, University of Pennsylvania, invariant geometry, th e Bergman metric, the automor­ Romania Philadelphia, PA phism groups of domains, extremal length, harmonic Complex Numbers from A to ... Z is STEVEN G. KRANTZ, Washington University, St. Louis, MO meas ure, boundary regularity of conformal maps, the an in trod uction to this fascinating subj ect, with a inhomoge neous Cauchy- Riemann equations, and the particular emphasis on key concepts and elementary corona problem. The author adroitly weaves these results conce rning these numbers. The reader learns Basic Real varied topics to reveal a number of delightful interac­ how co mplex numbers can be used to solve algebraic tions to capture the imagination of both advanced equati ons and to understand the geometric interpreta­ Analysis undergraduate and grad uate students. ANTHONY W. KNAPP, State tion of complex numbers and the operations involving 2005/ APPROX . 350 PP./HARDCOVER University of New York at them. The theoretical parts of the book are augmented ISBN 0-8176-4339-7/$ 69.95 (TENT.) CORNERSTONES Stony Brook, NY with ri ch exercises and problems at va ri ous leve ls of difficulty. 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CORNERSTONES commutative ring theory by mainly studying their spaces of fl ag domains. Ass uming only a basic familiarity illustrations and applications in plane curve with the concepts of Li e th eory and geometry, the wo rk Advanced Real Analysis theory.... The whole text is a real masterpiece of clarity, presents a complete structure theory for these cycle rigor, comprehension, methodical skill, algebraic and spaces and their applications to harmoni c analysis and ANTHONY W. KNAPP, State University of New York at algebraic geometry. The exposition, drive n by numerous Stony Brook, NY geometric motivation ... highly enlightening, motivating and entertaining at the same time ... One simply cannot examples, is presented from the complex geometric Featuring many examples and hund reds of problems do better in writing such a textbook." viewpoint, but the methods, applications, and mu ch of the motivation also come fro m real and complex (with hints and selected solutions),Advanced Real -ZENTRALBLATI MATH Analysis is suitable as a text in graduate courses such algebraic groups and their representations, as we ll as 2005/ APPROX. 300 PP., 40 lllUS ./SOFTCOVER other areas of geometry. as Fourier and functional analysis, modern analys is, ISBN 0-8176-4381-8/ $69.95 and partial differen tial equations. 2005/ APPROX. 350 PP., 20 lllUS./HARDCOVER 2005/ APPROX. 400 PP., 10 1llUS./HARDCOVER ISBN 0-8176-4391 -5/ $59.95 (TENT.) ISBN 0-8176-4382-6/ $59.95 (TENT.) CORNERSTONES Introduction to Commutative Algebra and Algebraic Geometry SPECIAL SET PRJCE: Order both Basic Real ERNST KUNZ, Universitiit Regensburg, Germany Analysis and Advanced Real Analysis for a special price of $89.95. Asavi ngs of more than 'fin exce//ent introduction to the subject ... The center $39.00! (Please use promo code Y9694 when of gravity lies in commutative algebra, and this book orde ring.) can serve as a preparation for more advanced topics. The presentation is very clear and the theory is accom­ panied by numerous interesting exercises ... This is a highly recommended text for students and lecturers. " Looking for mor e? -MATHEMATICA Find it on birkhauser.com 1997/ 256 PP./HARDCOVER/ ISBN 0-8176-3065-1 / $59.95

CALL: 1-800-777-4643 • FAX: (201) 348-4505 E-MAIL: [email protected] • www.birkhauser.com Please mention promotion #Y8589 when ordering. Prices are valid in the Americas only Birkhiiuser and are subject to change without notice. For price and ordering information outside the Americas, Boston · Basel · Berlin pl ease contact Birkhauser Verlag AG by E-mail: birkhauser@sp ringer.de 8/05 Promotion #Y8597 Notices August2005 of the American Mathematical Society Feature Articles

720 The p-adic Icosahedron Gunther Cornelissen and Fumiharu Kato The p-adic icosahedron is a structure, the set of ends of a sub-tree of the Bruhat-Tits tree, associated to a two-dimensional projective representation of the icosahedral group over a p-adic field. The authors explain this structure and some of its applications. 728 Walter Feit (1930-2004) Len Scott, Ron Solomon, john Thompson, john Walter, and Efim Zelma nov The authors recall the life and mathematical legacy of the influential American group theorist

Communications Commentary

738 WHAT IS ... a Compacton? 71 7 Opinion: Mathematics in Public Philip Rosenau- Richard Schaar 745 AMS President's Address at Abel 718 Letters to the Editor Celebration 7 40 Spaceland: A Novel of the Fourth ]ames Arthur Dimension-A Book Review 7 4 7 2 004 Annual Survey of the Reviewed by ]ody Trout Mathematical Sciences (Second Report) 743 Chance: A Guide to Gambling, Love, Ellen E. Kirkman, ]ames W. Maxwell, and the StockMarket, and]ust About Colleen A. Rose Everything Else-A Book Review , Reviewed by Rick Durrett Notices Departments of the American Mathematical Society Crossword Puzzle ...... 761 Mathematics People ...... 762 EDITOR: Andy Magid Hintikka and Caffarelli Receive Rolf Schock Prizes, Presidential ASSOCIATE EDITORS: Mentoring Awards Announced, Sloan Receives 2005 Susanne C. Brenner, Bill Casselman (Graphics Editor), Information-Based Complexity Prize, Haggstrom and O'Connell Robert j. Daverman, Nathaniel Dean, Rick Durrett, Susan Friedlander, Robion Kirby, Steven G. Krantz, Awar ded Rollo Davidson Prizes, National Academy of Sciences Elliott H. Lieb, Mark Saul, Karen E. Smith, Audrey Elections, Amer ican Academy Elections, Ferran Sunyer i Terras, Lisa Traynor Balaguer Prizes Awarded, Putnam Prizes Awarded, U.S.A. SENIOR WRITER and DEPUTY EDITOR: Mathematical Olympiad. Allyn jackson MANAGING EDITOR: Sandra Frost Mathematics Opportunities ...... 766 CONTRIBUTING WRITER: Elaine Kehoe NSF Focused Resea r ch Groups, NSF Mathematical Sciences PRODUCTION ASSISTANT: Muriel Toupin Postdoctoral Research Fellowships, AMS Scholarships for Math PRODUCTION: Kyle Antonevich, Stephen Moye, in Moscow, Call for Submissions for Sunyer i Balaguer Prize, Erin Murphy, Lori Nero, Karen Ouellette, Donna Nominations Sought for 2005 IBC Young Researcher Award. 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Schaar: Well, that is too bad. Were you good in reading? Mathematics in Public Person 1: Well, of course I was! Schaar: Being good in mathematics is equivalent in the In 1976, after receiving my Ph.D. in applied mathematics from twenty-first century to reading in the twentieth century. For the University of Chicago and after serving on the faculty at your children to do well in the current era, they will have to the University of Southern California, I left academic life and be knowledgeable of the skills that a mathematics education transitioned into the business world. For the next ten years can provide, like problem-solving skills as well as a lifelong of a now twenty-eight-year business career, I hid my mathe­ love of learning. The executives in your company and managers matics background. It was not shame or embarrassment that in your plant need high-level mathematical skills to ensure that inspired my actions, as I am quite proud of my achievements in the discipline and feel strongly that mathematics is a major they are making the right decisions with your resources. contributor to all of my business accomplishments. No, it Without those skills, your company's ability to succeed could was the knowledge, based on experience, that talking about be compromised. mathematics with those not steeped in the discipline would In addition to these one-on-one conversations, I have been steer a business conversation away from business and onto very fortunate in that I have been able to discuss these issues an entirely different plane. in the halls of Congress and with larger groups of business What was the conversation? I am sure that you have people and politicians. And they get it! The recognition is there had it. that mathematics mastery is becoming an issue of national Person 1: Dr. Schaar, I appreciated your comment on security and corporate competitiveness. education policy and the role that corporations can play in Here are some facts that highlight the criticality of the issue planning long-range programs. You seem to have such a deep and that have been getting attention: understanding of what educators want and need. What is • While business is willing to train in specialized disciplines your background? like running a semiconductor manufacturing site, the two­ Schaar: I am a mathematician and taught at the university year training program requires someone who has skills in level for several years. solving multistep problems. Person 1: Oh, I was never any good in math. Hated the • 53% of incoming college students will take remedial math­ subject actually. I could never figure out how I would use it ematics or English courses; over half will never graduate. after school and didn't get along with my teacher. ... • 56% of engineering Ph.D.'s earned at U.S. universities in 2000 I do not have to continue. But over the years I began to went to foreign nationals. realize that there was something hidden in Person 1 's • Between 1995 and 1999, engineering degrees awarded in remarks. It was an insinuation that Person 1 's nonmastery of China increased 37%; in the U.S. they declined 20%. mathematics was a nonissue. She was a successful business Finally, just being a well-informed citizen in today's com­ person in spite of it. So there! Her lack of mastery was vali­ plex society takes more mathematical knowledge and prob­ dated in the business world, and also by her peers, who lem-solving skills than ever before. The examples here are eagerly confessed their lack of mathematical savvy as if it numerous and growing. In the area of medicine, with headline invited entry into a secret club. These same leaders trumped after headline on the outcomes of prescription drug studies, their abilities to succeed in the business world while down­ what is a person to do? How does one weigh the risks of one playing the significance mathematics played in the equation. medication over another or of doing nothing without under­ What changed in 1987 that caused me to force the con­ standing the language of the studies? If I am in pain, should versation into the open? I take Celebrex or Vioxx, keeping in mind their heart risks? It was the confluence of two factors. First, I had joined Texas What are the issues surrounding the current debate on Instruments, Inc. (TI) two years before. It was then and is today social security? When, if ever, is the fund going to run out of a high-tech manufacturer of some of the most sophisticated money? What do the proposed ideas mean with regard to semiconductor and Digital Light Processing™ devices in the benefits now and in the future? These are massive issues that world. The company is populated by engineers, scientists, will affect everyone at some time in their life. They need to and mathematicians, and it needs more every day to fulfill its growing needs. Second, it had become obvious to those be critically understood. examining data like the SAT mathematics scores that our The steps in this understanding are ones that are familiar school population was declining in mathematical knowledge. to us: These two factors- an increasing need for high-tech 1. Develop a clear understanding of the question. employees and a decline in the ability of the U.S. to produce 2. Translate the question into one that is precise and can enough people to staff those jobs-created a personal pas­ be answered. sion in me to further the debate about the need for technical 3. Choose and use appropriate tools to answer the precise education whenever, wherever, and with whomever possible. question. My business card has had "Ph.D." on it for years in order 4. Evaluate the solution in terms of the original question. to stimulate the debate every time I hand one out. Now the These are the steps of mathematical problem solving, and discussion goes something like this: the importance of these steps needs to be emphasized at Person 1: Thank you for visiting our manufacturing plant. every opportunity. I noticed from your card that you have a Ph.D. What is it in? Schaar: I am a mathematician. - Richard Schaar Person 1: Oh, I was never any good in mathematics. Texas Instruments, Inc.

AUGUST 2005 NOTICES OF THE AMS 717 Letters to the Editor "However, abstract algebra has sub­ one might expect, that plural pronoun verted its own role in mathematics. Its "we" is not mere scholarly conven­ concepts were formulated to unify tion. Rather, the Diophantine prob­ History of Mathematics from a various seemingly diverse and dis­ lems selected by Artemiadis are Mathematician's Vantage Point similar mathematical domains as, for exactly the same as those selected example, group theory did. Having The AMS, one of the most important by Kline for page 142 of his book. formulated the abstract theories, mathematical organizations in the One can also find bits of Carl Boyer's mathematicians turned away from the world, has recently put its imprimatur history in Artemiadis's text as well, original concrete fields and concen­ the most obvious example being on a shoddily written and ineptly trated on the abstract structures. plagiarized version of Morris Kline's the idiosyncratic chronological table Through the introduction of hundreds which appears in an appendix. Mathematical Thought from Ancient of subordinate concepts, the subject to Modern Times. This ostensibly new I could cite further examples, but has mushroomed into a welter of in classic mathematical tradition, I book is entitled History of Mathe­ smaller developments that have little matics from a Mathematician's Van­ will leave this as an easy exercise for relation to each other or to the origi­ the interested reader. tage Point. Nicholaos K. Artemiadis nal concrete fields. The unification claims to be the author. Since the AMS is one of the largest has been succeeded by diversification and most visible organizations of I will provide one specific example and specialization. Indeed, most work­ of plagiarism for the sake of those mathematicians in the United States, ers in the domain of abstract algebra the books it publishes ought to be fortunate enough not to have wasted are no longer aware of the origins of fifty dollars on this book. Consider the distinguished by high standards of the abstract structures, nor are they writing and editing. It is hard for me striking thesis that Artemiadis pro­ concerned with the application of pounds at the conclusion of his chap­ to believe that Artemiadis's book was their results to the concrete fields." edited for style or content at all. Un­ ter on the history of abstract algebra These two paragraphs are isomor­ (pages 377-8): derstandably, an editor may not have phic. Artemiadis has not merely time to scrutinize each and every page "We can say that abstract algebra summarized Kline's thought without in a sense 'undermined' its own role of a manuscript that ends up on his citation, he has copied it line by line. desk, but surely it isn't too much to in mathematics. The various notions Differences in word choice are merely ask that he will at least examine the and principles were introduced in it, the inevitable product of translating first page of chapter one. This page, in order to unify the apparently dif­ Kline into Greek and then translating in Artemiadis's book, contains the ferent situations. This was achieved the translation back into English. by group theory. But after the for­ In a single hour I located a dozen following paragraph: mulation of the abstract theories, or so such "borrowings" before '"Moscow's Papyrus' dates back to mathematicians gradually distanced putting Artemiadis's book away in 1850 B.C. The most interesting result themselves from the concrete struc­ disgust. Sentences, paragraphs, even included in this papyrus is the calcu­ tures and concentrated their research whole pages of "his" text are stolen lation of the volume V of a truncated on these abstract structures. Hence, from Kline. Readers with access to square pyramid. If b = 0, then this with the introduction of hundreds of both works who are skeptical of my formula gives the volume of the particular notions, the object of study claims may wish to compare, for square pyramid." was divided into other more specific example, Artemiadis's chapter on In this passage, a completely su­ activities, which were more or less in­ topology (pp. 345-56) with Kline's perfluous symbol (V), never subse­ dependent from one another and were chapter entitled "The Beginnings of quently referred to, is introduced, not related to the concrete areas that Topology" (beginning on page 1158). while a mysterious quantity (b), never were considered initially. In other Such a comparison reveals that previously defined, plays a vital but words, the unification mentioned Artemiadis stole almost every sen­ necessarily incomprehensible role. above was followed by diversification tence in his chapter. Or compare Did the editors decide that these and specialization. Hence we have Artemiadis's take on Omar Khayyam compensating errors somehow nulli­ reached the point where many who and Arabic mathematics (page 163, fied one another and could therefore work in the area of abstract algebra beginning with the second paragraph, remain in the book? Had the editors ignore the tools of the abstract struc­ "Even though the solutions .. . ") to paid enough attention to notice such tures that they study and furthermore Kline's treatment of the same topics shoddy writing, they might have no­ they are not interested whether the (page 193, beginning with the third ticed the rampant plagiarism as well. results have any applications in paragraph, "Though the Arabs gave Artemiadis should bear the heaviest concrete areas." algebraic solutions ... "). The next page share of the guilt in this case, but the Indeed, the thesis is a bit too strik­ or so of the two texts will be found to editors have a lot to answer for as ing; rather like a playwright whose be nearly identical, right down to the well. character muses, "Shall I live, or shall diagrams and the labels thereupon. -Seth Braver I not live? That is the problem." The On page 143 of Artemiadis's book he University of Montana original passage occurs on page 115 7 writes, "We present some of the prob­ of Kline: lems considered by Diophantus." As (Received March 22, 2005)

718 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Letters to the Editor

Reply to Braver students staged a televised reenact­ The American Mathematical Society ment celebrating the Sbarro restau­ Submitting Letters to the views plagiarism with the utmost se­ rant bombing. Editor riousness. When Braver brought this Security restrictions such as check­ The Notices invites readers to matter to our attention, we immedi­ points and the security barrier have submit letters and opinion pieces ately ceased all sales of the book, been necessitated by repeated suicide on topics related to mathemat­ reviewed the evidence he had pre­ bombings. Victims of those attacks ics. Electronic submissions are sented, and gathered further evidence have included university students and preferred (notices-letters@ of our own. Based on that review, we staff-for example, the bombing at ams . o rg); see the masthead for decided to discontinue publication of the Hebrew University of Jerusalem. postal mail addresses. Opinion the book permanently. Professor Mumford seems to ne­ pieces are usually one printed Artemiadis has had a distinguished glect Israel's grave security concerns. page in length (about 800 words). career as a mathematician in Greece. For instance, just north of densely Letters are normally less than one populated Tel Aviv, Israel is less than When his book was put under contract page long, and shorter letters are is overlooked by for the Society's English-language ten miles wide and preferred. the hills of the West Bank. edition, it existed only in the original We hope for a peace in which the Greek. The accusation that the edi­ security fence can be removed. Its tors failed their duty by not combing temporary nature has been repeat­ for errors or plagia­ his manuscript edly emphasized, just as security mea­ rism is not realistic. Scholarly pub­ sures elsewhere can be relaxed when aspects of academic lishing, like many the threat disappears. life, necessarily rests on a foundation of trust towards authors. -D. S. Lubinsky The Society promotes high stan­ Georgia Tech dards of academic integrity and [email protected] regrets having participated, however and inadvertently, in a project that did -Paul Nevai not live up to those standards. Department of Mathematics The Ohio State University - John Ewing nevai @math.ohio-state.edu Executive Director, AMS [email protected] (Received May 11, 2005) (Received Aprilll, 2005)

What Summers Said Conditions Facing Israeli In the May 2005 issue of the Notices, Universities Judith Roitman and Carol Wood write: We believe comment is due on Pro­ "The president of Harvard stands up fessor Mumford's article on mathe­ in a room full of women scientists matics in the Near East (May 2005), and says that maybe women can't do since he did not elaborate on the pe­ first-rate science and math for genetic culiar conditions facing Israeli uni­ reasons." Of course, Lawrence Sum­ versities. mers made no such statement. Those Despite repeated wars by neigh­ interested in reading what he actually boring c ountries to destroy Israel, said can find it at www. president. Israeli universities have built a vibrant harvard.edu/speeches/ 2005/ scientific environment in which Arab nber. html. For an intelligent debate and Jewish Israelis- and Palestinians on some of the issues in his speech, like Iyad Suwan- can study. Israeli see www.edge.org/3rd_culture/ universities have successfully edu­ debateOS/ debateOS_index.html. cated hundred s of thousands of Jewish students whose parents were - ]. S. Milne Jewish refugees from Arab countries. University of Michigan In conjunction with Professor [email protected] Mumford's remark o n a meeting a t Bir Zeit about Palestinian prisoners (Received May 16, 2005) in Israeli jails, it is worthwhile to point out t hat th e same university 's

AUGUST 2005 NOTICES OF THE AMS 719 The p-adic Icosahedron Gunther Cornelissen and Fumiharu Kato

Editor's Note: The Notices has been pleased to feature color graphics. With this article, we initiate color text. -Andy Magid

he last proposition in Euclid's Elements for more than seventy years that the real numbers states that there are only five convex form only one of the many possible completions regular polyhedra, called the platonic of the field of rational numbers, the other possi­ Tsolids (after Platon, who listed them in his bilities being given by the p-adic numbers. So it Timaios around 3 50 B.C.): tetrahedron, seems only natural to ask for the analogue of the cube, octahedron, icosahedron, and dodecahedron. platonic solids in the p-adic world. The question This very short list of extremely beautiful and reg­ turns out to be relevant for the study of p-adic "orb­ ular mathematical objects has mystified scientists ifolds" and number-theoretic properties of, for in­ for many centuries. For instance, Kepler's Mys- stance, solutions to hypergeometric differential terium Cosmographicum from equations. We will illustrate the construction using 1597 (wrongly) models distances our own favorite polyhedron, the icosahedron, the between planets in the solar only platonic solid (with its dual polyhedron, the system using the platonic dodecahedron) with a simple group of symmetries. solids (Figure 1 ). More re­ After that we will show some examples from the cently, Grothendieck is sup­ theory of p-adic uniforrnization. posed to have said, "The platonic solids are so beau­ The Real Icosahedron tiful and exceptional that We will first recall a construc­ one cannot assume such ex­ tion of the usual icosahe- ceptional beauty will hold in dron. Let us agree that more general situations." when discussing a (Notices, vol. 51 , no. 10, p. 1196). The figure in the text, we Figure 1. platonic solids fit into the larger picture of "ADE­ relate part of the The solar classification(s)" and the theory of finite reflection picture to part of system groups, as is very well explained in John Baez's the text by giving according to Week 62 Finds [2]. both the same color Kepler's The solids belong to the "real" world: they are (red, green, or blue­ Mysterium part of geometry over the real numbers. But, fol­ up to Figure 11). The Cosmo­ lowing Hensel and Ostrowski, it has been known icosahedrmi in Fig­ graphicum. ure 2 consists of 12 Gunther Cornelissen is lecture r/ researcher at the Uni­ vertices, 30 edges with 30 versity of Utrecht, The Netherlands. His email address is Figure 2. The midpoints, and 20 faces (each of [email protected] . icosahedron. Fumiharu Kato is associate professor of mathematics which is an equilateral triangle) at Kyoto University, japan. His email address is with 20 barycenters. [email protected]. ac.jp. Projecting the icosahedron from its center to a The authors have written some ten papers on nonar­ circumscribed sphere maps each edge onto a part chimedean uniformization. This text is based on a of a geodesic lin~ on the sphere. These geodes lecture of the second author at th ic e Mathematical Society lines inters -of japan meeting of September 2003 held at Chiba ect at yertices, midpoints of edges, or University. barycenters of faces. They provide a tessellation of

720 NOTICES OF THE AMS VOLUME 52, NUMBER 7 the sphere by 120 triangles with an­ gles (rr / 2, rr / 3, rr / 5) (Figure 3). Observe that one would arrive at the same tes­ sellation starting from the dodeca- hedron (which is the Figure 4. Quotient of the Riemann sphere by I. dual polyhedron to Figure 3. Icosahedral the icosahedron), tessellation of the Riemann but with green ver­ {11 - cl,lc-a - b l,la - bi}= H . 1. H sphere. tices: in Figure 3, connecting five ad- (e.g., a = 11 / 60, b = - 1/ 60, c = 1/ 2). jacent green spots reveals a pentagon, the face of a dodecahedron. p-adic Numbers: A Brief Recap Let As denote the group of even permutations One construction of the real numbers is by con­ on five letters, i.e., the simple group with 60 ele­ sidering them as the completion of the rational ments. An icosahedral group is a copy of As em­ numbers Q w.r.t. the usual absolute value, i.e., by bedded in PC L(2, C), the automorphism group of adding to Q all (limits of) Cauchy sequences mod­ the Riemann sphere ( = complex fractional linear ulo null-sequences. A famous theorem of Ostrowski transformations). All icosahedral groups turn out states that, up to a certain natural equivalence, Q to be conjugate, and one of them is given explic­ carries exactly the following further absolute val­ itly by generators as follows: ues: let p be a prime number; for q E Q, define lqlr = p-e if we can write q = pe · u with u a rational number without pin the numerator and the denominator. In this context a number is small ) ). precisely when it is highly divisible by p. The completion of Q w.r.t. I · lr is called the set of where ( is a primitive fifth root of unity (e.g., p-adic numbers and carries a natural operation of ( = e2rri /S ). The icosahedral group is the orienta­ addition and multiplication that make it into a tion-preserving symmetry group of the icosahe­ complete field. As a typical example, the sum dron; it has 6 cyclic subgroups of order 5, 10 cyclic 1 + p + p 2 + p 3 + . · · (that diverges in R) con­ subgroups of order 3, and 15 cyclic subgroups of verges in the p-adic numbers, since for its general order 2. The respective fixed points of these sub­ term, Ipi Ir = p-i ~ 0 as i ~ + oo. The sum actually groups on the Riemann sphere are the 12 vertices, equals the rational number 1/ (1 - p), but of course 20 barycenters of faces, and 30 midpoints of edges there are many more p-adic numbers than just of the icosahedron. rational ones. A general p-adic number q can be The quotient of the Riemann sphere by the expanded as a "convergent Laurent series in p": group I is again a Riemann sphere. The quotient map q = a Np N + a N+ lPN+l + ... for some integer N is branched above three points on the sphere, with (possibly negative) with a; E {0, 1, ... , p - 1}. The branching degrees 2, 3, and 5 respectively (Figure 4). set Zr of p-adic integers consists of those p-adic The ramification points over the branch points of numbers q for which Iq Ir ::s; 1. These are exactly the degrees 5, 3, and 2 are exactly the vertices, barycen­ numbers for which only positive powers of p occur ters of faces, and midpoints of edges. Each pair in the above "Laurent series" (soN can be chosen consisting of a white and yellow triangle is a a positive integer). fundamental domain for the action of I, and each triangle is mapped onto one of the half-planes in the quotient. The p-adic Riemann Sphere The multivalued function inverse to this In order to find the p-adic analogue of the icosa­ covering map can be written as the ratio of two hedron, we just have to look at the construction independent solutions to the Gaussian hypergeo­ above: one finds the fixed points of an action of metric equation E(a, b, c): the cyclic subgroups of As on the Riemann sphere. So first of all, we have to introduce the p-adic ana­ d 2 u du logue of the Riemann sphere, which is an analytic x(l - x) dx2 + [c - (a + b + 1)x] dx - abu = 0, structure on the projective line P1 . The naive way of "doing analysis with the p-adic metric on the where the constants a, b, and c are any rational coordinates" does not work (because of total numbers such that disconnectedness). One of the most natural ways

AUGUST 2005 NOTICES OF THE AMS 721 of putting a genuine p-adic analytic structure on original "real" pic- P1 is by regarding it as a Berkovich space, but as ture. To visualize the phenomena we are interested in are already this and the corre­ visible at the level of the "skeleton" of that space, spondence be­ we will content ourselves with a description at the tween ends of T level of trees [9]. The Bruhat-Tits tree T of and points of P1 (K) PGL(2, Qp) is a graph, technically defined as in a clearer way, we follows: will now draw P1 (K) as an actual compact • Vertices are Q; -homothety classes [M] of Zp­ "sphere" and put the lattices M in Q~ . tree T inside it; see Fig­ vertices [M] and [N] are joined by an edge • Two Figure 6. The Bruhat­ ure 6. if and only if representatives M and N can be Tits tree of PGL(2, Q2) For any compact (e.g., chosen such that pM c N c M. 1 inside P1(Q2). finite) subset l: of P (K), The graph Tis actually a tree, and edges emanat­ we define a subtree T~ ing from any given vertex are in one-to-one corre­ of T that is minimal spondence with Fp-rational points of P1 . amongst all subtrees of T having l: as its set of The graph Tis a regular (p + 1)-valent tree, as ends. For example, if l: consists in Figure 5 (where p = 2 for simplicity). of three points, the sub­ We will actually need a slight extension of tree T~ is a "tripod", as this definition, because we will want the fixed in Figure 7. points of elements of order 2, 3, and 5 from A5 act- ing on P1 to be defined over the field we are work­ The p-adic ing with, and QP itself is Icosahedron not always good enough The matrix repre­ for that. So we let K be a sentation of the finite field extension of group I from the Q P that contains a primi­ first section makes tive third, fourth, and fifth sense in PGL(2,K), root of unity (i.e., all roots since K contains a primi- of X 60 - 1). The p-adic ab­ tive fifth root of unity (. Let Figure 7. A tripod. solute value extends l: denote the set of points of uniquely to K; denote this P1 (K) fixed by a nontrivial element of I. There are extension by I · 1. Let th 12 points fixed by at least one of the elements of be the set of integers inK: order 5 in I, 20 points fixed by at least one element th := {x E K: lxl :::; 1}, of order 3 in I, and 30 points fixed by at least one Figure 5. Part of the Bruhat-Tits tree which actually turns out element of order 2 in I; and these points together of PGL(2, Q2). to be a ring. Let rr denote form all of l:. We call the subtree associated to this a uniformizer of K, i.e., a l: the p-adic icosahedron: it is the structure that generator of the ideal { lxl < 1} in OK. Let k denote arises fromconnecting the fixed points of elements the residue field of K: k = th / rr; it is actually a fi­ of I via geodesics in the p-adic Riemann sphere, so nite field. All the above definitions make sense if its construction really parallels that of the real one replaces Q P by K, Zp by th, and p by rr. One icosahedron. The p-adic icosahedron is a tree wit4 arrives at the Bruhat-Tits tree T of PGL(2, K). 12 + 20 + 30 = 62 ends. Since the actual "position" The ends ofT are equivalence classes of infinite of points on P1(K) does not make sense, it is the half lines in T (two of which are identified if they combinatorial structure ofT~ , together witf1 a la­ only differ in finitely many edges), and these ends beling of vertiCes and edges by their stabilizers, are in one-to-one correspondence with K-rational that is of interest. We will do this labeling:as fol­ points of P1 . Since PGL(2,K) acts on homothety lows: if a group is cyclic, we just label by its order; classes of lattices in K 2, from its definition the otherwise, we indicate the full group. Ends are in­ tree T acquires a natural action of the group dicated by edges carrying arrows, and the stabilizer PGL(2, K), and via this correspondence its action of the end is written as a label on the arrow. Finally, on the ends of Tis the same as its natural action if two vertices are stable by the same group, it is on P1(K). understood that the same holds for the connect­ We then have a way to connect points of the ing edge. (topologically totally disconnected) space P1(K) If p > 5, the p-adic icosahedron is rather boring: (seen as ends of 'I) via infinite paths inside T , and it is the union of half-lines corresponding to the these paths play the role of the geodesics in the points of l: emanating from a single vertex, the

722 NOTICES OF THE AMS VOLUME 52, NUMBER 7 unique vertex fixed by the whole of I, which we call s s the center of T'f.; see Figure 8.

Figure 11. The dyadic icosahedron.

Figure 8. The p > 5-icosahedron. special status of the primes p :s: 5 will appear over In the next three pictures we consider what hap­ and over again in the sequel. pens if p :s: 5. The icosahedron is the right part of each figure, and the left part is a zoom-in on the "horizontal" part of the right picture. Application: p-adic Orbifolds If p = 5, the six lines fixed by the six cyclic sub­ One can perform the previous construction start­ groups of order 5 (so-called mirrors of order 5) are ing from the other finite subgroups of PGL(2,K) separated from the center by fixed points of a copy (such as A4, S4, etc.) to arrive at the full list of of D5 in I; see Figure 9. p-adic polyhedra. This is because the full list of finite subgroups of PGL(2) over any field is known up to conjugation: over a field of characteristic zero such as K, the list is identical to that over the complex numbers; over a field of positive charac­ teristic (which we will briefly touch upon later), there is Dickson's famous classification. In the end, all p-adic (or nonarchimedean) polyhedra can thus be explicitly drawn by the techniques from the previous section. They play a role in the construc­ tion of p-adic orbifolds and in classification re­ sults related to those. Figure 9. The pentadic icosahedron. Let us first briefly recall Mumford's theory of nonarchimedean uniformization of curves (cf. [5]), which is a mixture of the usual uniformization the­ If p = 3, 10 mirrors of order 3 are separated ory of Riemann surfaces by embedding the fun­ from the center, as in Figure 10. damental group in PSL(2, R) and the theory of Schottky uniformization. The general setup is a bit technical. Let K be a general nonarchimedean valued field, complete w.r.t. an absolute value that satisfies the strong triangle inequality Ia + bl :s: max{lal, lbl} for all a,b E K; for example, (K, I · I) = (Qp, I · lp) . If r is a torsion-free finitely generated discrete subgroup of PGL(2, K), let Lr de­ note the set of limit points for the action of r on P 1(K), let Or = P}an - Lr, and let Tr = TLr; here the superscript "an" refers to a K-analytic structure on P1 . Then Xr = Or ;r can be given the structure of a Figure 10. The triadic icosahedron. smooth projective curve over K . Technically speak­ ing, this curve admits a semistable model over the integers of K whose special fiber is a union of k­ Finally, if p = 2, the 15 mirrors of order 2 are rational curves intersecting in k -rational points. The separated from the center and from the mirrors of intersection dual graph of this special fiber is iso­ order 3; see Figure 11. Kazuya Kato from Kyoto Uni­ morphic to Tr. Conversely, every curve over K with versity proclaimed that these objects should be split multiplicative reduction is isomorphic to a seen as "the flowers in his p-adic garden". The curve obtained via such a construction; such a

AUGUST 2005 NOTICES OF THE AMS 723 More generally, if N is any (not necessarily free) finitely generated discrete subgroup of PGL(2, K) with set of limit points LN, let J N denote the set of all fixed points of elements of finite order inN. $ Let TrJ = TLNu:fw . • If N is torsion-free, then TJ = TN. • If N is finite, then LN = 0 , so TN= 0, but TJ is a p-adic polyhedron. Figure 12. Example of Tr, Tr If, and the reduction of Xr. If we let D.N = P}(an- LN, then the quotient XN := D.NIN carries a structure of smooth projec­ tive curve. Actually, there exists a finite index nor­ mal free subgroup r c N, and XN is the quotient of the Mumford curve Xr by the finite group N If. 222222 In our example, Xr is a curve of genus two that admits an automorphism of order t wo (on the above equation, it is just y ...... - y), and this can be seen within the above framework of "orbifold uni­ \tJ formization" as follows: we let N be genera ) ted b • -\Y•Y y three elements:

2+ rr a = -2(1 + rr) ) l +R ( ; -~ ) 'b = ( 2 -2- TT '

Figure 13. Action of Non TrJ , TNI f, and TrJ IN. c = ( ~ ; ) . curve is called a Mumford curve. Let us clarify these concepts on an example; see Figure 12. With Oi = ab and {3 = be, N is isomorphic to the Assume K does not have characteristic two, and free product of three copies of a cyclic group of two fix rr with 0 < lrrl < 1. Define a subgroup r of elements having r as normal subgroup of index two. PGL(2, K) generated by two elements We have displayed the corresponding pictures in Figure 13. Now Xr is a double cover of XN ~ P1 branched above six points (the ends of TJ IN). ( rr(2 + rr) - 2rr(1 + rr) ) ()( 4 rr2 - 2rr - 4 ' Application: Classification Results -rr(2 + rr) 2 In the correspondence between N and T J (of which {3 2(2 + rr ) ) ( - 2rr -rr2 - 2rr + 4 · an example was given above), the ends of TJ IN correspond to the points of XN over which the map Xr - XN is branched, and the stabilizer of such Part of the associated tree Tr with the action of an end is exactly the ramification group of the some elements from r is shown in Figure 12, to­ corresponding point in the cover. This is a general gether with the quotient Tr If and the reduction of phenomenon that can be used in the opposite the corresponding curve Xr (which is intersection direction: suppose one does not start from a group dual to the quotient graph in the following sense: N, but one instead is interested in classifying lines in the reduction are replaced b y vertices in coverings of the projective line P1 over K that are the graph, and vertices are connected if and only branched above a fixed number of points with if the corresponding lines intersect). This group r given ramification groups and such that the cover is free of rank two, the corresponding curve has is a Mumford curve. Example: coverings of P1 that genus two, and its reduction is a "dollar" sign are branched over four points with ramification (which has two holes, just like Tr /D. The fact that indices (2, 2, 2, 3). The strategy to classify them is the number two occurs three times in the previous then as follows (see Figure 14): sentence is no coincidence! The algebraic curve Xr • One constructs the list of p-adic polyhe has some equation dra (="atoms") TJ and draws the graphs TJ IN. Y2 = (x - al) ... (x - a 5), • One tries to bond together these graphs TrJ IN along common ends by folding them together and a suitable change of coordinates (x, y ) leads to (="chemical compound"). In this procedure, one a good model, of which the special fiber is gotten assures that in the bond only four ends remain by reducing everything modulo rr. (with the correct stabilizers). On the level of

724 NOTICES OF THE AMS VOLUME 52, NUMBER 7 2 2 2 2 2 2 (A) (B) connect! Os As 04 5 4 Ds *z5 As D4 *z S4 A s a----s 2 3 2 4 3

2 2 2 2 (C) (D)

3 2 03 A4 Oz 3 2

2 D3 *z3 A4 3 2 D2 *z2 D3 3 2 2 Figure 15. Four possible (2, 2, 2, 3)-coverings.

As .______5 _____. Ds matrices, and one fixed by a cyclic subgroup of order 8. Again, this list of polyhedra can be used to clas­ sify coverings of P1 by Mumford curves branched 3 2 above two or three points in positive characteris­ tic and leads to a sharp upper bound for the num­ Figure 14. "Inorganic chemistry method". ber of autoinorphisms of such Mumford curves X: if X is a Mumford curve of genus g over a field of abstract groups, this process is known as "amal­ positive characteristic, then gamation" of finite groups (cf. [9]). Aut(X) .:5 max{12(g - 1), 2.../9(.../9 + 1)2 } . • One makes sure that the corresponding group Returning to the case where K is p-adic, if N pro­ subgroup of PGL(2, K) exists as a discrete duces a covering of P1 branched above exactly (="existence problem of the compound"; cf. [8]). three points, one calls N a p -adic triangle group (of In the example of (2, 2, 2, 3)-branched coverings of Mumford type). The first ones were found by Yves P1 for p > 5, one gets a list of possible abstract Andre [1]. By the inorganic chemistry method above, structures of the group N, as in Figure 15. Each of the second named author has shown that they these can be realized by a Mumford curve. As a mat­ exist only if p = 2, 3, or 5 (again, p .:5 5) and that In 16 we dis­ ter of fact, (A), (C), and (D) are realized by there are infinitely many such. Figure p-adically open loci in a pencil of genus six curves play the tessellation of the unit disk correspond­ ing to a classical (2, 4, 6)-triangle group together on a Del Pezza quintic surface studied by Edge in with its triadic companion. The parallel is as fol­ the early 1980s [7]. lows: the classical group has limit points on the It follows from the Riemann-Hurwitz-Zeuthen boundary of the Poincare unit disk that correspond X symmetries (large formula that curves with many to the brown ends in the triadic case. The fixed 1 automorphism group) arise as' coverings of P points of elements of finite order (2, 4, or 6) in the branched above at most three points. If X is a disk are the blue, green, and red vertices of the Mumford curve of genus g, then our classification triangles occurring in the tessellation (we have can be used to bound the number of such sym­ colored them in only one triangle), whereas in the metries, since for X = Xr, Aut(X) = N /fwith N the triadic case the fixed points of elements of finite normalizer of r in PGL(2,K). We can recover the order (2, 4, or 6) are the blue, green, and red ends. following result of Herrlich: If X is a Mumford The classical Riemann-Hilbert correspondence curve of genus g ~ 2 over a p-adic field, then the between representations of the orbifold funda­ following sharp bound holds: Aut(X) .:5 c · (g - 1) mental group and differential equations has a with c = 12 if p > 5, c = 30 if p ·= 5, c = 24 if p-adic analogue via the theory of tempered cover­ p = 3, and c = 48 if p = 2 (again, p .:5 5 is excep­ ings due to Yves Andre (cf. [1]). Our particular tional). triangle group ~(2, 4, 6) corresponds in this way to There is no reason to restrict to p-adic fields K; the Gaussian hypergeometric differential equation E( I 7 5 )· one might as well develop the theory if K is a non­ 24' 24' 6 . archimedean valued field of positive characteris­ d 2 u ( 5 4 ) du 7 tic [4], such asK = Fq((t)). Then PGL(2,K) has x(l - x) dxz + 6 - 3x dx - 576 u = O. more finite subgroups, but all polyhedra can be classified. There is, for example, such an exotic The fact that this differential equation arises as specimen as the N = PGL(2, ?)-polyhedron in above implies that the ratio of two nonpropor­ characreristic 7, whose 'l'J IN-graph has two ends: tional 3 -adic solutions to the equation can be glob­ one fixed by the subgroup of upper triangular ally continued on a finite cover of P1 : this is a very

AUGUST 2005 NOTICES OF THE AMS 725 rare phenomenon in the p-adic situation, where discretely; for varying t this produces a nonisotrivial there is no good analogue of analytic continuation. family of Mumford curves of genus six with As as automorphism group. Now on the algebraic side, The "Conformal-Hyperbolic" Dictionary we know that such a curve is a cover of P1 branched Various invariants of the covering Xr ~ XN of al­ over four points with ramification indices 2, 2, 2, 3. gebraic ("conformal") curves can be computed Fixing three of these points by an automorphism group theoretically ("hyperbolically") on 'lJ . For ex­ of P1 , we are left with one degree of freedom: the ample, the genus g of the curve XN is the same as location of the fourth point. Again, we see that the cyclomatic number c of the quotient graph the deformation space is one-dimensional. In [3] 'lJ 1N (the smallest number of edges which must one finds two calculations of the dimension of this be removed such that no circuit remains): deformation space (even in positive characteristic): g(XN) = c('iJ IN). one in the "conformal" world of algebraic curves As a second example, we have the following and on:e in the "hyperbolic" world of the graphs combinatorial group theory formula of Karass, 'lN. In characteristic zero (where the formula has Pietrowski, and Solitar [6]: also been found by Herrlich), the formula says that the number of points b of XN above which there g(XN) - 1 = I _ 1_ - I _ 1_ ' is ramification equals IN lfl eE£ INe I vEV INv I b(XN) = I d(Nv) - I d(Ne), where E is the set of edges and V is the set of ver­ vEV eE£ tices of 'iN 1N (and N * is the stabilizer of * for the where d(G) = 2 if G is cyclic and d(G) = 3 other­ action of Non some lift of * to 'iN). The left-hand wise. The fact that these two numbers agree in side of this formula is "algebra-geometric", since general appears as a statement in combinatorial N If is the (finite) covering group of Xr ~ XN. group theory of which we do not know a direct Another instance occurs when one computes in proof (in the example, we get 4 = 3 + 3 - 2 ). It is two ways the equivariant deformation space of a interesting to note that the computation of the finite group acting on a Mumford curve. As an ex­ equivariant deformation space uses the "decom­ ample, an embedding of a group of abstract type position" of 'lJ 1N into nonarchimedean polyhe­ N = (A) as in Figure 15 is given by conjugating the As to its standard form "!"; any dihedral group of dra to reduce the calculations to those for the order ten that shares the cyclic group of order 5 action of a finite group on the nonarchimedean Riemann sphere. generated by (g nwith this I is then embedded in PGL(2,K) by References [1] YVES ANDRE, Period Mappings and Differential Equations. Ds = \ ( g ~ ) ,( ~ ~ ) ) , From ([ to Cp. MSJ Memoirs, volume 12, Mathemati­ cal Society of Japan, Tokyo, 2003. T6hoku-Hokkaid6 where tis a free "deformation parameter" restricted lectures in arithmetic geometry, with appendices by only by the condition that Ds should be embedded F. Kato and N. Tsuzuki.

limit points ~~'1\:---r--:7\"--3~~ ~ ~- ---... -- ~-iJi:iiiliiii~

Figure 16. A triangle group t.(2, 4, 6).

726 NOTICES OF THE AMS VOLUME 52, NUMBER 7 [2] JOHN BAEZ, This week's finds in mathematical physics (week 62), August 28, 1995, math. ucr. edu/home/ baez/week62.html. About the Cover (3] GUNTHER CORNELISSEN and FUMIHARU KATO, Equivariant Dyadic icosahedra deformation of Mumford curves and of ordinary curves The cover for this month exhibits fanciful in positive characteristic, Duke Math. ]. 116 (2003), renderings of the dyadic icosahedra dis­ 431-470. cussed in the article by Gunther [4] GUNTHER CORNELISSEN, fUMIHARU KATO, Cornelissen and ARISTIDES and Fumiharu KoNTOGEORGIS, Discontinuous groups in positive Kato. characteristic and automorphisms of Mumford curves, -Bill Casselman Math. Ann. 320 (2001), 55-85. Graphics Editor (5] LOTHAR GERRITZEN and MARIUS VAN DER PUT, Schottky ([email protected]) Groups and Mumford Curves, Lecture Notes Math., volume 817, Springer, Berlin, 1980. [6] A. KARRAss, A. PIETROWSKI, and D. SOUTAR, Finite and infinite cyclic extensions of free groups, ]. Austral. Math. Soc. 16 (1973), 458-466. (7] FUMIHARU KATO, Mumford curves in a specialized pen­ cil of sextics, Manuscripta Math. 104 (2001), 451-458. [8] __ , Non-archimedean orbifolds covered by Mum­ ford curves,]. Algebraic Geom. 14 (2005), 1-34. [9] JEAN-PIERRE SERRE, Trees, Springer Monogr. Math., Springer-Verlag, Berlin, 2003.

Where Do Notices Covers Come From? Usually Notices covers come from the articles inside the Notices. In practice, most covers are created specifically to relate to articles that have been accepted for publication. Sometimes the cover image will come straight from the article, but more often it takes off from an idea in the article, even sometimes a mere hint. But it is possible to go the other way-occasionally articles have been written to go with an idea for a cover. If you have an image that you think would make a good cover, before submitting it you should write an article to go with the cover. The article should be of sufficient quality to be accepted on its own. But it need not be long; in principle, it would be reasonable for the article to simply explain the picture. The simplest criterion to keep in mind is that the picture should try to explain some­ thing mathematical. If the picture is striking enough that it could stand on its own, then the accompanying article could explain the picture, rather than the picture illustrating the article. -Bill Casselman, Graphics Editor, ([email protected])

AUGUST 2005 NOTICES OF THE AMS 727 WalterFeit (1930-2004)

Leonard Scott, Ronald Solomon, john Thompson, john Walter, and Efim Zelmanov

alter Feit died on July 29, 2004, at "Walter Feit was born in Vienna, Austria, in 1930. age seventy-three after a long ill­ In August of 1939 his parents saved his life by W ness. He had been on the faculty at placing him on the last train (KinderTransport) Yale for forty years, and the follow­ allowed to carry Jewish children out of Austria. He ing is taken from his obituary at the arrived in England just as the British government Yale website. It summarizes Walter's achievements was evacuating all children from London. After and stature, and provides touching detail on Wal­ being relocated a few times, he settled in a refugee ter's childhood during the Second World War. hostel in Oxford. In 1943 he won a scholarship to "Professor Feit's 1963 paper with John G. Thomp­ an Oxford technical high school. His teachers were son, 'Solvability of groups of odd order', filled an very encouraging, and he recorded that it was at this entire issue of the Pacific journal of Mathematics time that he became 'passionately interested in and is widely regarded as the most influential paper mathematics'. ever written on finite group theory. It energized the "In 1946 Walter moved to the United States to field, providing both inspiration and technical tools stay with an aunt and uncle. In a letter recovered for the research that finally culminated in the from the time of his arrival in New York, he complete classification of simple finite groups. poignantly describes his first experiences of the "Finite group theory was only one of several new world; see http: //www. math.yale.edu/ areas invigorated by Professor Feit's insights. His public_html/WalterFeit/ToNewYork/ paper with Graham Higman became a fundamen­ Welcome. html . tal building block and stimulated a large body of "The following September he entered the research on combinatorial structures. His work on University of Chicago and joined its energetic Schur indices revitalized progress in that subject mathematical community. Within four years he as well. had obtained the university's master's degree in "Feit joined the Yale faculty of mathematics in mathematics; he later received his Ph.D. from the 1964. He served the Yale mathematics department University of Michigan. In 1953, at the age of twenty­ in several administrative roles, acting as director of two, he joined the Cornell University mathematics undergraduate studies, director of graduate stud­ faculty. ies, and chairman. His standing in the mathematics "Walter Feit visited Oxford University many community was marked by award of the American times, but the 1990 International Symposium on Mathematical Society Cole Prize in Algebra, election the Inverse Galois Problem held there at University to the National Academy of Sciences and the Amer­ College in honor of his sixtieth birthday was an ican Academy of Arts and Sciences, editorship of especially joyful occasion. various journals, and vice presidency of the Inter­ "In October 2003, on the eve of Professor Feit's national Mathematical Union. retirement, colleagues and former students

728 NOTICES OF THE AMS VOLUME 52, NUMBER 7 gathered at Yale for a special four-day Conference for all those whom it on Groups, Representations and Galois Theory to touched as victims. honor him and his contributions. Nearly eighty But this was a part of researchers from around the world met to ex­ history which caught change ideas in the fields he had helped to create. up with him in his "Professor Feit is survived by his wife, Dr. Sidnie youth without giving Feit, of Hamden, Connecticut; his son, professor of him any choice. mathematics Paul Feit, of Odessa, Texas; and his Walter had earned daughter, artist Alexandra Feit, of Haines, Alaska. A bachelor's and mas­ memorial service was held on Sunday, October 10, ter's degrees from the 2004, at the New Haven Lawn Club, 193 Whitney University of Chicago. Avenue, New Haven, CT." Because of his inter­ This memorial article presents five contribu­ ests, his advisors rec­ tions, in rough historical order, from mathemati­ ommended he go to cians commenting on Walter, both mathematically Michigan, where and personally, at various times in his career, Richard Brauer was on all mentioning the odd order paper. These are the faculty. Michigan followed by some quoted excerpts from remarks was an attractive place delivered by Walter's Yale colleagues George Selig­ for us to be. T. H. man, Roger Howe, and Dan Mostow at the memo­ Hildebrandt was then rial service. Another selection from that service, by chairman and had Shreeram Abhyankar, is included in a section on built up the depart­ appointing Walter Feit Walter's later years. Walter's graduate students ment, and postdocs, and the conferences and volumes Brauer just after the written in his honor are listed in a final section. end of World War II. There was a lot of interesting - Len Scott activity in many fields. For example, Raoul Bott was starting his career there and was a focus of at­ the leader in topol­ The first contribution is from john Walter, who tention. Raymond Wilder was ogy. Also active were Edwin Moise and Hans was Walter Feit's roommate during part of their time Samelson. R. M. Thrall was working on the theory together at Michigan. john was himself a major of rings. Among the junior faculty were Jack player in the coming developments regarding groups MacLaughlin, whom I knew from Cal tech, and Alex of even order and the early days of the Classifica­ Rosenberg, who had just come from Chicago. ially in his work with Gorenstein. john tion, espec Walter stood out, having done well in an ad­ us from the days at Michigan to the Chicago takes vanced and very competitive mathematics program theory year, 1960- 61, where much of the group at Chicago led by an outstanding faculty. I am not was done. work on the odd order paper, cited above, sure what aroused his interest in group theory, but The Early Years I remember knowing that he was advised to go to Michigan to work with Brauer. He reflected the john H. Walter feisty and competitive spirit that existed at Chicago, along with a sense of fellowship among the un­ I would like to look back to the early years of a fifty­ dergraduate math students, and he carried this three-year friendship with Walter Feit in an effort over to Michigan. At the basis of this was an ethic to remember and convey the circumstances of his that valued good work and a profound respect for first years as a mathematician. I met Walter in the mathematics as a discipline. I remember the some­ fall of 1951 at the University of Michigan, where what presumptuous discussions about who was we both had entered graduate school. He was the more important algebraist, Andre Weil or born in Austria and had emigrated first to England Richard Brauer. But I h ave always felt that the and then to the United States, where he was raised basis for this impertinence was Walter's strongly in Miami by an aunt and uncle. His parents were felt respect for mathematical accomplishment and unable to obtain a visa and vanished in the Holo­ a loyalty to institutions that served him well in his caust. He never spoke much about this. I did not career. Because of our common interest, there was understand why at the time. However, it was clear a lot to talk about. then and more clear now that he had a sense of The group theory program at Michigan being history, and mathematics gave him the opportunity led by Brauer certainly fulfilled our expectations. to participate. The Holocaust was certainly a tragedy His seminar was on the modular representations of finite groups, a subject which he initiated. This John H. Walter is retired from the department of mathe­ was a stimulating and memorable event in a very matics at the Un iversity ofIllinoi s, Urbana-Champaign. His exciting year. Walter additionally took an informal email address is wa lter@math. ui uc. edu.

AUGUST 2005 NOTICES OF THE AMS 729 reading course from Brauer on class field theory. exceptional character theory of groups containing In the summer of 1952 Brauer invited Michio Suzuki Frobenius groups as subgroups. In the meanwhile, to Michigan for a few weeks. He talked in the sem­ Suzuki, using the exceptional character theory, inar on his recent thesis [9], in which he charac­ had proved the solvability of finite groups of odd terized the linear fractional groups PSL(2, p). His order in which the centralizer of every nonidentity argument was based on character theory, where he element was abelian [1 0]. This result was published focused on a particular class of irreducible char­ in 1957. Then in 1959 John Thompson finished acters, called exceptional characters, which are pre­ his thesis at Chicago, in which he developed some sent when there exist subgroups of a simple group new techniques in constructing maximal subgroups whose conjugates intersect only in the identity sub­ containing Sylow groups. He also noted the rele­ group. A great deal of information about these ir­ vance of Feit's work on exceptional character reducible characters can be obtained directly from theory that is associated with Frobenius groups. the irreducible characters of these subgroups and Based on [3], [4], [5], and the methods of John's the characters that they induce. It was clearly an im­ thesis [11], they saw the possibility of extending portant concept, and it seemed to us that it might Suzuki's work to show the solvability of finite open up a new direction that could be usefully ex­ groups of odd order. Thus Walter and John began ploited. Indeed, this is what happened. an important and fruitful collaboration. At first At the end of the academic year, Brauer with Marshall Hall, they showed the solvability of announced that he had accepted a position at Har­ groups of odd order in which the centralizer of vard. Walter was already working with Brauer, and every element is nilpotent [7]. This prepared the way he continued this relationship by correspondence. for showing that finite groups of odd order are He had found an improved and useful bound for solvable. the number of ordinary characters in a p-block, Taking note of this activity, the mathematics which he and Brauer later extended [1]. I worked department of the University of Chicago, led by with Jean Dieudonne, who replaced Brauer at Michi­ Adrian Albert, decided to have a Finite Group Theory gan. During the next year Walter and I, together with Year in 1960-61. This was a remarkably well-timed another student of Brauer, W. P. Brown, lived to­ decision. I was then investigating groups with a gether at an apartment in Ann Arbor. In that at­ dihedral Sylow 2-subgroup in which the centralizer mosphere, representation theory was often dis­ of a central involution has an abelian 2 complement, cussed. with the hope of solving the problem using Suzuki's Dieudonne was an interesting, dynamic leader exceptional character theory and obtaining a gen­ in the Bourbaki group. He lectured on the classi­ eralization of Suzuki's thesis. So when Walter told cal groups at Michigan. G. de B. Robinson was me about the Group Theory Year, I applied to visiting ]. S. Frame at Michigan State, and they, Chicago and received an offer of a visiting assistant together with Thrall, ran a seminar on the charac­ professorship. Again Walter and I crossed paths. ters of the symmetric group, which alternated Many stimulating mathematicians were there between Ann Arbor and East Lansing. We all for the Year. Feit and Thompson set the pace work­ attended. I worked with Dieudonne on the classi­ ing on the odd order problem. At the afternoon teas cal groups, and this led me to other problems after there were stimulating conversations; in particu­ I finished at Michigan. R. M. Thrall was in the lar, one could follow the latest about the status of process of changing his field of interest to game Feit and Thompson's work. Michio Suzuki had theory, and Walter worked on his game theory been invited and was characterizing an important project as a convenient way of gaining support; he class of doubly transitive groups that are now did not talk much about his mathematical efforts known as the Suzuki groups. Daniel Gorenstein in this direction. His real interest was in finite was starting to turn his attention to finite group groups and algebraic number theory. At the end of theory, and we worked together on groups with the year he accepted an instructorship at Cornell dihedral Sylow 2-subgroups. Among the other and departed. He continued to work with Brauer attendees were Graham Higman, Jon Alperin, Paul by correspondence. In the summer of 1954 he Fong, Norman Blackburn, Noburo Ito, and G. E. Wall. returned to Michigan to clear up some formal During the Year a lot of important work was requirements for his degree. Brauer had super­ done. Feit and Thompson reduced the odd order vised and approved his thesis but had resigned conjecture to a problem concerning generators and from Michigan's faculty; nevertheless, the necessary relations, which was solved in the next academic institutional arrangements were made (with Thrall year [8]. In the following summer, Walter also as the formal advisor) for the awarding of Walter's collaborated with Graham Higman on a crucial doctorate. result in the theory of finite EN-pairs of rank 2 [6]. During the years 1954-59 I kept track of what Gorenstein and I solved the first dihedral Sylow was going on in finite groups, often by talking with 2-subgroups problem mentioned above. Then, based Walter. He worked on some problems in the on the pattern of argument worked out in the odd

730 NOTICES OF THE AMS VOLUME 52, NUMBER 7 order paper, we started on the characterization of subtlety with which groups with dihedral Sylow 2-subgroups (without Walter handled a vari­ the previous restriction on the centralizer of a ety of character-theo­ central involution). Alperin worked on p-groups retic situations. and broadened his field of interests to both finite Suzuki and, of course, groups and representation theory. Graham Higman Brauer appreciated worked on an interesting class of 2-groups related Walter's strength. But to the Suzuki groups mentioned above. Truly, these only Walter and I were exciting events, and we can look back to the knew just how inter­ crucial role that Walter played in them. twined our thinking was over a period of References more than a year. (1) RICHARD BRAUER and WALTER FEIT, On the number of There was a false irreducible characters of finite groups in a given block, dawn of a few days Proc. Nat. Acad. Sci. USA 45 (1959), 361 -365. when we thought the [2) WALTER FEIT, On a conjecture of Frobenius, Proc. A mer. thing was done. Wal­ Math. Soc. 7 (1956), 177-187. ter then discovered [3) _ _ , On the structure of Frobenius groups, Canad. that there was one ]. Math. 9 (1957), 587-596. case that our tech­ [4) _ _ , On groups which contain Frobenius groups as niques did not cover, Walter Fe it and John Thompson Pure Math., Vol. 1, Amer. subgroups, Proc. Sympos. and he told me of this. Math. Soc., Providence, RI, 1959, pp. 22-28. If had not found the gap, I almost certainly [5) __ , On a class of doubly transitive permutation Walter groups, Illinois]. Math. 4 (1960), 170-186. would not have found it; we would have submit­ (6) WALTER FElT and GRAHAM HIGMAN, The nonexistence of ted a flawed manuscript, and eventually someone certain generalized polygons, ]. Algebra 1 (1964), would have blown the whistle. If that had hap­ 114-131. pened, it is doubtful that we could have generated (7) WALTER FEIT, MARSHALL HALL ]R., and jOHN G. THOMPSON, a new head of steam to bust the difficulty, which Finite groups in which the centralizer of any non­ in fact took us several additional months of thought identity element is nilpotent, Math. Z. 74 (1960), 1-17. and nail biting. (8) WALTER FEIT and joHN G. THOMPSON, Solvability of groups For forty-five years Walter and I were in touch of odd order, Pacific]. Math. 13 (1963), 775-1029. often, and I was always comfortable being with [9) MICHIO SuzuKI, A characterization of simple groups him. We had fun, we shared mathematical interests, I, 6 (1951), LF(2,p),]. Fac. Sci. Univ. Tokyo, Sect. and we shared views on the passing parade. One 259-293. reasonably ask for more from a friend. [10) MICHIO SuzUKI, The nonexistence of a certain type of cannot simple groups of odd order, Proc. Amer. Math. Soc. 8 (1957), 686-695. The next contribution was written by the editor­ [11) JoHN G. THOMPSON, Normal p-complements for finite organizer of this Notices article, Len Scott, who was groups,]. Algebra 1 (1964), 43-46. Walter's first student at Yale. The time was the height of the emotional impact of the then just­ Next, john Thompson takes us through the time published odd order paper. of the odd order paper itself. john has, of course, received many honors, including the Fields Medal Walter as an Icon and the Wolf Prize, in addition to the Cole Prize he shared with Walter. After that time, he and Walter Len Scott continued to share mathematical interests and re­ The work that Walter and John did was once mained personal friends. john was a speaker at described by the mathematici.an R. H. Bruck as a both the retirement conference held for Walter at cosmic event of the first order of magnitude. It Yale in 2003 and the memorial service for Walter brought literally hundreds of young mathemati­ a year later. cians into group theory. I guess I was one of them. Walter and I arrived at Yale in the same year, 1964, For Walter

john Thompson John Thompson is Rouse Ball Professor Emeritus of Pure Mathematics at Cambridge University, England, and pro· I was lucky to team up with Walter. He had com­ fessor of mathematics at the University of Florida. His pleted his Ph.D. with Brauer; I had studied Hall's email address is jthompso@math. ufl. edu. work; we both benefited from Suzuki; and we both Len Scott is the joseph Moore McConnell and David Meade had the confidence to attack the odd order prob­ Bernard Professor in the mathematics department of the lem, which still looks to me like granite. I think there University of Virginia. His email address is LLS2L@ are only a few who understood the precision and vi rgi ni a. edu.

AUGUST 2005 NOTICES OF THE AMS 731 and I took Walter's first course taught at Yale, something, probably without much detectable Characters of Finite Groups. It was pretty tough on conviction. me, taking thirty hours outside of class just to Walter's enormous stature in my mind only grew keep up. A high point was the proof that CN groups as I progressed toward my degree. I remember of odd order were solvable, an early model case for when some of the earliest sporadic simple groups the odd order paper that Feit and Thompson had beyond the Mathieu groups were beginning to treated in collaboration with Marshall Hall. The emerge. Zvonomir Janko came to Yale to give a talk name CN comes from the defining property that about a sporadic group he was proposing, not yet centralizers of elements are nilpotent. The work proved to exist at the time. An actual existence builds on a paper of Suzuki, demonstrating solv­ proof was often quite laborious, and before it was ability of odd order groups in which centralizers attempted, one could try to see if the proposed of elements are abelian. As enthusiastic and in­ group had a plausible subgroup structure. A fur­ tensely interested as I was, I rarely even heard ther approach was to study consequences of the what Walter was saying in class, since it required subgroup structure for the characters of repre­ so much attention to copy down what was written sentations. Any inconsistency and the hope for a on the board for later study, but I did get many possible new group would have to be given up. But chances that year to talk to Walter during his of­ when Janko gave his talk, he was quite confident fice hours, where I would bring in some difficulty and even buoyant, describing how beautifully the I was having. I suppose you could call the sessions proposed group's subgroup structure seemed to inspiring, since they left me with some realization fit. When one of the audience members asked the of how far I had yet to go. I remember in particu­ inevitable question about the characters, Janko lar struggling with the proof of a character isom­ seemed prepared and said, "My group is safe from etry result which involved an intricate argument the character theory." When the audience member with three summation indices, none of which could persisted, Janko simply continued, "Because Wal­ be manipulated in the usual way by exchanging two ter Feit has stopped trying to find contradictions in its character table." There were no further ques­ at a time. Walter handled my question easily, then tions. explained, "It's just a triple sum that has to be In later years I returned to Yale, one year as an straightened out." assistant professor and still later as a visiting Now, I have given this example to illustrate professor for a term. With the Classification on what it was like taking a course from Walter, and the horizon, I had by then moved toward Lie I believe Walter's line here and in other cases was theory and algebraic groups, but always with delivered with the entirely constructive purpose of representations of finite groups in mind. I would showing me where I needed to be. But as I got to sometimes see Walter at a conference or other know Walter over the years, I began to realize he occasion (he made some brief visits to my univer­ really was the master of the disarming one-liner, a sity), and we would reminisce over dinner and playful turn of phrase that could completely change discuss the topics of the day. But though he the perceived context of a conversation. I have always treated me as a colleague and a friend, I thought through the examples of these things that never escaped thinking of him as my teacher and I have heard from the Feit family, and I have to say larger than life. the best one in my memory comes from Sidnie. But it is so much like Walter, I have to wonder if they Ron Solomon was Walter's student at Yale in had somehow, directly or indirectly, collaborated. an exciting period. Today he and Richard Lyons The year was 1966, just a few days past the time continue the production, begun with Daniel Goren­ that, here in New Haven, my wife had given birth stein's collaboration, of a multivolume set which to our son. We called him Walter, certainly partly will eventually detail a second-generation proof of in honor of Walter Feit, but also partly in honor of the classification of finite simple groups. Of course, my paternal grandfather, who was also named at the time on which Ron focuses his discussion, the Walter. But my total immersion in Walter's courses first proof was only beginning to be considered a was so well known at Yale, it was hard to persuade possibility, and many of the sporadic finite simple anyone there that my grandfather had anything to groups had yet to be discovered. do with it. One day Sidnie came up to me and said, "It was so nice of you to name your son after my The Classification Years, and History husband." In something of a stumble, I tried to ex­ plain that, "Well, I also had a grandfather named Ron Solomon Walter." Sidnie quickly interrupted, "And he didn't Walter Feit's name will always be inextricably linked mind." This little addendum of course completely with his greatest accomplishment, the odd order pa­ changed the framework and meaning of my reply, per of Feit and Thompson [FT] . As I wrote in [So], and I was completely unprepared. I stumbled out this paper was "a moment in the evolution of finite

732 NOTICES OF THE AMS VOLUME 52, NUMBER 7 group theory analogous to the emergence of fish experience have made clear what a rare and re­ onto dry land." It defined the monumental scale of markable privilege it was to study there at that time. the classification project for finite simple groups Fueling the excitement in the field were the dis­ and threw down a gauntlet to other researchers in coveries each year of new sporadic simple groups. the field. It resolved a seemingly intractable case Indeed, I had the pleasure of presenting Lyons a of the problem and offered entirely new and pow­ congratulatory cigar on the occasion of Charlie erful ways of thinking about finite simple groups­ Sims's delivery of a healthy Lyons group. Conway ways of thinking that proved powerful enough to had recently constructed three new groups in­ complete the entire project. volved in the automorphism group of the remark­ By the time I arrived at Yale as a graduate student able Leech lattice. This motivated a long paper by in the autumn of 1968, evolution had progressed, Walter on integral representation theory in which fish were walking, and I was already enamored of he managed to blend many of his favorite topics, finite groups, though I knew little more than Sylow's including number theory, modular representations, theorems. Walter was teaching the third semester finite reflection groups, and low-dimensional of a course on modular representation theory that representations. In particular, he achieved a char­ would later form the opening chapters of his book acterization of the Conway groups Co 2 and C o3 as on that subject. I would have to content myself with groups with a faithful rational-valued irreducible reading the Yale Lecture Notes, which instilled in me character of degree 23. This permitted Walter's a lifelong affection for Green's theory of vertices and student, Dan Fendel, to characterize Co 3 by the sources. centralizer of a central involution, which in turn set A year later, while taking his course on charac­ the stage for my dissertation problem. Walter was ter theory, I asked Walter to be my thesis advisor. also interested at the time in the determination of He offered me the choice of the two problem areas all primitive subgroups of SL(n, C) for small values he thought most promising: the classification of of n, a project going back to the work of Moore, finite simple groups and the representation theory Dickson, Blichfeldt, and Mitchell. At one point I of finite groups of Lie type. The latter area was heard someone tell David Wales, "Walter Feit says closer to the character theory course I was taking, that problem is easy." To which David responded, and had been pioneered by Steinberg, whose recent "Everything is easy for Walter Feit." stay at Yale had led to the wonderful Lectures on Walter loved conversation, and his judgments Chevalley Groups. But, feeling my strengths were and opinions-whether mathematical, political, or not in character theory, I prudently chose the culinary-were never hedged or falsely polite, but classification problem, where the character theory always were leavened with wit and delivered with appeared largely to have already been done, thanks a twinkle in his eye. When I asked his opinion of a to Brauer, Suzuki, and Feit, and now the focus certain new paper in representation theory, he for attacking the general case had become the replied that the author had "found an excellent way "local analysis" methods of Thompson, Gorenstein, of encoding our ignorance on the subject." When and Walter. There was an element of sadness I expressed my fears in 1976 that the Classifica­ in foregoing the benefits of my character theory tion Project would soon be finished, he reassured education, but I did get later some solace from me that it would keep me busy for many more finding a characterization of U3 (4) that invoked decades- quite prescient. With equal confidence, Feit's Coherence Criterion. when I told him my fears about the drift of Amer­ In a tradition of which I was doubly a beneficiary, ican politics around 1994, he asserted that the John Thompson sent his best recent Ph.D. stu­ pendulum would soon swing back to the middle. dents to Yale as postdocs, and Walter reciprocated After a visit to IHES (Bures-sur-Yvette) he said that by sending his to Chicago. (I profited from this he now had a constructive proof of the existence arrangement upon graduation in 1972.) Thus Gold­ of the worst bakery in France. schmidt came to Yale in 1969, and Lyons in 1970. Though Walter never formally lectured on the Also, Len Scott returned from his Chicago postdoc history of our subject, his personal relationship to spend the 1970-71 year at Yale. And so I was with the great men of the past was palpable. "Schur blessed to study with four of the finest group was the idea man," he would say, and you almost theorists and four of the finest human beings felt Walter had been there in Berlin in 1910. anyone could ever hope to encounter. Indeed, the Walter was especially fond of Burnside, whose entire mathematical environment at Yale combined portrait stared down from his office wall. Walter the highest intellectual standards with the finest wrote: "When I first studied group theory I found collegial atmosphere. Passing years and greater his book a cornucopia of interesting results, and thumbing through it, I often found new and Ron Solomon is professor of mathematics at The Ohio interesting observations." And of Burnside's paqb State University. His email address is sol omon@mat h . theorem, he said: "I would guess the elegance of ohi a - state. edu. both the statement and the proof have attracted

AUGUST 2005 NOTICES OF THE AMS 733 more people to the study of characters than any and politics, which were very educational for a other result in the subject." I'm sure Walter real­ young American. ized that the odd order paper, titanic rather than Walter liked to tease people. It was always done elegant, had likewise attracted many brilliant with wonderful humor and with that special young minds into his beloved subject. He would twinkle in his eyes. And he enjoyed being answered have treasured these comments I received on in kind. October 7, shortly before the memorial service for I never felt any difference in age. Walter, from Raphael Rouquier: Now I think that I was so lucky to have met Walter and to have been his colleague. I had a mythical vision of him [Walter], as I was fascinated by the Odd Order More Quotes from Colleagues paper more than fifteen years ago, and, We quote here some of the remarks of other of like many others I imagine, that pushed Walter's Yale colleagues, made at the memorial me in this field. Later on, when I met conference in October of last year. him, he turned out to be very humane The first is by George Seligman. "My acquain­ and very accessible to the beginning tanceship with Walter dates from his coming to Yale mathematician I was. in 1964.... Our lunchtime conversations treated mainly history and society, both mathematical and References general. I was surely the beneficiary, especially [FT] WALTER FEIT and ]OHN G. THOMPSON, Solvability of when it came to British history. groups of odd order, Pacific]. Math. 13 (1963), "An exception to his generally easygoing nature 775-1029. could be recognized when it came to the quality and [So] RONALD SOLOMON, A brief history of the classification the status of the mathematics department. As of the finite simple groups, Bull. Amer. Math. Soc. chairman he joined a revolt of the chairs when (N.S.) 38 (2001), 315-352. salaries were being targeted to bear the force of budgetary cutbacks. In consideration of appoint­ The final authored contribution comes from Efim ments, he stood for aggressive campaigns to recruit Zelmanov, a Fields Medalist and Walter's colleague and appoint scholars on the basis of quality, with for many years at Yale before moving to his present only secondary consideration as to field. He was a position at UCSD. He spoke at both the retirement model for us all." conference for Walter and the later memorial By Roger Howe: " .. .Many people have said that service. he [Walter] always had a twinkle in his eye and a funny quip. He knew how to be serious, but he Walter as a Colleague preferred humor. Efim Zelmanov "He was quiet, he was modest, but he was com­ pletely self-confident. For example, he was far from I first met Walter in 1989, when I came to the athletic. In the U.S. today many might think that United States. The thing that impressed me most was something to apologize for, but for Walter it was how unassuming and approachable and was part of his philosophy of life. He would never normal he was. And yet he was the Feit of the harangue, but when there was a news item about Feit-Thompson Odd Order Theorem- that is, a some prominent athlete getting injured, Walter semi-god. He was so different from the scientific would point out how dangerous sports are .... " bosses in the Soviet Union. By Dan Mostow: ".. .Anyone ...who ever discussed I must say that in my opinion, by its elegance world affairs with Walter knows what a history and forcefulness, the Odd Order Theorem is buff he was. He knew, in detail, the history of every easily the best single theorem in group theory. country, ancient or modern, as far as I could tell. (The Classification of Finite Simple Groups, which So it is significant that he refrained from telling his is the culmination of all efforts, looks rather like own history to his children until begged by [his a sequence of theorems.) daughter] Alexandra ten years ago to relate his Walter n ever preached; it was the priceless family history.... casual side remarks that he made. For example, I "I conjecture he remained silent all those years remember he said that all most interesting cases because he did not want to exploit his status as a are always low-rank and low-dimensional- that's child of the Holocaust. Closely related was his where all exceptional and unexpected things determination to enjoy the positive side of life happen. He also made some remarks about history despite the traumatic separation from and tragic loss of his parents . . . . Efim Zelmanov is professor of mathematics at the Uni­ "Walter's positive outlook shaped his life both versity of California San Diego. His email address is professionally and personally. In his mathematical e z elmano@euclid. ucsd.edu. career he achieved historical standing. In his

734 NOTICES OF THE AMS VOLUME 52, NUMBER 7 personal life he aimed high and competed suc­ there was a nutcracker in front of us, so I filled cessfully for the hand of the comely, brilliant Cor­ myself with nuts and learned about group theory. nell undergraduate Sidnie Dresher. As a parent he "It is so sad to miss him. Well, let me end. Thank was able to offer his children the love and moral you." support that his parents did not live long enough to offer him. Students, Postdocs, and Dedications "Walter and Sidnie have donated generously to Walter's graduate students were Clark Benson and charities, especially those that help refugees. They Marcel Herzog at Cornell; then, at Yale: Len Scott, have been generous with their hospitality for stu­ Harvey Blau, Mark Benard, Daniel Fendel, Eliza­ dents and colleagues. They have done much to beth Wall Ralston, Ron Solomon, Martin Pettet, Carl help make Yale a friendly mathematical center." Bumiller, Stephen Doro, Leonard Chastkovsky, Daniel Corro, Ying Cheng, In-Sok Lee, Josephine Later Years Shamash, Donald White, Li-qian Liu, Sidney Porter, In Walter's later years his interests turned to Galois and John Swallow. Mathematicians who studied theory as well as to older interests in representa­ with Walter at Yale in a postdoctoral or junior fac­ tion theory. He was the coorganizer of a number of ulty capacity include Don Passman, Bernd Fischer, conferences in the former subject, and organizers Larry Dornhoff, Dave Goldschmidt, Len Scott, of conferences in his honor often also invited a Richard Lyons, Dave Benson, and Dave Sibley (de­ Galois theory contingent. This was especially true ceased). Three conferences have been held in Wal­ at the sixtieth birthday celebration conference held ter's honor: an Oxford conference at the time of his sixtieth birthday, a conference at Ohio State on at Oxford, which emphasized the inverse Galois the occasion of his sixty-fifth birthday, and a con­ problem. One of the speakers there was Walter's old ference at Yale on the occasion of Walter's retire­ friend from Cornell, Shreeram Abhyankar, who ment at age seventy-three. Principal organizers in­ also spoke at Walter's memorial. Here are some of cluded Michael Collins (Oxford, University College); his remarks from the latter occasion: Ron Solomon (Ohio State); and Ron Solomon, Len "I met Walter in 1957- Walter and Sidnie both­ Scott, and George Seligman (for the Yale confer­ when I went to Cornell as an assistant professor, ence). At the Oxford conference Walter was pre­ as was Walter, and immediately we all three became sented by Len Scott with a dedicated two-volume very close friends. issue of the journal ofAlgebra (a journal for which "Now there are many amusing memories of that Walter served as managing editor from 1985 to year. We used to have lunch together almost every 2000). After the Ohio State conference, a confer­ day in the faculty club, where there was good apple ence volume, Representation Theory ofFinite Groups pie, and so we both felt that maybe we put on too (de Gruyter, 1997), was edited by Ron Solomon, who much weight, so we decided to go on a diet together. is now editing a memorial journal ofAlgebra issue. And the condition was that in a month or so, the Walter remained mathematically active in spite of person who would succeed more was to get a his illness, and was disappointed when his treat­ quarter. In a month Walter gained one pound, and ment caused him to miss speaking at the Ischia I gained two. And so we never settled our quarter. Group Theory 2004 conference, held in honor of Each time I mentioned it, he would say, 'Ram, where the retirement of one of his first students, Marcel is the quarter?' ... Herzog. "But then-let us move forward by many years­ As mentioned at the beginning of this article, so it was in '89 when I realized that much of alge­ there was a full memorial service held for Walter braic geometry, in particular Galois theory and in New Haven in October of 2004. Walter's son, fundamental groups, which I have been doing, Paul, was master of ceremonies. A Yale Web page needs this knowledge of group theory. detailing some of the activities has already been "This was brought home to me by Serre, who told mentioned, and we give the URL for that page here: me we both ought to learn group theory if we are http://www.math.yale.edu/public_html/ doing this [Galois theory] problem. For a while he WalterFeit/WalterFeit.html. provided me with information, but pretty soon it The present article was prepared by Len Scott became clear that I should better go to the real with the cooperation of the other authors, and the experts. special advice of Ron Solomon and George Selig­ "Now this famous group theorist, Walter Feit, is man is gratefully acknowledged. Photos and early my old friend, so I came down to New Haven and access to Web page materials were provided by was a house guest of the Feits for a week, and in Sidnie Feit. one week he tried to pull me up by the bootstraps. "He tried to teach me what had happened in group theory in thirty years in one week in a simply charming, friendly manner. And all the time

AUGUST 2005 NOTICES OF THE AMS 735 - ~."." AMERICAN...: MATHEMATICAL ADVERTISERS' fORUM AMSSOCIETY Mathematical World

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Inviting applications for the 2006--2007 year, featuring three programs:

Computational Applications of Algebraic Topology (Fall) (August 14 to December 18, 2006) Algebraic topology provides measures for global qualitative features of geometric and combinatorial objects that are stable under defmmations, and relatively insen­ sitive to local details. Considerable momentum has developed in recent years toward applications of algebraic topology in contexts related to data analysis, object recognition, discrete and computational geometry, combinatorics, algorithms, and distributed computing. This program will gather the workers in these areas for concentrated interactions, and will make a strong effott to communicate the nature of these developments to the more general mathematical public. Program Committee: G. Carlsson, P. Diaconis, S. Holmes, R. Jardine, G. l'vl. Ziegler.

Geometric EYolution Equations (Academic Yea•·) (August 14, 2006 to May 21, 2007) The focus will be on geometric evolution equations, function theory and related elliptic and parabolic equations. Geometric flows have been applied to a variety of geometric, topological, analytical and physical problems. Linear and nonlinear elliptic and parabolic pmtial differential equations have been studied by continuous, discrete and computational methods. There are deep connections between the geometry and analysis of Riemannian and Kahler manifolds. Program Committee: B. Chow, P. Daskalopolous, R. Hamilton, G. Huisken, P. Li, L. Ni, G. Tian.

Dynamical Systems (Spring) (January 8 to May 21, 2007) This program will take place at the intetface of the evolving mathematics of dynamical systems and the areas to which is applied. The goal is to assess the current state-of-the-rut and define directions for future resem-ch. We will bring together researchers who are using the techniques of dynamical systems in applied m·eas and mathematicians who are developing the new generation of ideas in dynamical systems. Program Committee: C. Jones, J. Mattingly, I. Mezic, A Stumt, L-S. Young.

COMPLElVIENTARY PROGRAlVI: In addition to these three programs, MSRI also continues the program in which applications from candidates working in any field of mathematics are welcome. Candidates should specifY why a fellow­ ship at MSRI at this time is particularly relevant for their research, for example, by desct·ibing potential interactions with one ofthe above fields, or indicating interest in one or more ofMSRI's joint industrial fellowships or internships.

Three award categories available from MSRI to applicants: • Research Professors. For mathematicians with Ph.D.s awarded in 2000 or earlier. Provides $5 ,000 per month up to five months for semester programs (10 months for yearlong program). Application deadline: October 7, 2005. • Postdoctoral Fellows. For mathematicians with Ph.D.s awarded in 2001 or later. Provides $4,000 per month up to five months for semester programs (10 months for yearlong program). Application deadline: December 16, 2005. • General Members. May provide patiial support towm·d living atld travel expenses. It is expected that General Members will come with partial or full suppoti :fi·om other sources. Application deadline: December 16, 2005.

Further information: www. msri.org 00 Online application: www.mathjobs.org W H A T I S a Compact on? Philip Rosenau

A soliton is a special solitary traveling wave that turning any period between two troughs into an after a collision with another soliton eventually isolated entity. We may now remove any such emerges unscathed. Solitons are solutions of par­ period and connect its edges with the trivial U = 0 tial differential equations that model phenomena solution like water waves or waves along a weakly anhar­ (2) U(x- At)= 2A cos2 [x ~At]. monic mass-spring chain. The existence of soli­ tons critically depends on special mathematical where lx - Ml :::; rr and U vanishes elsewhere. properties of the model equations. Typically This is the sought-after compact wave. Its second such equations have solitary wave solutions whose derivative has a jump at U = 0, but since UUss interaction is almost, but not exactly, clean: the ~ s 2 H(s) I 0, where H(s) is the Heaviside function, reemerging waves appear perturbed, and the it satisfies our equation. mathematical miracle whereby, among other Unlike the usual solitonic case, in which there things, one can explicitly describe the interaction is is an instant runaway of its initial support, in our lost. Since all solitary waves have infinite tails, it case, because u vanishes at the edge of the support, is natural to seek model equations that generate the degeneration of the dispersive mechanism solitary waves with a finite span. Two such waves (uuxxh blocks an instantaneous spread of the front. would interact only for a finite time and then, Instead of infinite tails we obtain a wave of finite unlike solitons, would be completely oblivious to span that propagates with constant velocity. each other. This is somewhat analogous to a search We return to (1) and look for solitary traveling for wavelets with compact support. We define a waves. Two easy integrations give compact wave as a robust solitary wave with com­ pact support beyond which it vanishes identically (3) u Z 0, (1) Ut + (um)x + [ ua(ubhx Jx = 0, = ub- l Us ~ s "":1 H(s) ! 0, U(s) satisfies (1) and each with a + b =n ~ 1, and m ~ a - 1. For n = b = 1 period between the troughs is an isolated entity. and m = 2, 3, (1) reduces to the celebrated Kdv and Removed and connected with the trivial states, the m-KdVequations, respectively, which are the home 1-period wave solution turns into a compact wave. base of solitons. But it is when n > 1 that the Form= n, we have second nonlinearity enables formation of compact I patterns. 1 (4) = [ cos2 ) s)] m-l Consider first the special case of (1) wherein u ~ cm2~ m = 2 and a= b = 1. We seek a traveling solution, U(s = x - At), with velocity A. Integrating once gives when lsi :::; m~l and zero elsewhere. Figure 1 shows U[-A + U + Ussl =Co. To avoid singular solutions, a clean interaction of three typical K(2, 2) compact we set Co = 0 and obtain U = A(1 + Ao cos s). If waves (b = n = m = 2 in (1)). This and many other Ao = 1, then the trough of the periodic wave experiments tempt us to declare them as com­ touches U = 0, where the last term in equation (1) pactons despite the formation of small ripples. degenerates (and the solution's uniqueness is lost), The infinite number of conservation laws in a con­ ventional soli tonic case would imply that collisions Philip Rosenau is professor of applied mathematics at are slightly inelastic. However, K(2, 2) has only four Tel Aviv University. His email address is rosenau@ local conservation laws (u, u3 , ucosx, and usinx), post.tau.ac.il. so clean interactions and a ripple can, in principle,

738 NOTICES OF THE AMS VOLUME 52, NUMBER 7 u(x) coexist [1]. Though analysis is needed to settle the question, extensive numerical studies of (1) indicate that the mechanism underlying the inter­ action of compact waves is very different from 1.5 that of solitary waves or solitons. Stationary Compactons: When w < 0, (1) sup­ X o.s ports stationary compact waves. Some of them '5 may be seen as solitons in "mass units", and thus 0.5 they inherit the integrability of their antecedents. 140 Let u be a density of some quantity. Then the map X - Z = eoo U(X, t)dx defines the "mass" of 150 u in (- oo, x). For a typical soliton the "total mass" is finite, and in these coordinates u is compact. Moreover, since shifts in time do not change the mass distribution of the soliton, it is stationary in mass units. Thus in the m-KdV case u = J2Xcosh- 1 [.JX(x - At)]= J2Xsin(z/J2), 0 ~z ~ Figure 1. Interaction of three K(m = 2, n = 2) compact waves J2rr. In mass units interaction of N-solitons turns (co~rtesy o~ M. ~taley). Nume~ically they seem to emerge from N-stationary compactons, and KdV ultimately into the mteract•.on mtac!, yet the mteraction site is marked by a and m-KdV equations are mapped into (1) with very small npple wh1ch decomposes into compacton­ m - m + 1, a = 3, b = 1, and thus w = -1. The anticompacton pairs [1 ]. singularity now confines the dynamics to the initial support. Application to a motion of curves As h increases, in a plane is given in [2] . breathers become Compact Breathers. Consider the vibrations of stable at higher a chain of particles interconnected by springs: and higher ampli­ (5) tudes, and their y~' + 4>' (yn) = ~ [ T(Yn+lh- Yn) _ T(Yn - :n- l)]. basin of stability increases dramat­ Here h is the interparticle distance, T is the ically as well [3]. attraction between two adjacent mass points, and Clearly the sin­ gularities pre­ 4>'(yn) is the force exerted by the ambience on the X nth node. The continuum limit, y(x, t) =Yn(t), sented are not yields esoteric mathe­ Figure 2. Continuous (line) and two matical entities, discrete breather profiles for h = 0.4, 1, (6) Ytt + 4>' (y) = T(Yxlx . but a natural limit respectively. . which describes the motion of a string. When the of a very localized boundary layer. This appears to be a generic prop­ stretch u = Yx is small, T(u) ~ u + ua, ()( > 1. Bal­ crete genuinely nonlinear dynam­ anced with a weak force due to the discreteness, erty of many dis For instance, a Lotka-Volterra-like it begets a KdV-like equation. Being interested in ical systems. problem, 2hilj = , maybe seen as a dis­ the opposite limit of a very strong anharmonicity, u]+1 - u]_1 K(2, 2) equation with the we assume that T(u) ~ u3. (6) is now singular when­ crete antecedent of the solitary waves having a super-exponentially de­ ever the stretch and thus the wave speed cZ(u) ~ u 2 caying front, which in the quasi-continuum limit be­ vanish. If 4>' (y) = y - y 3 , we find a space-time sep­ comes strictly compact. A similar conclusion arable solution for both the string and the chain. emerges from a recently published work with It yields a periodic motion in both time and space. A. Pikovsky on phase compactons in chains of dis­ For the string the degeneracy at Yx = 0 enables us persively coupled oscillators. to connect a 1-period of the solution with the trivial state, yielding a stationary compact solution, References a breather, which oscillates in time. ROSENAU HYMAN, Phys. Rev. Lett. 70 (1993), How does the discrete breather behave? Though (1] P. and]. M. 564. in principle the discrete lattice does not support (2] P. ROSENAU, Phys. Lett. A. 275 (2000), 193. that compact solutions, a careful analysis reveals (3] P. ROSENAU and S. SCHOCHET, Phys. Rev. Lett. 94 (2005), the spread beyond the compact domain is con­ 045503. fined to a very narrow boundary layer where the decay is supeJ;"-exponential [3]. Figure 2 reveals that neither the shape of the breather nor its support seems to depend on the number of mass points.

AUGUST 2005 NOTICES OF THE AMS 739 Book Review

Spaceland: A Novel of the Fourth Dimension Reviewed by ]ody Trout

Spaceland: A Novel of the Fourth Dimension But, alas, greed Rudy Rucker and the Fourth Di­ Tor Books mension do not mix Hardcover, 2002, US$24.95, ISBN 0-765-30366-3 well, either. This is Paperback, 2003, US$13.95, ISBN0-765-30367-1 one of the many lessons that our con­ Having a cell phone and living in Vermont are flicted, thirty-some­ two things in my life that don't mix well. The thing protagonist, modern technology of cell phones and their tiny Joe Cube, learns antennas are no match for the ancient granite sr <1. c c:r.. I <1. L\ J along the way. Joe mountains and hills of Vermont, nor for the locals' works as a low-level stubborn opposition to those ghastly metallic tech manager for towers and their bad environmental kharma. :RVlY :RVC KE:t Kencom, a small Convenience be darned! But, what if my cell phone hardware dotcomin had a small antenna that went up and over our Silicon Valley. He is three-dimensional space into the unobstructed helping his boss, hyperspace of the Fourth Dimension and trans­ Ken Wong, develop mitted my voice directly to the extradimensional the ultimate idio·t antenna of your cell phone? Could you hear me box to pacify the masses: the 3Set, a truly three­ now? The IPO for that little gizmo would make dimensional television set. Instead, he will end up Google's look like a mere giggle. This is the basic romping across the dimensions of space and' time to technological twist of Space/and, the latest foray save our universe from destruction! This book has into four-dimensional sci-fi by Rudy Rucker, a a complex and convoluted plot, which I will now de­ mathematician and computer scientist who has scribe in more detail. twice won the Phillip K. Dick award for best science The story opens on New Year's Eve 1999, which even fiction novel. Rucker has also written several the most adept computer wizards feared would herald mankind's return to a New Dark Age, popular introductions to the mathematics and when all of our little electronic familiars were sup­ geometry of the Fourth Dimension. posed to choke on a simple date flip . Midnight ]ody Trout is associate professor of mathematics at would be the switching hour that released the evil Dartmouth College. His email address is jody. trout@ Y2K bug onto a species that doesn't know how to dartmouth. edu. make change for itself in the grocery line. iwould like to thank Allyn jackson and the referee for their Joe has an idea to ride out the coming madness helpful comments in preparing this review. and destruction and try to perk up his failing

740 NOTICES OF THE AMS VOLUME 52, N UMBER 7 marriage at the same time. Absconding with the sides of our 3-dimensional universe, called 3Set from the lab, he hopes to spend a romantic "Spaceland", which separates the realms of Dronia evening with his young but demanding wife and and Klupdom like an opaque screen, yet they can some champagne and seafood, and hail the third watch what goes on in our world without hin­ millennium in 3D from their small-but-expensive drance. Along the way, he is trailed by a demonic­ Silicon Valley pad. looking Dronner named Wackle, who is stealing his However, his wife, J ena Bonk, who is half Yavapi money. As the story progresses, Wackle-who Indian and half Norwegian, has other plans. seems part mammal, part plant, and part sea After greeting the New Year, which arrives without anemone-breaks up into several self-similar ver­ the apocalyptic electronic fireworks, they go out sions of himself, much like the reproducing heads bar-hopping with friends and tipsily return home, of the legendary Hydra. But of course looks can be where she falls asleep, leaving Joe to amuse him­ deceiving, especially when viewing them from one self with the grainy images of the beta 3Set. But dimension less. The various pieces of Wackle speak when he turns his attention to the imaging tank, to Joe in a cryptic Rastafarian-surfer manner that he sees that something very unusual is happening. seems confusing and threatening at first. Ulti­ The device is full of pink blobs that won't go away, mately, Joe finds there are some ulterior motives even when he turns off the set. Even worse, these behind Momo's new technology and a dangerous blobs begin to speak to Joe and manifest themselves threat for our universe. outside of the 3Set. The blobs introduce them­ It seems that the true purpose of the Mophone selves as "Momo", a friendly visitor from something antennas is to leak energy out of Spaceland's 3D called the Fourth Dimension! membrane, thus violating our universe's Law of Joe soon has the living daylights scared out of Conservation of Energy, until the energy pops a big him by Momo and her grotesquely undulating 3D hole in the membrane and tears the fabric of our cross-sections. But a quick trip into the Fourth Di­ space like a pair of tight Levi's on an elephant. The mension convinces Joe that he is not dreaming or Kluppers will then no longer have any obstruction hallucinating in some alcoholic haze. Momo has to blasting their Dronner enemies into oblivion, be­ chosen him to help her bring a change to our world cause the obscuring barrier of Spaceland will no by introducing a wonderful new form of technol­ longer hide them. Joe realizes all the Mophones they ogy to benefit humanity. Joe will eventually learn have sold must be shut down before it's too late! the hard way to respect an update to that old Greek Things develop quickly as Joe discloses the Klup­ chestnut, "Beware 4D beings bearing gifts." per's evil plan to the Dronners, who help him track Momo physically augments Joe by giving him a down the remaining Mophones. However, his wife slight four-dimensional thickness with some 4D ends up having the last Mophone, and Jena's call skin, thus protecting his "vinn" and "vout" sides is the proverbial pin that pops the bubble. Joe uses that are exposed to the extra dimension of her his augmented 4D abilities to stop the expanding reality, called the "All". This will allow him to "peel" spatial rip by holding the edges like a dimensional himself out of our space and even propel himself band-aid. Joe calls out to the Dronners, and they in the Fourth Dimension like a flatfish. She also temporarily sew the hole with hyperropes like an gives him an extra eye at the end of a stalk per­ embroidery loop. They tell him that he must make pendicular to his "flat" 3D body, which allows him a pilgrimage across High Dronia to the mysterious to see into the larger dimension of the All. Momo Drabk, the Sharak of Okbra, to get a piece of space then leaves him alone for a time to get used to to permanently seal the breach. The Wackles will his new physical abilities and the new reality they hold off the assault of the Kluppers in the mean­ represent. Joe quickly finds out that this extra eye time. Joe uses a 4D flying saucer stolen from Momo allows him to see through walls and many other to make the veritable Alice-in-Wonderland trip to things, much as we can see everything in the 2D the higher-dimensional hideout of the Sharak. plane of Flatland without restriction. Along the way Joe meets many strange creatures Joe's many adventures begin with a trip to Las and learns a lot about himself, the various dimen­ Vegas to get capital to develop Momo's new tech­ sions, and the interconnectedness of all reality. nology "for the good of mankind and the Kluppers In the end, of course, he saves the universe, saves (Momo's people)." (Imagine playing blackjack when his company, and, most of all, saves his failing you can see everyone's hand from the vantage of marriage. the Fourth Dimension.) Joe and others then create Rucker's Spacelandis another companion/sequel a venture company called Mophone Inc., which will novel to Edwin A. Abbott's mathematically minded market the new technology of the 4D cell phone an­ nineteenth-century classic novel, Flatland: A Ro­ tennae. As Joe learns more about Momo's world and mance of Many Dimensions (1884). Other Flat­ the Kluppers, he learns of the Klupper's mortal landesque novels are Sphereland (1965) by Dionys enemy, the Dronners. The Kluppers and Dronners Berger, The Planiverse (1984) by A. K. Dewdney, and both live in the Fourth Dimension on opposite Flatterland (2001) by Ian Stewart. (See the author's

AUGUST 2005 NOTICES OF THE AMS 741 review of Ian Stewart's Flatterland in the April 2002 (pardon the pun) and not very likable. Their moti­ issue of the Notices for a discussion of Flatland vations are shallow and all too transparent. Their history and its sequels.) The fact that over one love quadrangle, which is the most unappealing as­ hundred twenty years after Flatland was published pect of the story, plays out like a dull soap opera authors are still writing homages to this little book set in Silicon Valley. Not to mention that such a dys­ is a testament to its timeless popularity and liter­ functional emotional entanglement would certainly ary value. Rucker's previous Flatland homage ruin an upstart venture company! The Kluppers are was a wonderful short story, "Message Found in a mostly irrational medieval capitalists. The most Copy of Flatland", which appeared in his now out­ intriguing characters in the story are the devilishly of-print anthology Mathenauts: Tales of Mathe­ cryptic, bohemian, and sage Wackles. And although matical Wonder (1987). It was set in modern-day there is some socioeconomic commentary from London and explored a dark answer to the ques­ Rucker's frenzied look into the biz-tech dotcom tion, "What if Flatland were in the basement of world, the detailed ins and outs of starting a new a shady restaurant?" technology venture don't necessarily make for There are many parallels (pardon the pun) the most compelling reading. It is also frequently between Flatland and Spaceland. Recall that in difficult to tell where Spaceland is trying to be Flatland the humble 2D protagonist, A. Square, is satirical and where it is taking itself (sometimes contacted by an entity, A. Cube, from the Third too) seriously. As a result, readers may be left in Dimension on the last day of the 1999th year of ambivalent confusion or may simply conclude that the Flatland world. Rucker picks up on this by hav­ the book is downright silly. Despite these short­ ing the protagonist, J. Cube, contacted by the en­ comings, Spaceland is a fun read-and everyone tity Momo from the Fourth Dimension on New needs a fun read now and then. Year's Eve 1999, with a little Y2K hysteria added in the mix. Also, both stories are told in the first person by the main characters. Flatland was an in­ genious satire on Victorian society and misogy­ nistic views and treatment of women, as well as an excellent introductory didactic of higher dimen­ sions and their geometry. Although Rucker's hard sci-fi satire puts some witty and imaginative spins on the notion of communication between beings with different, even multidimensional, points of view, the story contains some weak literary ele­ ments. The accounts that Rucker gives of basic 4D geometry and how ordinary human beings would experience the world of the Fourth Dimension are interesting and mind-bending enough, but readers will most probably get the idea long before the narrative is through telling them about it-again and again. There is too much discussion of how strange and nauseating the constantly changing and undulating 3D cross-sections of a 4D being would appear to a 3D being. These discussions could have been supported by a few more (and better drawn) diagrams and pictures, such as in Clifton Pick­ over's didactic and X-Files-ish novel Surfing through Hyperspace (1999). The physics premise of the story that the Mophones leak energy out of the fabric of Spaceland is weakened by the fact that beings who are "vinn" or "vout" of Spaceland can see what is transpiring in Spaceland. Hence, energy (in the form of photons) is already leaking out of Spaceland. But, of course, one must take some lit­ erary license to move the plot in the right vector. Another weak spot is that the characterization in the book is a bit flat. All of the main human char­ acters-Joe, Jena, Joe's coworker Spazz, and Spazz's girlfriend, Tulip- are rather one-dimensional

742 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Book Review

Chance: A Guide to Gambling, Love, the StockMarket, and just About Everything Else Reviewed by Rick Durrett

Chance: A Guide to Gambling, Love, the Stock I will tell some of Market, and Just About Everything Else these tales. Amir D. Aczel The Monty Hall Thunder's Mouth Press, 2004 Problem. Behind Hardcover, US$21.00 one of three curtains ISBN 1-56858-316-8 is a new car. You pick curtain # 1. The The inside flap at the back of this book says that emcee opens curtain Aczel is also the author of Fermat's Last Theorem: #3 to show you a Unlocking the Secret of an Ancient Mathematical donkey. Should you Problem, which has been translated into fifteen switch to curtain #2? languages. I doubt if the book under review will When this problem be that successful. The first thing one notices appeared in Marilyn about the book is that it is tiny. The text is 121 pages vos Savant's column minus a dozen pages that are blank or have full­ in Parade magazine, page figures, plus a 29-page appendix on gambling several hundred by coauthor Brad Johnson. The book's short length readers wrote to tell is matched by a small text width of 3.3 inches and her in forceful terms text height of 5.5 inches, which is about 60 percent that she was a moron-by symmetry the two re­ of the size of a small-footprint text such as those maining choices must have equal probability. Her in the Springer Series in Statistics. When you divide answer, which is the correct one, is that before the the $21 cost by the number of characters, the ratio emcee showed you curtain #3, your probability of does not rise to that of [insert the name of your winning was 1/ 3 and nothing has happened to favorite evil publisher], but the book is hardly a change that, so curtain #2 must have probability bargain. 2/ 3. As Louie says at the end of the movie Chevalier de Mere's Miscalculation. It is bad Casablanca, the book "rounds up the usual sus­ enough to make a mistake, such as overestimating pects." In addition to the standard definitions and the probability of weapons of mass destruction, but formulae one needs to explain the subject, the it is awful to have people talk about it for 2 50 book plays some of the greatest hits of the eigh­ years. Since 4/ 6 = 24/ 36, our seventeenth-century teenth century, the nineteenth century, and today. French gambler thought that the probability of For the benefit of readers who may not be famil­ throwing a six in four attempts is the same as iar with probability theory, "one of the most amaz­ throwing a double six in twenty-four attempts. ing inventions-or discoveries-of the human race," However, thinking in terms of the probability of not getting a success, we see the two probabilities are Rick Durrett·is professor of mathematics at Cornell 1- (5 /6)4 = 0.5177 > 0.4914 = 1- (35 / 36)24, University. His email address is rtdl@co rne 11 . edu.

AUGUST 2005 NOTICES OF THE AMS 743 AMERibAN MATHEMATICAL SOCIETY I explaining why he made money with the first bet Journal of Geometric and lost with the second. Analysis and Journal of Inspection Paradox. On the back cover we find the question: "Does the bus always seem to take Operator Theory longer than average to arrive? There's a mathe­ matical reason for this." To see the reason, mark Available Online in 2006 the bus arrival times as X's on a line. We pick a point at random from the line(= go to the bus stop at a Special Offers ... randomly chosen time). The point falls in an interval - Free access for print subscribers between two X's, and that interval is chosen with probability proportional to its length. Thus the - lower rates for electronic-only interval in which the point falls will be longer than subscriptions the typical interval. The Birthday Problem. What is the probability that in a class of twenty-five people two people will THF; The Journal of Geometric Analysis have the same birthday? This sounds rather Journal (JGAN) publishes top-quality unlikely OF GEOMETRIC until you realize that there are articles which clearly exhibit the 25 · 24/ 2 = 300 ANALYSIS pairs of people. If we pretend symbiotic relationship among the events are inde­ pendent, analysis, geometry, and partial then the probability of no match is differential equations. The journal (1- 1/ 365)300 ""exp(-300/365) = .4395. continues to maintain the highest standards of innovation and A more accurate computation shows that the exact excellence in the field. probability is .4313. How to Gamble If You Must. As Dubins and Sav­ Managing Editor: Steven G. Krantz, Washington age explain in their book with this name, the best University, St. Louis, MO strategy to beat an unfavorable game is bold play. In other words, if you are down to $10 and need The Journal of Operator Theory to win enough at roulette to pay the $1,280 rent (JOT) produces significant JOURNAL on your outrageously expensive Collegetown OF research articles in all areas of OPERATOR THEORY apartment, the best strategy is to place a bet on operator theory. It is published red and hope you win seven times in a row. On quarterly by the Theta the other hand, this ignores the benefit of getting Foundation (Bucharest, Romania). a few free drinks as you lose your money gradu­ Editors: W.B. Arveson, ally by betting $1 at a time. University of California, How to Find a Good Wife. To quote the book: Berkeley, K.R. Davidson, "You will maximize the probability of finding the University of Waterloo, ON, Canada, N.K. best spouse if you date a fraction e- 1 of the avail­ Nikolski, Universite Bourdeaux, Talence, France, able women and then choose to stay with the next 5. Stratila, Institute of Mathematics at the Romanian candidate who is better than all of the ones you Academy, Bucharest, and F.-H. Vasilescu, have seen before." This is usually formulated as Universite des Sciences et Technologies de Lille, the "secretary problem". The quoted algorithm Villeneuve d' Ascq, France results in picking the best individual with positive These journals are distributed by the probability independent of the size of the set. How­ ever, in the romantic setting the rate of convergence American Mathematical Society. is painfully slow. As you can see from the stories I cited, there is For pricing and more information about these and other journals available from the AMS, go to some interesting material here. However, most of www.ams.org/ bookstore/journals or contact these stories can be found in other books. Aczel AMS Membership and Customer Services, does a good job of telling these stories, but his treat­ phone 1-800-32 1-4267 (U.S. and Canada) or ment of the preliminaries is somewhat brief. His 1-401 -455-4000 (worldwide); email [email protected]; fa x 1-401 -455-4046. discussion is clear, but overall I feel that the book is a little light in content. A list of alternative books, many of which are better than the one under ®AMS review, can be found on the Web page for David AMERICAN MATHEMATICAL SOCIETY Aldous's freshman probability course at Berkeley, O FFERING THE FINEST IN Stat 24:http://www.stat.berkel ey . edu/ users/ SCHOLARLY M ATHEMATICAL al dous/24/ index.html. PUBLISHING

744 NOTICES OF THE AMS VOLUME 52, NUMBER 7 AMS President's Address at Abel Celebration ]ames Arthur

Editor's Note: Peter Lax was awarded the 2005 Abel Prize in Oslo on May 24, 2005. AMS president James Arthur made the following remarks at the dinner that evening in honor of Lax.

Your Majesty, Your Excellencies, Ladies and Gen­ school. The unknown quantities are not numbers, tlemen. but functions which describe the behaviour of It is a great honour for me to respond to the physical quantities under fundamental laws of address of the minister of education. I would like nature. to express the deep gratitude of mathematicians Peter Lax is perhaps the greatest living mathe­ to the Norwegian government, and to the Norwe­ matician working in this venerable area. He has made gian people, for establishing the Abel Prize. The lack extraordinary contributions to our understanding of of a Nobel Prize in mathematics was long regarded differential equations and their solutions. These as an anomaly that diminished public perception range from the explanation of counterintuitive phe­ of the importance of mathematics in society. The nomena in nature, such as supersonic shock waves, vision and generosity that led to the creation of the to the discovery of completely unexpected relations Abel Prize has now put mathematics on an equal between basic applied problems and a beautiful part footing with the other sciences. of pure mathematics that goes back to Niels Henrik It is also an honour and a pleasure on this Abel. glorious occasion to congratulate Professor Peter I am sure that the story of Abel is fa- Lax. It goes without saying that the Abel Prize is miliar to everyone here. People who the highest honour a mathematician can achieve. are not mathematicians might be The decision is made by a jury of mathematical surprised to find that Abel is peers, who work with a large pool of nominees known to countless students taken from the greatest mathematicians in the as an adjective: abelian. I world. The circumstances of the award make the should say that when a sci­ Abel Prize as close as one could imagine to a Nobel entist discovers something Prize in mathematics. However, with laureates of especially noteworthy, his the distinction of Peter Lax, and Jean-Pierre Serre, name gets attached to it. Sir Michael Atiyah, and Isadore Singer before him, However, the supreme mea­ perceptions might change. Perhaps physicists will sure of recognition comes when this adjective is no longer capital­ some day refer to that prize presented in Stock­ ized! In this sense, Abel is in the holm as "an analogue for physics of the Abel Prize"! same company as Archimedes, The professional landscape of Peter Lax is the - Newton, and Gauss. area of differential equations. This is the branch Abel received an excellent edu­ of mathematics that has had the greatest influ­ cation in high school, thanks iron­ ence on the rest of science. Laws of physics, chem­ ically to a horrifying example of istry, biology, engineering, and medicine are all ex­ mathematical pedagogy de­ pressed quantitatively in terms of equations derived scribed in the Abel Prize from the differential calculus discovered by Leibnitz and Newton. The problem is to solve them! The equations are not of the kind one sees in high Niels Abel

AUGUST 2005 NOTICES OF THE AMS 745 RIEMANN-FINSLER GEOMETRY

Shiing-Shen Chern Nankai Institute of Mathematics, P R China

Zhongmin Shen Indiana University Purdue University Indianapolis,

204pp May 2005 981-238-357-3 US$38 981-238-358-1 (pbk) US$19 Peter Lax receiving the Abel Prize from HRH the Related publicJtions by S S Chern Crown Prince Regent of Norway. I Lectures on Differential Geometry US$58 • US$30 (pbk) Wolf Prize in Mathematics (Volume 1) US$129 booklet. At university he studied mathematics on Wolf Prize in Mathematics (Volume 2) US$148 his own, since there was no formal degree in the Contemporary Trends in Algebraic Geometry and Algebraic Topology US$67 natural sciences. He then received a government The Collected Papers of Wei-Liang Chow US$1 01 grant to travel to the leading mathematical centres To place your orders, please call +1800 227 7562 (toll-free from the US) abroad. In six short years Abel made mathemati­ or visit www.worldscibooks.com/mathematics/mathematics.shtml cal discoveries that were beyond the imaginings of or email: [email protected] his contemporaries, and that remain foundations ~ W ld S . t"f" 27 Warren Street, Suite 401 -402, of the mathematics we do today. Who knows what fll or Clen I IC Hackensack, NJ 07601, USA. he might have accomplished had his life not been I www.worldscientific.com Toll-Free Fax: 1888 977 2665 ' cut short tragically by tuberculosis at the age of twenty-six? We take comfort in the knowledge that he lives today in the enduring vitality of his work. The Abel Prize stimulates mathematical research at the very highest levels. It is of enormous benefit for other reasons as well. The effective teaching of mathematics is essential for the future well-being of society. Talented students need to be encouraged to pursue the subject. It is equally important that young men and women see the teaching of mathe­ matics as an honourable calling. Public recognition as Abel Laureates for extraordinary leaders such as Peter Lax resonates the world over. It becomes a source of pride and inspiration for students and teachers alike. I have yet one more reason to express gratitude. The Abel Prize Fund is now supporting the Interna­ tional Mathematical Union in its work of fostering mathematical education and research in developing countries. Such wisdom and foresight is helping to make mathematics a truly global enterprise. It brings us all one step closer to realizing a dream, a wonderful dream, of being able to nurture talent wherever it might be found. Once again, warmest congratulations to Peter Lax from everyone, and heartfelt thanks from the math­ ematical community to Norway for the creation of the Abel Prize.

746 NOTICES OF THE AMS VOLUME 52, NUMBER 7 2004 Annual Survey of the Mathematical Sciences (Second Report)

Updated Report on the 2003-2004 U.S. Doctoral Recipients Starting Salary Survey of the 2003-2004 U.S. Doctoral Recipients

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

Update on the 2003-2004 This Second Report of the 2004 Annual Survey gives an update of the U.S. Doctoral Recipients 2003-2004 new doctoral recipients from the First Report, which ap· peared in the Notices of the AMS in February 2005, pages 236-51. Prior Introduction to 2000 this report included information about faculty size, depart· The Ammal Survey of the Mathematical Sciences cole mental enrollments, majors, and graduate students for departments of mathematical sciences in four-year colleges and universities in the lects information each year about departments, United States. This information is now published as a third report in faculties, and students in the mathematical sci­ the September Notices of the AMS. The First Report gave salary data ences at four-year colleges and universities in the for faculty members in these same departments. It also had a section United States. Definitions of the various groups on new doctoral recipients in statistics that is not updated here. surveyed in the Annual Survey can be found on The 2004 Annual Survey represents the forty-eighth in an annual page 756 of this report. series begun in 1957 by the American Mathematical Society. The 2004 This Second Report includes data from two parts Survey is under the direction of the Data Committee, a joint commit· of the 2004 Annual Survey. First, we update infor­ tee of the American Mathematical Society, the American Statistical mation about new doctoral recipients reported Association, the Institute of Mathematic;al Statistics, and the Mathematical Association of America. The current members of this committee are earlier in the February 2005 issue. Second, we Amy Cohen-Corwin, Donald M. Davis, Nicholas M. Ercolani, J. Douglas present the starting salaries of the new doctoral Faires, Naresh Jain, Donald R. King, Ellen E. Kirkman (chair), David J. recipients who responded to a follow-up survey. Lutzer, James W. Maxwell (ex officio), Polly Phipps, David E. Rohrlich, The names of the 2003-2004 doctoral recipi­ and Henry Schenck. The committee is assisted by AMS survey analyst ents and their thesis titles were published in Colleen A. Rose. Comments or suggestions regarding this Survey "Doctoral Degrees Conferred" (Notices, February Report may be directed to the committee. 2005, pages 264-82). This list has been supple­ mented by forty additional new doctorates. The gathered with a questionnaire, Employment supplemental listing appears at the end of this Experiences of New Doctoral Recipients (EENDR). report on pages 757-8. The EENDR was sent in early October 2004 to all Information about recipients of doctoral degrees new doctoral recipients whose address was known. awarded between July 1, 2003, and June 30, 2004, When a new doctoral recipient did not respond or was collected from doctorate-granting departments no address was known, information supplied by the beginning in late spring 2004 and from a follow-up department was used. census of individual degree recipients beginning in October. The "2004 Annual Survey First Report" (Notices, February 2005, pages 236-51) presented Ellen E. Kirkman is professor of mathematics, Wake Forest survey results obtained about new doctoral University. ]ames W Maxwell is AMS associate executive recipients from the departments. Here we update director for Meetings and Professional Services. Colleen A. information for new doctoral recipients using data Rose is AMS survey analyst.

AUGUST 2005 NOTICES OF THE AMS 747 2004 Annual Survey of the Mathematical Sciences

Updated Employment Status of 2003-2004 Highlights U.S. Doctoral Recipients Table 1A shows the fall and final counts of doctoral recipients in the mathematical sciences awarded by • There were 1 ,081 doctoral recipients from U.S. institutions for U.S. institutions in each year from 1994 through 2003-2004, up 44 (4%) from the previous year. This is the 2004. Final counts include those new doctoral re­ highest number of new Ph.D.'s reported since 1999-2000. cipients reported from departments who missed the • The number of doctoral recipients who are U.S. citizens is 513, deadline for inclusion in the First Report. This year up 14 (3% increase) from last year's number; this year's num­ the total number of new doctoral recipients is ber is the highest number reported since 2000-2001. The per­ . 1,081, up from the previous year by 44. centage of U.S. citizens among all doctoral recipients this year is 47%, down from 48% last year. The number of new doctoral Table 1A: U.S. Doctoral Recipients: recipients who are not U.S. citizens is 568, up 30 from last Fall and Final Counts year's number. • Females totaled 333 (31% of all new doctoral recipients), up Year Fall Final in number and percentage from 308 (30%) last year. Of the 1994-1995 1148 1157 51 3 U.S. citizen new doctoral recipients, 166 are female (32%, 1995-1996 1098 1099 the same as last year). The highest percentage of females 1996-1997 1123 1130 among the annual counts of U.S. doctoral recipients was 34%, reported for 1 998-1 999. 1997-1998 1163 1176 • The number of doctoral recipients whose employment status 1998-1999 1133 1135 is unknown is 119, down 74 from last year's number of 193. 1999-2000 1119 1127 • The final unemployment rate for 2003-2004 doctoral recipi­ 2000-2001 1008 1065 ents was 4.4%. 2001-2002 948 960 • Of the 962 new doctoral recipients whose employment sta­ tus is known, 910 reported having employment in fall 2004 2002-2003 1017 1037 with 792 (87%) finding employment in the U.S.; last year this 2003-2004 1041 1081 percentage was 86%. • The number of new doctoral recipients taking positions in U.S. business and industry was 11 0 in fall 2004, an 11% increase Table 1 B: U.S. Doctoral Recipients: Citizenship from last year's number, which was at a four-year low. The percentage of doctoral recipients employed in the U.S. tak­ Year U.S. Non-U.S. TOTAL ing nonacademic positions has decreased each of the past five 1999-2000 566 561 1127 years, from 28% in fall 2000 to 15% in fall 2004. 2000-2001 532 533 1065 • The number of doctoral recipients taking U.S. academic po­ 2001 - 2002 428 532 960 sitions has reached a five-year high of655, up from 551 last 2002-2003 499 year. Doctoral hires into U.S. academic positions are up in all 538 1037 groups except Group 1 (Private) (down to 71 from 84 last year) 2003-2004 51 3 568 1081 and Group B (down to 1 04 from 1 08 last year); the biggest percentage increases are in Group Va (111 %) and Group IV Table 1B shows trends in the number of new doc­ (69%). Doctoral hires into non-U.S. academics positions are toral recipients for the past five years broken down also up. by U.S. citizens and non-U.S. citizens. This year the • Non-U.S. citizens accounted for 54% of those employed in the number of new doctoral recipients who are U.S. cit­ U.S. (last year this percentage was 44%). izens is 513, an increase of 14 over last year and • There were 52 5 new doctoral recipients responding to the the highest number reported since 2000-2001. The EENDR survey; of the 449 who found employment in the U.S., number of non-U.S. citizen new doctoral recipients 49% reported obtaining a permanent position (last year this has reached a five-year high of 568, but it was 679 percentage was 54%). This is the lowest percentage reported in 1992-1993. in the last five years and the only time in the last five years when the number of temporary hires exceeded the number Table 1C: 2003-2004 U.S. Doctoral Recipients of permanent hires. by Type of Degree-Granting Department • The percentage of temporarily employed respondents whore­ Group' I (Pu) I (Pr) ported taking a postdoctoral position increased from 76% in II Ill IV Va fall 2003 to 77% in fall 2004. The number of respondents who Number 205 187 223 111 265 90 reported taking a postdoctoral position in fall 2004 was 1 76, Percent 19 17 21 10 25 8 up from 164 for fall 2003. 1 For defm1t1ons of groups see page 756.

Table 1C gives a breakdown of the 1,081 doctoral degrees awarded in the mathematical sciences

748 NOTICES OF THE AMS VOLUME 52, NUMBER 7 2004 Annual Survey of the Mathematical Sciences

Table 2A: Fall 2004 Employment Status of 2003- 2004 U.S. Doctoral Recipients: Field of Thesis (updated April 2005)

FIELD OF THES IS

Real, Comp., Discr. Math./ Numerical Linear Differential, Algebra Funct., & Combin./ Analysis/ Nonlinear Integral, & Number Harmonic Geometry/ Logic/ Statistics/ Applied Approxi- Optim./ Difference Math. Other/ TYPE OF EMPLOYER Theory Analysis Topology Comp. Sci. Probability Bios tat. Math. mations Control Equations Educ. Unknown TOTAL

Group I (Public) ' 19 4 9 5 3 4 9 7 1 10 0 0 71 Group I (Private) 10 6 18 3 2 0 6 0 0 9 0 1 55 Group II 16 8 10 6 2 1 6 3 0 18 0 0 60 Group Ill 4 3 4 4 2 10 2 1 0 1 3 0 34 Group IV 0 0 0 0 2 63 1 0 0 0 0 0 66 Gro up Va 1 0 0 3 1 1 3 6 0 3 1 0 19 Master's 11 9 3 7 2 15 5 8 3 3 2 0 68 Bachelor's 15 13 14 11 4 15 6 8 3 11 4 0 104 Two-Year College 6 5 6 1 0 1 0 3 0 2 0 0 24 Other A cademic Dept. 5 2 6 8 3 57 19 7 4 3 6 0 120 Research In stit ute/ 2 2 5 3 1 12 3 3 0 3 0 0 34 Other Nonprofit Government 3 2 1 4 0 8 4 2 2 1 0 0 27 Bus iness and Industry 9 2 5 8 6 56 15 4 1 4 0 0 110 Non-U.S. Academic 19 11 14 12 3 10 11 5 5 17 0 1 108 Non-U.S. Nonacademic 1 0 0 1 0 5 2 0 0 1 0 0 10 Not Seeking Employment 1 0 0 1 0 6 0 1 0 1 0 0 10 St ill Seeking Employment 8 1 4 7 1 10 6 1 2 2 0 0 42 Unknown (U.S .) 11 6 3 7 1 20 3 6 2 4 1 0 64 Unknown (non-U. S.)' 10 6 3 8 2 17 4 3 0 2 0 0 55 TOTAL 151 80 105 99 35 311 105 68 23 85 17 2 1081

Column I 'Male 11 3 58 75 74 28 186 80 49 19 S6 8 2 748 Subtotals I Female 38 22 30 25 7 125 25 19 4 29 9 0 333 1 For defin itions of groups see page 7S6. 2 Includes those whose status is reported as "unknown" or "sti ll seeking employment".

Table 2B: Fall 2004 Employment Status of 2003- 2004 U.S. Doctoral Recipients: Type of Degree-Granting Department (updated April 2005)

TYPE OF DOCTORAL DEGREE-GRAN TI NG DEPARTMENT Group I Group I Row (Publi c) (Private) Group II Group Ill Group IV Group Va Subtotals TYPE OF EMPLOYER Math. Math. Math. Math. Statistics Appli ed Math. TOTAL Male Female

Group I (Publ ic)' 33 25 8 0 1 4 71 54 17 Group I (Private) 15 30 6 0 0 4 55 45 10 Group II 2 1 16 18 2 1 2 60 4 1 19 Group Ill 5 8 6 9 6 0 34 21 13 Group IV 1 1 0 2 6 1 1 66 48 18 Group Va 1 3 1 0 0 14 19 15 4 Master's 11 3 26 18 9 1 68 46 22 Bac helor's 14 10 5 1 17 8 4 104 7 1 33 Two-Year College 4 0 9 10 1 0 24 15 9 Other Academic Dept. 6 14 14 15 51 20 120 70 50 Research Institute/ 7 8 5 0 12 2 34 20 14 Other Nonprofit Government 5 3 7 1 8 3 27 15 12 Business and Ind ustry 1 3 1 5 10 10 53 9 110 76 34 Non-U.S. Academ ic 33 23 25 10 8 9 108 83 25 Non-U.S . Nonacademic 0 4 0 0 4 2 10 9 1 Not Seeki ng Em ploym ent 1 1 2 2 4 0 10 4 6 Sti ll Seeking Employment 6 8 12 5 7 4 42 28 14 Unknown (U .S.) 15 8 16 5 1 5 5 64 46 18 Unknown (non-U.S.)' 14 7 7 5 16 6 55 4 1 14 TOTAL 205 187 223 111 265 90 1081 748 333 Column I Male 156 137 159 72 158 66 748 Subtotals I Female 49 50 64 39 107 24 333 1 For definitions of groups see page 756. 2 Includes those whose status is reported as "unknown" or "sti ll seeking employment".

AUGUST 2005 NOTICES OF THE AMS 749 2004 Annual Survey of the Mathematical Sciences

Table 2C: Field of Thesis of 2003-2004 U.S. Doctoral Recipients: by Type of Degree-Granting Department (Updated April 2005)

FIELD OF THESIS

TYPE OF DOCTORAL Real, Comp., Discr. Math./ Numerical Lin ear Differential, Algebra Funct., & Combin./ Analys is/ Nonlinear Integral, & DEGREE-GRANTING Number Harmonic Geometry/ Logic/ Statistics/ Applied Appro xi- Optim./ Difference Math. Other/ DEPARTMENT Theory Analys is Topology Camp. Sci. Probability Biostat. Math. mations Control Equations Educ. Unknown TOTAL Group I (Public)' 56 26 33 21 9 6 17 11 1 25 0 0 205 Group I (Private) 45 15 35 22 10 6 30 4 1 18 0 1 187 Group II 36 31 29 27 4 10 23 28 12 19 4 0 223 Group Ill 14 8 8 18 2 19 8 11 2 9 12 0 111 Group IV 0 0 0 0 6 256 3 0 0 0 0 0 265 Group Va 0 0 0 11 4 14 24 14 7 14 1 1 90 TOTAL 151 80 105 99 35 311 105 68 23 85 17 2 1081 1 For defimt1ons of groups see page 756.

Table 2D: Percentage of Total Employed New Doctoral recipients plus forty additional doctoral recipients Recipients by Type of Employer reported late. These tables are partitioned by field of thesis research, by the survey group of their U.S. Employed Non-U.S. Employed TOTAL degree-granting department, and by type of employer. NUMBER Academic Nonacademic Academic Nonacademic EMPLOYED New doctoral recipients are grouped by field of Fall 2000 62% 28% 10% 1% 957 thesis using the Mathematical Reviews 2000 Mathe­ matics Subject Classification list. A complete list Fall 2001 63% 27% 9% 2% 914 of these groups is available on the AMS website at Fall 2002 67% 22% 10% 1% 829 www.ams.org/employment/Thesis_groupings. Fall 2003 70% 17% 12% 2% 792 pdf. At the time of this Second Report, the fall2004 Fall 2004 72% 15% 12% 1% 910 employment status of 962 of the 1,081 doctoral recipients was known. The fall 2004 unemployment rate for new doc­ between July 1, 2003, and June 30, 2004, by type toral recipients, of degree-granting department. based on information gathered by Tables 2A, 2B, and 2C display updates of employ­ the time of the Second Report, was 4.4%. Figure 1 ment data, found in these same tables in the First presents the fall1980 through fall2004 trend in the Report, for the fall count of 2003-2004 doctoral final unemployment rate of new doctoral recipients. The counts on which these rates are determined do

Figure 1: Percentage of New Doctoral Recipients Unemployed'

Year Percentage 1980 0.9 1981 0.0 1982 1.8 1983 2.2 1984 2.1 1985 0.8 1986 2.3 1987 3.0 1988 1.4 1989 3.0 1990 2.2 1991 5.0 1992 6.7 1993 8.9 1994 10.7 1995 10.7 1996 8.1 1997 3.8 1998 4.9 1999 4.7 2000 3.3 2001 3.7 2002 2.9 2003 5.0 2004 4.4

1 As reported in the respective Annual Survey Second Reports.

750 NOTICES OF THE AMS VOLUME 52, NUMBER 7 2004 Annual Survey of the Mathematical Sciences

Table 3A: New Doctoral Recipients Taking Employment in the U.S.

Type of Degree-Granting Department

Group' I (Pu) I (Pr) II Ill IV Va TOTAL Academia Business/ Academia Business/ Academia Business/ Academia Business/ Academia Business/ Academia Business/ Academia Business/ Industry Industry Industry Industry Industry Industry Industry

Fall 2000 144 33 82 28 126 37 79 24 131 83 28 18 590 223 Fall 2001 159 28 71 15 126 27 80 26 108 75 30 23 574 194 Fall 2002 133 18 86 12 107 19 91 7 102 65 34 15 553 136 Fall 2003 123 19 90 14 118 5 61 8 119 46 40 7 551 99 Fall 2004 118 13 118 15 144 10 73 10 150 53 52 9 655 110

' For defmltlons of groups see page 756. not include those new doctoral recipients whose fall employment status was unknown at the time Table 3B: New Doctoral Recipients Taking of the Second Report. After spiking to a high of 19 3 U.S. Academic Positions last year, this year the number of recipients whose employment status was reported as unknown Type of Hiring Department dropped to 119. Group' I-III IV Va M&B Other TOTAL Of the 962 new doctoral recipients whose employment is known, 792 were employed in the Fall 2000 216 51 11 180 132 590 U.S., 118 were employed outside the U.S., 42 were Fall 2001 214 49 11 178 122 574 still seeking employment, and 10 were not seeking Fall 2002 222 45 10 148 128 553 employment. Fall 2003 216 39 9 158 129 551 Table 2D presents the trend in the percentage 220 19 172 178 655 of employed new doctoral recipients by type of em­ Fall 2004 66 1 ployer for the last five years. Academic employment For definitions of groups see page 756. includes those employed by research institutes and other nonprofits. The percentage of the total Table 3C: Females as a Percentage of employed new doctoral recipients that are in U.S. 2003-2004 U.S. Doctoral Recipients academic positions has increased in each of the last five years, and consequently the percentage of the Degree-Granting Department total employed in U.S. nonacademic positions (U.S. % Female I (Pu) I (Pr) II Ill IV Va TOTAL government, U.S. business and industry, and non­ U.S. nonacademic) has decreased each of the past Produced 24% 27% 29% 35% 40% 27% 31% five years. Hired 24% 18% 32% 38% 27% 21% 27% Among new doctoral recipients who are employed, the percentage taking nonacademic employment from 108 last year); the biggest percentage varied significantly by field of thesis. For those increases are in Group Va (111%) and Group IV whose field of thesis is in the first three columns (69%). Doctoral hires into non-U.S. academic in Table 2A, this percentage is the lowest at 8% positions are also up. (down from 11%), while the percentage for those Table 3C gives information about the production with theses in probability or statistics is the highest and hiring of female new doctoral recipients in at 26% (down from 30%). the doctoral-granting departments of this survey. Table 3A shows that the fall 2004 total number From Table 3C we see that the percentage of females of doctoral recipients taking positions in business hired ranges from a high of 38% in Group III to a or industry is 110; this number reflects an overall low of 18% in Group I (private). The percentage of increase of 11% since last year. All groups have female new doctoral recipients produced is high­ shown an increase in number of graduates finding est in Group IV (40%). employment in business and industry, except Updated Information about 2003-2004 U.S. Group 1 Public. Doctoral Recipients by Sex and Citizenship Table 3B shows that the number of new doctoral Tables 3D and 3E show the sex and citizenship recipients taking U.S. academic positions has of the 1,081 new doctoral recipients and the fact increased to a five-year high of 655, from 551 in that 792 new doctoral recipients found jobs in the 2003. Doctoral hires into U.S. academic positions U.S. this year. This is 87% of the 910 new doctoral are up in all groups except Group I Private (down recipients known to have jobs in fall 2004. Last year to 71 from 84last year) and Group B (down to 104 this percentage was 86%.

AUGUST 2005 NOTICES OF THE AMS 751 2004 Annual Survey of the Mathematical Sciences

Table 3D: Citizenship of 2003-2004 Male U.S. Doctoral Recipients by Fall 2004 Employment Status

CITIZENSHIP TOTAL MALE NON-U.S. CITIZENS DOCTORAL U.S. CITIZENS TYPE OF EMPLOYER Perm anent Visa Temporary Visa Unknown Visa RECIPIENTS U.S. Employer 242 39 244 12 537 U.S. Academic 197 27 213 9 446 Groups' I, II, Ill , and Va 76 11 86 3 176 Group IV 12 2 30 4 48 Non-Ph.D. Department 105 14 81 2 202 Research Institute/Other Nonprofit 4 0 16 0 20 U.S. Nonacademic 45 12 31 3 91 Non-U .S. Employer 56 1 31 4 92 Non-U.S. Academic 52 1 28 2 83 Non-U.S. Nonacademic 4 0 3 2 9 Not Seeking Employment 2 1 1 0 4 Still Seeking Employment 16 2 10 0 28 Subtotal 316 43 286 16 661 Unknown (U.S.) 30 1 12 3 46 Unknown (non-U.S.)' 1 1 28 11 41

TOTAL 347 45 326 30 748

' For definitions of groups see page 756. 2 Includes those who se status is reported as "unknown" or "still seeking employment".

Table 3E: Citizenship of 2003-2004 Female U.S. Doctoral Recipients by Fall 2004 Employment Status

CITIZENSHIP TOTAL FEMALE NON-U .S. CITIZENS DOCTORAL U.S. CITIZENS TYPE OF EMPLOYER Permanent Visa Temporary Visa Unknown Visa RECIPIENTS U.S. Employer 126 22 102 5 255 U.S. Academic 105 19 81 4 209 Groups' I, II , Ill, and Va 25 8 29 1 63 Group IV 11 3 4 0 18 Non-Ph.D. Department 64 8 39 3 114 Research Institute/ Other Nonprofit 5 0 9 0 14 U.S. Nonacademic 21 3 21 1 46 Non-U.S. Employer 18 0 8 0 26 Non-U.S. Academic 18 0 7 0 25 Non-U.S. Nonacademic 0 0 1 0 1 Not Seeking Employment 4 0 2 0 6 Still Seeking Employment 7 4 3 0 14 Subtotal 155 26 11 5 5 301 Unknown (U .S.) 9 3 4 2 18 Unknown (non-U.S.)' 2 0 10 2 14

TOTAL 166 29 129 9 333 ' For defmrtrons of groups see page 756. 2 In cludes those whose status is reported as "unknown" or "still seeki ng employment".

Sex and citizenship are known for all of the the number of female U.S. citizens and the num­ 1,081 new doctoral recipients. The final count of ber of male U.S. citizens represent an increase over new doctoral recipients who are U.S. citizens is 513 last year's counts of 158 and 341, respectively. (4 7%) (down from 48% last year). For the last five Table 3F shows that non-U.S. citizens accounted years this figure has remained very close to 50%, for 54% of those employed in the U.S. (last year the largest percentage reported by the Annual this percentage was 44%). U.S. academic doctoral Survey since the mid-1980s. Pages 241-4 of the departments, Groups I through Va, hired 41% U.S. First Report present further information related to citizens, while groups M, B, and all other academic the citizenship of the 2003-2004 new doctoral departments hired 51% U.S. citizens (last year these recipients. percentages were 52% and 61%, respectively). U.S. Of the 513 U.S. citizen new doctoral recipients citizens represented 48% of those hired into nonaca­ reported for 2003-2004, 166 are female and 347 demic positions (last year 56%). Among the 792 are male. While females accounted for 32% of the new 2003-2004 doctoral recipients employed in U.S. citizen total both this year and last year, both the U.S., 17% took nonacademic employment

752 NOTICES OF THE AMS VOLUME 52, NUMBER 7 2004 Annual Survey of the Mathematical Sciences

Table 3F: Number of 2003-2004 Doctoral Recipients Employed in the U.S. by Citizenship Table 4A: Number (and Percentage) of Annual EENDR and Type of Employer Respondents Taking U.S. Positions by job Status

U.S. Employed CITIZENSHIP U.S. EMPLOYER U.S. Non-U.S. TOTAL Temporary Unknown Permanent Temporary Postdoctoral Academic, Groups I-Va 124 181 305 Permanent Total Total not available Permanent Total Academic, Other 178 172 350 not available Nonacademic 66 71 137 Fal l 2000 3 17(59) 218(41) 92(42) 157(72) 55(35) 1 TOTAL 388 424 792 Fal l 2001 266(56) 205(43) 1 07(52) 143(70) 42(29) 2 Fall 2002 264(52) 245(48) 90(37) 203(83) 69(34) 1 (government or business and industry.) This per­ Fall 2003 253(54) 216(46) 87(40) 164(76) 53(32) -- centage is down from 19% in 2002-2003 and from Fall 2004 220(49) 229(51) 81(35) 176(77) 49(28) -- 24% in 2001-2002.

New Information from the EENDR Survey Table 4B: Percentage of Annual EENDR Respondents Taking Of the 1,041 new doctoral recipients reported U.S. Positions by Employment Sector within Job Status in the First Report, the 914 whose addresses were known were sent the Employment Experiences of U. S. Employed New Doctoral Recipients (EENDR) survey in Octo­ Permanent Temporary ber 2004, and 525 (50%) responded. The response Business/ Academia Government Business/ Academia Government rates varied considerably among the various sub­ Industry Industry groups of new doctoral recipients defined by their Fal l 2000 59% 4% 36% 95% 2% 2% employment status as reported by departments. -- Among those who were employed, the highest re­ Fall 2001 62% 6% 32% 9 5% 4% sponse rate, 62%, was from those in academia in Fall 2002 70% 6% 23% 93% 6% 1% the U.S., while the lowest, 38%, was from those in Fall 2003 76% 4% 20% 94% 3% 3% non-U.S. nonacademic. Fall 2004 72% 5% 23% 97% 3% -- The EENDR gathered details on employment ex­ periences not available through departments. The rest of this section presents additional information Table 4B shows the employment trends of available on this subset of the 2003-2004 doctoral permanent and temporary positions broken down recipients. by sector for the last five years. After steadily Table 4A provides the trend in EENDR respon­ increasing over the last four years, the percentage dents taking permanent and temporary positions of permanently employed EENDR respondents in the U.S for fall2000 through fall2004. This year taking employment in academia has declined this we see that among the 449 employed in the U.S., 220 year, and there was an offsetting increase in the reported obtaining a permanent position and 229 proportion of permanently employed EENDR a temporary position; this is the only time in the last five years when the number of Figure 2: Age Distribution of 2003- 2004 EENDR Respondents temporary hires exceeded the number of permanent hires. 80 Of the 229 in temporary po­ 70 sitions, 81 (35%) reported tak­ ing temporary employment 60 because a suitable permanent r- position was not available, >- 50 1.1 and 176 (77%) classified their s::::

AUGUST 2005 NOTICES OF THE AMS 753 2004 Annual Survey of the Mathematical Sciences

respondents taking positions in business and Readers should be warned that the data in this industry. report are obtained from a self-selected sample, and Among the 220 who reported obtaining a per­ inferences from them may not be representative manent position in the U.S. in fall 2004, 72% were of the population. employed in academia (including 1% in research in­ Key to Tables and Graphs. Salaries are listed stitutes and other nonprofits), 5% in government, in hundreds of dollars. Nine-month salaries are and 23% in business or industry. Women held 36% based on 9-10 months' teaching and/ or research, of the permanent positions. not adding extra stipends for summer grants or Among the 229 individuals with temporary em­ summer teaching or the equivalent. Years listed ployment in the U.S. this year, 97% were employed denote the survey cycle in which the doctorate was in academia (including 9% in research institutes and received: for example: survey cycle July 1, 2003- other nonprofits), less than 1% in government, and June 30, 2004, is designated as 2004. Salaries are 3% in business or industry. those reported for the fall immediately following Figure 2 gives the age distribution of the 525 new the survey cycle. M and F are male and female doctoral recipients who responded to this question. respectively. Some persons receiving a doctoral The median age of new doctoral recipients was 31 degree had been employed in their present posi­ years, while the mean age was 33 years. The first tion for several years, so those who had "one year and third quartiles were 29 and 35 years, respec­ or less experience" were analyzed separately tively. In the previous six years the median age has from the total. Male and female figures are not generally been 30 and the mean age has been 32, provided when the number of salaries available with first and third quartiles at 28 and 34 years, for analysis in a particular category was five or respectively. fewer. Also, quartile figures are not available for 1970 through 1980. All categories of "Teach­ Previous Annual Survey Reports ing/Teaching and Research" and "Research Only" The 2004 First Annual Survey Report was pub­ contain those recipients employed at academic lished in the Notices in the February 2005 issue. For institutions only. The "Academic Research Only, the last full year of reports, the 2003 First, Second, 9-10-Month Salaries" category was dropped from and Third Annual Survey Reports were published the published analyses in 1998 because so few in the Notices in the February, August, and Sep­ recipients responded in this category that the data tember 2004 issues respectively. These reports were not considered meaningful. Starting salaries and earlier reports, as well as a wealth of other for those reporting a 9-1 0-month salary postdoc­ information from these surveys, are available on toral position are available for an eighth year. These the AMS website at www. ams . o rg/ emp 1 oyment/ salaries are also included within the "Academic surveyreports.html. Teaching/Teaching and Research, 9-1 0-Month Salaries" table and boxplot on page 753. Graphs. The graphs show standard boxplots sum­ marizing salary distribution information for the years 1997 through 2004. Values plotted for 1997 Starting Salary Survey of the through 2003 are converted to 2004 dollars using the implicit price deflator prepared annually by the 2003-2004 U.S. Doctoral Bureau of Economic Analysis, U.S. Department of Recipients Commerce. For each boxplot the box shows the first quar­ The starting salary figures for 2004 were com­ tile (Q1), the median (M), and the third quartile piled from information gathered on the EENDR (Q3). The interquartile range (IQR) is defined as questionnaires sent to individuals who received Q3-Ql. Think of constructing invisible fences doctoral degrees in the mathematical sciences 1.5xiQR below Q1 and 1.5xiQR above Q3. Whiskers during the 2003-2004 academic year from uni­ are drawn from Q3 to the largest observation that versities in the United States (see previous section falls below the upper invisible fence and from Q1 for more details). to the smallest observation that falls above the The questionnaires were distributed to 914 lower invisible fence. Think of constructing two recipients of degrees using addresses provided more invisible fences, each falling 1.5xiQR above by the departments granting the degrees; 525 or below the existing invisible fences. Any obser­ individuals responded between late October and vation that falls between the fences on each end April. Responses with insufficient data or from of the boxplots is called an outlier and is plotted individuals who indicated they had part-time or as o in the boxplots. Any observation that falls out­ non-U.S. employment were excluded. Numbers side of both fences either above or below the box of usable responses for each salary category are in the boxplot is called an extreme outlier and is reported in the following tables. marked as * in the boxplot.

754 NOTICES OF THE AMS VOLUME 52, NUMBER 7 2004 Annual Survey of the Mathematical Sciences

Academic Teaching/Teaching and Research Academic Postdoctorates 9-1 0-Month Salaries 9-1 0-Month Salaries (in hundreds of dollars) (in hundreds of dollars) Reported Ph .D. Median in Year Min Ql Median Q 3 Max 2004$ 1975 90 120 128 135 173 365 1980 105 155 171 185 250 343 1985 170 230 250 270 380 388 1990 230 305 320 350 710 425 ' Reported 1995 220 320 350 382 640 411 Ph.D. Median in 1996 240 333 360 400 636 415 Year Min Ql Median Q 3 Max 2004$ 1997 180 340 366 400 840 415 1997 180 350 385 410 450 437 1998 140 340 370 410 700 415 1998 290 350 390 420 500 438 1999 180 360 400 430 700 442 1999 130 365 400 418 540 442 2000 250 380 415 450 650 449 2000 300 385 420 450 550 455 2001 259 400 420 461 660 444 2001 250 400 425 450 566 449 2002 230 400 450 500 840 468 2002 230 425 450 487 595 468 2003 220 415 450 510 920 460 2003 240 420 450 480 600 460 2004 285 420 450 500 1234 450 2004 300 420 450 490 625 450 2000 M 250 380 415 450 650 2000 M 300 390 420 450 550 2000 F 321 380 413 450 620 2000 F 360 389 448 458 544 2001 M 259 490 430 475 660 2001 M 2001 F 310 390 413 443 620 250 400 430 454 566 2001 F 310 395 421 438 490 2002 M 230 420 450 500 840 2002 F 300 400 441 498 610 2002 M 230 425 450 488 595 2002 F 380 430 450 485 589 2003 M 220 420 450 509 855 2003 F 359 414 444 512 920 2002 M 230 425 450 488 595 2002 F 380 430 450 485 589 Total (146 male/78 female) 2004 M 285 420 450 490 850 2003 M 220 420 450 509 855 2004 F 300 421 450 500 1234 2003 F 359 414 444 512 920 One year or less experience (123 male/58 female) Total (55 male/20 female) 2004 M 300 420 450 490 850 2004 M 300 420 450 480 625 2004 F 300 420 450 490 1234 2004 F 400 440 470 500 606

1500 1500

1400 1400

1300 1300 ...... 1200 * ...... 1200 "'.... "'.... ~ 1100 ~ 1100 0 -0 "'C 1000 "'C 1000 '- ....>- res 400 res 400 iii iii Ill ~ Ill ~ ~ 0 300 300 0 0 0 ~ ~ ~ 0 ~ 0 ~ 8 ~ 0 0 ~ ~ 0 0 ~0 0 8 0 0 l 0 ~ 0 200 0 200 * 0 100 100 *

1997 1998 1999 2000 2001 2002 2003 2004 1997 1998 1999 2000 2001 2002 2003 2004

AUGUST 2005 NOTICES OF THE AMS 755 2004 Annual Survey of the Mathematical Sciences

Academic Teaching/Teaching and Research Academic Research Only 11-12-Month Salaries 11-12-Month Salaries (in hundreds of dollars) (in hundreds of dollars) Reported Reported Ph.D. Median in Ph .D. Median in Year Min Median Max 2004$ Year Min Median Q Max 2004 $ 1975 87 145 204 413 1975 90 119 180 339 1980 143 195 350 391 1980 120 180 321 361 1985 220 230 273 300 470 424 1985 190 295 342 400 520 531 1990 225 318 365 404 670 484 1990 180 280 300 365 546 398 1995 300 354 410 478 600 482 1995 196 280 340 370 587 400 1996 150 302 340 390 720 392 1996 192 270 330 400 585 381 1997 260 370 400 497 650 454 1997 190 300 350 400 600 397 1998 275 405 480 575 700 539 1998 200 333 360 428 617 404 1999 200 374 420 469 650 465 1999 270 390 440 500 720 487 2000 300 400 485 600 1170 525 2000 300 384 400 555 1000 433 2001 350 420 465 615 870 492 2001 300 367 420 625 800 444 2002 310 439 500 597 840 520 2002 270 380 440 500 700 457 2003 345 438 475 550 780 485 2003 300 415 470 613 900 480 2004 350 450 495 583 980 495 2004 300 384 440 543 1250 440 2000 M 300 390 460 650 1170 2000 M 300 390 400 486 1000 2000 F 395 465 500 570 750 2000 F 300 360 410 580 630 2001 M 350 420 443 498 870 2001 M 300 348 425 655 800 2001 F 380 465 588 658 750 2001 F 342 400 420 588 700 2002 M 310 420 485 595 840 2002 M 270 388 440 500 650 2002 F 400 453 500 558 700 2002 F 310 350 440 505 700 2003 M 397 440 490 555 780 2003 M 300 420 450 510 820 2003 F 345 400 440 513 620 2003 F 310 390 480 650 900 Total (32 male/8 female) Total (37 male/19 female) 2004 M 350 448 487 533 980 2004 M 300 385 440 660 1250 2004 F 380 465 545 605 650 2004 F 350 383 440 495 820 One year or le ss experience (28 male/8 female) One year or less experience (31 male/16 female) 2004 M 350 440 483 520 980 2004 M 300 368 440 560 863 2004 F 380 465 545 605 650 2004 F 350 378 410 452 780

1500 1500

1400 1400

1300 1300 ..... 1200 1200 * VI ..... VI..... ra 1100 ra 1100 0 0 "C 1000 ~ 1000 """0 0 ~ 900 0 900 ..... r .....N 0 800 0 800 VI VI "C "C Q) Q) ..... 700 r r ..... 700 "C "C s::: s::: :I 600 :I .s::: .s::: 600 s::: s::: '-" 500 '-" 500

400 400

300 300

200 200

100 100

1997 1998 1999 2000 2001 2002 2003 2004 1997 1998 1999 2000 2001 2002 2003 2004

756 NOTICES OF THE AMS VOLUME 52, NUMBER 7 2004 Annual Survey of the Mathematical Sciences

Government Business and Industry 11 - 12-Month Salaries 11 - 12-Month Salaries (in hundreds of dollars) (in hundreds of dollars) Reported Reported Ph.D. Median in Ph.D. Med ian in Year Min Median Q Max 2004 $ Year Min Ql Medi an 0 3 Max 2004 $ 1975 78 182 247 518 1975 11 4 --- 187 --- 240 533 1980 156 244 50 1 489 1980 190 --- 284 --- 400 569 1985 263 294 325 381 440 505 1985 260 360 400 420 493 621 1990 320 345 378 430 587 50 1 1990 320 438 495 533 700 657 1995 370 440 494 507 650 58 1 1995 288 480 568 690 1250 667 1996 360 420 427 504 650 492 1996 250 510 580 610 1000 669 1997 350 454 573 600 750 650 1997 300 483 600 658 1000 68 1 1998 320 475 540 736 1250 606 1998 240 550 650 750 2250 729 1999 400 495 550 65 1 720 608 1999 360 600 680 761 2450 75:< 2000 440 540 600 640 830 649 2000 200 640 720 800 1500 779 2001 400 580 644 758 920 681 2001 475 716 770 865 1850 814 2002 450 551 650 775 1005 676 2002 325 734 780 850 1400 81 1 2003 290 668 705 763 1008 720 2003 300 700 800 900 1250 817 2004 510 720 738 780 920 738 2004 400 728 817 900 1800 817 2000 M 440 563 620 649 830 2000 M 200 640 730 800 1500 2000 F 530 545 566 593 650 2000 F 200 645 690 788 980 200 1 M 400 590 647 780 920 2001 M 520 717 788 875 1700 200 1 F 450 550 630 670 896 200 1 F 475 710 750 850 1850 2002 M 450 55 1 642 725 1005 2002 M 325 738 782 858 11 00 2002 F 540 600 700 850 880 2002 F 600 713 768 838 1400 2003 M 290 648 710 788 830 2003 M 550 725 840 920 1250 2003 F 600 683 695 723 1008 2003 F 300 628 780 816 900 Total (9 male/8 female) Total (33 male/11 fema le) 2004 M 520 700 730 740 910 2004 M 400 710 813 900 1800 2004F 510 733 749 790 920 2004 F 480 789 850 900 11 00 One year or less experience (8 male/5 fema le) One year or less experience (2 1 male/9 female) 2004 M 520 675 732 780 910 2004 M 500 680 800 850 1000 2004 F 510 720 738 743 820 2004 F 400 615 800 900 1100 (Note: One salary above $150 ,000 is not shown .) 1500 1500 1400 1400 * * 0 0 1300 1300 0

0

1200 0 1200 0 VI VI ...... 0 r .!!! 11 00 r 0 .!!! 11 00 0 0 0 0 -c r -c 1000 r r 1000 0""" """0 ~ 900 0 900 ...... N 0 0 f- 800 800 f- Ill Ill 1- -c -c t- QJ QJ .... 700 f- .... 700 t- -c -c 1- f- f- t: f- t: ::I 600 ::I 600 .s::: .s::: L t: s:::: L

~ 500 ~ 500 0 >- L.. 8 .... 0 0 400 ra 400 0 ra 0 VI 300 300 * 0 0 200 200 0 8 100 100 8

1 997 1 998 1 999 2000 2001 2002 2003 2004 1997 1998 1999 2000 2001 2002 2003 2004

AUGUST 2005 NOTICES OF THE AMS 757 2004 Annual Survey of the Mathematical Sciences

Acknowledgments Definitions ofthe Groups The Annual Survey attempts to provide an accurate appraisal and analysis of various aspects of the aca­ As has been the case for a number of years, much of the data in demic mathematical sciences scene for the use and these reports is presented for departments divided into groups benefit of the community and for filling the infor­ according to several characteristics, the principal one being the mation needs of the professional organizations. highest degree offered in the mathematical sciences. Doctoral­ Every year, college and university departments in granting departments of mathematics are further subdivided An­ according to their ranking of"scholarly quality of program faculty" the United States are invited to respond. The as reported in the 1995 publication Research-Doctorate Programs nual Survey relies heavily on the conscientious in the United States: Continuity and Change.l These ran kings update efforts of the dedicated staff members of these those reported in a previous study published in 1 982.2 Consequently, departments for the quality of its information. the departments which now comprise Groups I, II, and Ill differ On behalf of the Annual Survey Data Committee significantly from those used priorto the 1 996 survey. and the Annual Survey Staff, we thank the many The subdivision of the Group I institutions into Group I Public secretarial and administrative staff members in and Group I Private was newforthe 1996 survey. With the increase the mathematical sciences departments for their in number ofthe Group I departments from 39 to 48, the Data cooperation and assistance in responding to the Committeejudged that a further subdivision of public and private survey questionnaires. would provide more meaningful reporting of the data for these departments. Other Data Sources American Association of University Professors, Inequities Brief descriptions oft he groupings are as follows: Persist for Women and Non-Tenure-Track Faculty: The Group I is composed of 48 doctoral-granting departments with Annual Report on the Economic Status ofthe Profession scores in the 3.00-5.00 range. Group I Public and Group I 2004-2005, Academe: Bull. AAUP (March/April2005), Private are Group Idoctoral-granting departments at public Washington, DC. institutions and private institutions respectively. American Statistical Association, 2004-2005 Salary Re­ Group II is composed of 56 doctoral-granting departments port of Academic Statisticians, AmStat News (Decem­ with scores in the 2.00-2.99 range. ber 2004), Alexandria, VA. Group Ill contains the remaining U.S. doctoral-granting __ , Salary Survey Results: Biostatistics and Other departments, including a number of departments not Biomedical Statistics Departments and Units, AmStat included in the 1 995 ranking of program faculty. News (December 2004), Alexandria, VA. Group IV contains U.S. doctoral-granting departments (or Commission on Professionals in Science and Technology, programs) of statistics, biostatistics, and biometrics Professional Women and Minorities, 15th ed., CPST, reporting a doctoral program. Washington, DC, 2004. Group Vcontains U.S. doctoral-granting departments (or programs) _ _ , Salaries of Scientists, Engineers, and Technicians: A of applied mathematics/applied science, operations Summary of Salary Surveys, 20th ed., CPST, Washing­ research, and management science. ton, DC, 2003. Group Va is applied mathematics/applied science doctoral­ Conference Board of the Mathematical Sciences, Statistical granting departments; Group Vb, which is no longer Abstract of Undergraduate Programs in the Mathematical surveyed as of 1998-99, was operations research and Sciences in the United States: Fall 2000 CBMS Survey, management science. American Mathematical Society, 2002. Group M or Master's contains U.S. departments granting a _ _ , Statistical Abstract of Undergraduate Programs in master's degree as the highest graduate degree. the Mathematical Sciences in the United States: Falll995 Group Bor Bachelor's contains U.S. departments granting CBMS Survey, MAA Reports No.2, 1997. a baccalaureate degree only. National Opinion Research Center, Doctorate Recipients Listings of the actual departments which comprise these from United States Universities: Summary Report 2002, groups are available on the AMS website at Survey of Earned Doctorates, Chicago, IL, 2003. www.ams.org/outreach. National Research Council, Strengthening the Linkages between the Sciences and the Mathematical Sciences, 1Research-Doctorate Programs in the United States: Continuity and Change, National Academy Press, Washington, DC, 2000. edited by Marvin L. Goldberger, Brendan A. Maher, and Pamela Ebert Flat­ __, U.S. Research Institutes in the Mathematical Sciences: tau, National Academy Press, Washington, DC, 1995. Assessment and Perspectives, National Academy Press, 2 These findings were published in An Assessment of Research-Doctorate Washington, DC, 1999. Programs in the United States: Mathematical and Physical Sciences, edited by Lyle V. jones, Gardner Lindzey, and Porter E. Coggeshall, National _ _ , Research-Doctorate Programs in the United States: Academy Press, Washington, DC, 1982. The information on mathematics, Continuity and Change, National Academy Press, Wash­ statistics, and computer science was presented in digest form in the April ington, DC, 1995. 1983 issue of the Notices, pages 257-67, and an analysis of the classifi­ National Science Board, Science and Engineering Indica­ cations was given in the june 1983 Notices, pages 392-3. tors-2004. Two Volumes (Volume 1, NSB 04-01; Volume 2, NSB 04-lA), National Science Foundation, Arlington, VA, 2004.

758 NOTICES OF THE AMS VOLUME 52, NUMBER 7 2004 Annual Survey of the Mathematical Sciences

National Science Foundation, Characteristics of Doctoral University of California, San Diego Scientists and Engineers in the United States: 2001 (NSF 03-310), Detailed Statistical Tables, Arlington, VA, 2003. (10) __, Graduate Students and Postdoctorates in Science and MATHEMATICS Engineering: Fall2002 (NSF 05-310), Arlington, VA, Chang, Frank, Division algebras over generalized local 2005. fields. __ ,Science and Engineering Degrees: 1966-2001 (NSF Kroyan, julia, Trust-search algorithms for unconstrained 04-311 ), Detailed Statistical Tables, Arlington, VA, 2004. optimization. __, Science and Engineering Degrees, by Race/Ethnicity Lu, Shaoying, Scalable parallel multilevel algorithms for of Recipients: 1992-2001 (NSF 04-318), Detailed solving partial differential equations. Statistical Tables, Arlington, VA, 2004. McMurry, Timothy Lewis, Infinite order flat-top kernels in nonparametric regression. __ ,Science and Engineering Doctorate Awards: 2002 (NSF 04-303), Detailed Statistical Tables, Arlington, VA, Melcher, Tai, Hypoelliptic heat kernel inequalities on Lie groups. 2003. Mendes, Anthony A., Building generating functions brick __, Statistical Profiles of Foreign Doctoral Recipients in by brick. Science and Engineering: Plans to Stay in the United Ovall, jeffrey Scott, Duality-based adaptive refinement for States(NSF 99-304), Arlington, VA, 1998. elliptic PDEs. __, Women, Minorities, and Persons with Disabilities in Parker, Cameron, Block bootstrap methods for unit root Science and Engineering: 2004 (NSF 04-417), Arlington, testing. VA, 2004 Sanchez, Rino, A construction of small unitary represen­ tations. Schuman, Michele Ann, A new look at problems of Herstein and Kaplansky. Doctoral Degrees FLORIDA University of Florida (1) Conferred 2003-2004 STATISTICS Supplementary List Kim, Myung ]oon, Constrained Bayes and empirical Bayes estimators under squared error and balanced loss func­ The following list supplements the list of thesis titles published in tions. the February 2005 Notices, pages 264-82. KENTUCKY ALABAMA University of Kentucky (4) Auburn University (4) STATISTICS MATHEMATICS AND STATISTICS Berhane, Indrias, Consistency and generalization error Granado, Michael, On the moving off property and weak bound of feed forward neural network trained with additivity of local connectedness and metrizability. smoothing regularizer. Holliday, John, The Shields-Harary number graphs. Kim, Kyoungmi, Empirical likelihood ratio method when additional information is known. Logan, Sasha, Maximal sets of Hamilton cycles. Peng, Xuejun, Simultaneous inference and sample size Muse, William, Orthogonal quadruple systems and considerations for microarray data analysis. 3-frames. Smith, Michelle, Markov chain analysis and statistical CALIFORNIA inference for start-up demonstration test.

University of California, Irvine (4) NEW JERSEY MATHEMATICS Rutgers University, Graduate Boutchaktchiev, Vilislav, Mixed Hodge structure on Brill­ School (4) Noether stacks. STATISTICS Gurtas, Yusuf, Positive Dehn twist expressions for some elements of finite order in the mapping class group. Eyheramendy, Susana, Bayesian text categorization. Tsai, Yen-Lung, Non-abelian Clemens-Schmid exact Liu, ]un, Stochastical control problems with limitations on sequences. the set of allowable controls. Yun, Myung Sik, Numerical simulation of microstructural Thompson, Wesley, Transformation and selection of evolution of inhomogenous elastic media. covariates estimating equations. Zhang, ]ingshan, Scalar scale analysis of multivariate data­ robust testing based on scale curves.

AUGUST 2005 NOTICES OF THE AMS 759 2004 Annual Survey, Mathematical Sciences

PENNSYLVANIA Temple University (S) STATISTICS Allen, Shannon Eileen, Analysis of hierarchical factorial layouts when observations are sampled from unbalanced finite populations of finite effects. Chin, ]ie, Bayesian approaches to simultaneous testing of multiple hypotheses. Gagnon, Robert Charles, Experiments with unknown parameters in variance. Li, Susan Xuemei, Further contributions to Fisher's and Sims' tests. Pasles, Elise B., Mutually nearly orthogonal Latin squares and their applications.

University of Pittsburgh (8) BIOSTATISTICS Kelly, Mary E., Zero inflation in ordinal data: applications of a mixture model. McHenry, Michael Brent, New estimation approaches in survival analysis with Aalen's additive risk model. Ruppert, Kristine, Assessment of the use of biopsies collected as part of nonsystematic follow-up of liver transplant patients. Shen, Changyu, Regression analysis in longitudinal stud­ ies with nonignorable missing outcomes. Szatkiewicz, ]in Peng, Mapping genes for quantitative traits using selected samples of sibling pairs. Wang, ]iping, Use of receiver operating characteristic curve in medical decision making. Xu, Lei, Covariate adjustment partial least squares for the extraction of the spatial temporal pattern. Ye, Yunrong, The correlated random parameters model for longitudinal binary response data with missing covariates.

760 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Crossword Puzzle

By Byron Walden

ACROSS 1 "Great Expectations" protagonist 4 Jewel box contents 7 Where Gian-Carlo Rota taught 10 Location of Technion Univ. 13 Moment of __ 15 Distances found by dividing the area of a triangle by its semiperimeter 17 Q[2] and Q[i], for example 19 Classic containers in probability 20 New Zealand native 21 Stink 22 Fair hiring abbr. 23 Corporals and sergeants, e.g. 25 Sound from a radiator 26 Diarist Ana'is 27 Spoken stumbles 29 Liters 38 Make a speech 39 The Sof AMS 40 Stink 41 Objects of study for Kummer 44 Person in a crew 45 Voluminous ref. work 46 It may be bruised 49 Unwelcome sign on a dorm shower 53 Game whose strategy is based on binary representations 56 The "Jungle Book" star 58 Bigwig 8 Greatest lower bound 36 Fish eggs 59 Plea from a child 9 Part of TNT 37 Soon-to-be grads 60 Object of study for Abel 10 Runs in place? 42 Kind of board 63 Disregard 11 Polygon data 43 Sears associate 64 Home of the newspaper "The 12 Actuarial concern 46 Suffix for Zola California Aggie" 14 Map lines: abbr. 47 Haggard 65 Co. which produces the GRE 16 __ Lingus 48 Lines of departure? 66 Many moons __ 18 Quadrennial games org. 50 Cuckoo 67 Squeeze (out) 23 Comment to one returning from a 51 Honest __ Animal in a gang 68 sabbatical 53 Born yesterday 24 Logician with a famous stroke 54 How some tuna is packed DOWN 26 Part of TNT 55 Home of the Belarusian State 1 Irked state 28 Place University 2 Accustom 29 __ auvin 57 Durhamsch. 3 Famous axiomatizer of number 30 Home of the Univ. of Montevideo 59 El overseers, for short theory 31 Pasture comment 61 Actress Carrere of "Wayne's World" 4 Geom. point 32 Fl neighbor, on many keyboards 62 Summer cooler 5 Certain 4-sided figure 33 Function in De Moivre's Theorem 6 "Paradise Lost" character 34 Post -surgery locale Answers: Page 767 7 Processor prefix 35 Yada equivalent?

AUGUST 2005 NOTICES OF THE AMS 761 Mathematics People

of mathematics, including distributive normal forms, H:intikka and Caffarelli Receive independence-friendly logic, definability, infinitely deep Rolf Schock Prizes languages, and extremality assumptions in mathematical theories. Two mathematicians are among the winners of the Rolf ]aakko Hintikka was born in Vantaa, Finland, in 1929. Schock Prizes for 2005. The Schock Prize in Logic and He received his Ph.D. from the University of Helsinki in Philosophy was awarded to ] AAKKO HINTIKKA of Boston 1956. He has taught at Helsinki, at the Academy of Fin­ University "for his pioneering contributions to the logical land, Florida State University, and Stanford University and analysis of modal concepts, in particular the concepts of has been at Boston University since 1990. He has authored knowledge and belief." The Schock Prize in Mathematics or coauthored more than thirty books and monographs, was given to LUIS A. CAFFARELLI of the University of Texas including The Principles of Mathematics Revisited, and his at Austin "for his important contributions to the theory works have been published in nine languages. Five volumes of nonlinear partial differential equations." of his selected papers have been published, and a com­ The versatile philosopher and artist Rolf Schock prehensive examination of his thought, The Philosophy of (1933-86) described in his will a prize to be awarded in ]aakko Hintikka, appeared in 2004 as part of the Library such widely differing subjects as logic and philosophy, of Living Philosophers. He has held the John Locke Lec­ mathematics, the visual arts, and music. The Royal Swedish tureship at Oxford University, the Hager strom Lectureship Academy of Sciences, the Royal Swedish Academy of Fine at Uppsala University, and the Immanuel Kant Lectureship Arts, and the Royal Swedish Academy of Music have at Stanford University. He has been the recipient of the awarded these prizes every other year since 1993. Each Wihuri International Prize (1976), a Guggenheim Fellow­ prize carries a monetary award of SEK 400,000 (about ship (1979-80), and honorary doctorates from the US$ 5 6,400). University of Liege, the Jagiellonian University of Cracow, and the Universities of Uppsala (2000), Oulu (2002), and Jaakko Hintikka Turku (2003). ]aakko Hintikka is known as the main architect of game­ theoretical semantics and of the interrogative approach Luis A. Caffarelli to inquiry and also as one of the architects of distributive Luis A. Caffarelli is the world's leading specialist in free normal forms, possible-world semantics, tree methods, boundary problems for nonlinear differential equations. infinitely deep logics, and the present-day theory of Differential equations are the mathematician's foremost inductive generalization. He was one of the philosophers aid for describing change. In the simplest case, a process who established "possible-world" semantics for modal that depends on one variable alone-for example, time­ logic, a form of semantics that attempts to improve our may be described by an ordinary differential equation. understanding of modal concepts, not only such concepts But more complex phenomena are dependent on many as "necessary" and "possible" but also concepts such more variables: perhaps time plus one, two, or three as "knowledge", "belief", "ought", "right", and "wrong". spatial variables. These processes require the use of Hintikka's system is based on the concept of a "model set", partial differential equations and are very common in that is, a set of sentences that may be understood as a mathematical descriptions of natural phenomena. Usu­ partial description of a possible world. In his semantics, ally, important data are locked at a boundary- the earth's systems of such model sets are investigated. Hintikka surface, for example, when studying weather. But mathe­ has applied his semantics to many different fields. His matical solutions become much more complicated if the semantic analysis of the concepts of "knowledge" and boundary is free-that is, if it can vary, such as, for example, "belief" has led to what was later called epistemic logic, the boundary between frozen and unfrozen soil. Caf­ which has been highly influential both within and outside farelli's work has provided pioneering solutions to many of philosophy. For example, it is of fundamental impor­ such problems that have long defied mathematicians. tance for pioneering work in datalogy and game theory. Luis A. Caffarelli was born in Argentina in 1948. He His mathematical interests are in logic and foundations received his Ph.D. in mathematics from the University of

762 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Mathematics People

Buenos Aires in 1972. He has taught at the University of program engaging girls (grades 8 and 9) in mathematics Minnesota, the Courant Institute of Mathematical Sciences, and science activities on the ESU campus. Her Interdisci­ the University of Chicago, and the Institute for Advanced plinary Science and Mathematics provides ESU students Study. He holds honorary doctorates from the Ecole Nor­ with opportunities for early research experiences. Partic­ mal Superieure, Paris; the Universidad Aut6noma de ipants include students majoring in biological sciences, Madrid; and the Universidad de la Plata. piiysical sciences, mathematics, and computer science. Mathematicians who have previously received the Schock Among the institutional awards are the following: Prize are: Solomon Feferman (2003), Richard P. Stanley The Department of Mathematics at the University of Iowa (2003), Elliott H. Lieb (2001), Yuri Manin (1999), Dana S. is the largest single awarder of mathematics doctorates to Scott (1997), Mikio Sato (1997), Andrew Wiles (1995), and minorities in the nation. Articulated less than ten years Elias M. Stein (1993). ago, Iowa's commitment to increasing the numbers of minority graduate students has resulted in a well-crafted -From a Royal Swedish Academy news release recruiting campaign to convince students that the envi­ ronment is a supportive one. A standing committee has responsibilities from student admissions to monitoring Presidential Mentoring Awards their progress. Alliances with other institutions including, Am1ounced but not restricted to, those serving minority students has resulted in substantial support from external grants and On May 16, 2005, President Bush announced the recipients new and continuing collaborations with minority faculty of the 2004 Presidential Award for Excellence in Science, elsewhere. Currently, the department has 21% underrep­ Mathematics, and Engineering Mentoring, a program resented minority graduate students. It is ensuring conti­ supported and administered by the National Science nuity by institutionalizing structures, thereby permitting Foundation (NSF). Each award includes a US$10,000 grant the growth of a community where organizations work for continued mentoring work. together. The awards honor individuals and institutions that have The Society for the Advancement of Chicanos and enhanced the participation of underrepresented groups­ Native Americans in Science (SACNAS) has established an such as women, minorities, and people with disabilities­ array of mentoring activities at scientific meetings, teacher in science, mathematics, and engineering education at all levels. Since its inception in 1996, the PAESMEM program workshops, and through its own annual conference. It has recognized eighty-seven individuals and sixty-seven engages in broad partnerships with other professional institutions. Each year's awardees add to a widening organizations. The society provides and supports oppor­ network of outstanding mentors in the United States, tunities for students to strengthen their presentation skills assuring that tomorrow's scientists and engineers will and self-confidence and to make connections with scien­ better represent the nation's diverse population. This year, tists. Recently established and expanded student chapters nine individuals and five institutions received the award. have brought to 2,862 the number of student members, Among the individual awardees are the following: which should broaden the organization's reach. An ongo­ LENORE BLUM of Carnegie Mellon University helped pioneer ing project to develop biographies of Hispanic/Latino the Expanding Your Horizons program at Mills College in and Native American scientists serves as an inspiration to 1973. The program-designed to introduce young female students from these populations. students to women in science and related careers-has since gone national through the Math/Science Network. Blum's -From an NSF announcement leadership has also been instrumental in transforming the culture of computing at Carnegie Mellon to embrace diversity as critical for the field and future of our nation and by creating a model mentorship organization, Sloan Receives 2005 Women@SCS, for women students in computer science. Information-Based RICHARD LADNER of the University of Washington pio­ neered computer networking for the deaf-blind using Complexity Prize large print and paperless Braille displays. He is dedicated to increasing the number of students with disabilities who The recipient of the 2005 Information-Based Complexity will pursue graduate degrees. Ladner's mentoring efforts Prize is IAN SLOAN, Scientia Professor at the University of extend beyond the university, reaching students at the New South Wales, Sydney, Australia. The prize consists of high-schoollevel. He is also a strong advocate for women US$3,000 and a plaque. The award was presented at in science and engineering and a supporter of NSF's the Foundations of Computational Mathematics (FoCM) ADVANCE program. Conference in Santander, Spain, in June 2005. ELIZABETH YANIK of Emporia State University (Kansas) is This annual prize is given for outstanding contributions considered a passionate teacher who directs and sustains to information-based complexity. a half dozen mentoring programs at the school. Her MASTER IT program is a weeklong residential summer - joseph Traub, Columbia University

AUGUST 2005 NOTICES OF THE AMS 763 Mathematics People

Haggstrom and O'Connell Ferran Sunyer i Balaguer Prizes Awarded Rollo Davidson Prizes Awarded The Trustees of the Rollo Davidson Trust give notice that The Ferran Sunyer i Balaguer Foundation has awarded the they have awarded the Rollo Davidson Prize for 2005 to Ferran Sunyer i Balaguer Prizes for 2005 to ANTONIO OUE HAGGSTROM, Chalmers University of Technology, for his AMBROSETTI and ANDREA MALCHIODI, both of the International work across discrete probability and interacting systems; School for Advanced Studies of Trieste (SISSA/ ISAS), for and to NEIL O'CoNNELL, University College, Cork, for his their monograph Perturbation Methods and Semilinear work in networks, large deviations, and random matrices. Elliptic Problems on Rn and to JosE SEADE of Universidad Further details of the Rollo Davidson Trust may be Nacional Aut6noma de Mexico for his monograph On the found at http: //www .statslab.cam.ac . uk/ Rollo/ Topology of Isolated Singularities in Analytic Spaces. index. html . The Ferran Sunyer i Balaguer Foundation (http: I /www. crm. es/FerranSunyerBal aguer/ffsb. htm) of the In­ - From a Rollo Davidson Trust announcement stitut d'Estudis Catalans (IEC) awards this international prize every year to honor the memory of Ferran Sunyer i Balaguer (1912-67), a self-taught Catalan mathematician National Academy of Sdences who gained international recognition for his research in mathematical analysis despite the serious physical Elections disabilities with which he was born.

The National Academy of Sciences (NAS) has announced -From a Ferran Sunyer i Balaguer Foundation the election of seventy-two new members and eighteen announcement foreign associates. The following mathematical scientists are among the newly elected members: MALcoLM H. CHISHOLM, Ohio State University; lAIN M. JoHNSTONE, Stanford Univer­ sity; SERGIU KlAINERMAN, Princeton University; Ji\Nos KOLLAR, Putnam Prizes Awarded Princeton University; STANLEY OsHER, University of Califor­ The winners of the sixty-fifth William Lowell Putnam nia, Los Angeles; and MARGARET H. WRIGHT, Courant Insti­ Mathematical Competition have been announced. The tute of the Mathematical Sciences. Am SHAMIR of the Putnam Competition is administered by the Mathematical Weizmann Institute of Science, Rehovot, Israel, was elected Association of America and consists of an examination a foreign member. containing mathematical problems that are designed to test both originality and technical competence. Prizes are - From an NAS announcement awarded to both individuals and teams. The five highest ranking individuals, listed in alpha­ betical order, were REm W. BARTON, Massachusetts Institute American Academy Elections of Technology; VLADIMIR V. BARzov, Massachusetts Insti­ tute of Technology; ANA CARAIANI, Princeton University; Nine mathematical scientists have been elected to mem­ DANIEL M. KANE, Massachusetts Institute of Technology; bership in the American Academy of Arts and Sciences for and AARoN C. PIXTON, Princeton University. 2005. They are M. SALAH BAOUENDI, University of California, Institutions with at least three registered participants San Diego; HERBERT EDELSBRUNNER, Duke University; ERic M. obtain a team ranking in the competition based on the rank­ FRIEDLANDER, Northwestern University; JEROME H. FRIEDMAN, ings of three designated individual participants. The five Stanford University; THOMAS G. KURTZ, University of Wis­ top-ranked teams (with team members listed in alpha­ consin, Madison; GREGORY LAWLER, Cornell University; LINDA betical order) were Massachusetts Institute of Technology PREISS RoTHSCHILD, University of California, San Diego; and (Reid W. Barton, Daniel M. Kane, Emanuel I. Stoica), Prince­ BARRY SIMON, California Institute of Technology. ALEXANDER ton University (Ana Caraiani, Suehyun Kwon, Mihai Manea), LuBOTZKY, Hebrew University of Jerusalem, Israel, was Duke University (Nikifor C. Bliznashki, Oaz Nir, Lingren elected a foreign member. Zhang), University of Waterloo (Olena Bormashenko, Ralph The American Academy of Arts and Sciences was Furmaniak, Michael A. Lipnowski), and California Insti­ founded in 1780 to foster the development of knowledge tute of Technology (Po-Ru Loh, Mehmet B. Yenmez, as a means of promoting the public interest and social Rumen I. Zarev). progress. The membership of the academy is elected The top five individuals in the competition received and represents distinction and achievement in a range of cash awards of US$2,500; the next ten received US$1,000. intellectual disciplines-mathematical and physical The first-place team was awarded US$25,000, with each sciences, biological sciences, social arts and sciences, and team member receiving US$1,000. The team awards for humanities and fine arts. second place were US$20,000 and US$800; for third place, US$15,000 and US $600; for fourth place, US$10,000 and -From an AAAS announcement US$400; and for fifth place, US$5,000 and US$200.

764 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Mathematics People

The Elizabeth Lowell Putnam Prize is awarded period­ ically to a woman whose participation in the Putnam Com­ petition is deemed particularly meritorious. In the recent competition, this prize went to ANA CARAIANI of Princeton University. The prize carries a cash award of US$1,000.

-Elaine Kehoe

USA Mathematical Olympiad The thirty-fourth annual USA Mathematical Olympiad was held April19 and 20, 2005. The students participating in the Olympiad were selected on the basis of their perfor­ mances on the American High School and American Invitational Mathematics Examinations, which involved hundreds of students. The twelve highest scorers in the USAMO, listed in alphabetical order, were ROBERT CORDWELL, Albuquerque, New Mexico; ZHou FAN, Parsippany, New Jersey; SHERRY GoNG, Exeter, New Hampshire; Rrsm GuPTA, Palo Alto, California; HYUN Soo KIM, Hackensack, New Jersey; BRIAN rMOU LAWRENCE, Silver Spring, Maryland; ALBERT Nr, Aurora, Illinois; NATEE PITIWAN, North Andover, Massachusetts; ERIC PRICE, Alexandria, Virginia; PENG SHI, Toronto, Ontario, Canada; Yr SuN, San jose, California; and YuFEI ZHAO, North York, Ontario, Canada. The twelve USAMO winners will attend the Mathematical Olympiad Summer Program (MOSP) from June 12 through - "' .J July 2. Then six of the twelve students will be selected as -~ the United States team to compete in the International Mathematical Olympiad (IMO) to be held in Merida, Mexico, july 8- 19, 2005.

- From an American Mathematics Competitions announcement

l J , J

AUGUST 2005 NOTICES OF THE AMS 765 Mathematics Opportunities

mathematics and/ or computer science) the chance to NSF Focused Research Groups spend a semester in Moscow studying mathematics. The The Focused Research Groups (FRG) activity of the Division AMS provides a small number of scholarships to students of Mathematical Sciences (DMS) of the National Science to attend the program. Foundation (NSF) supports small groups of researchers in Math in Moscow provides students with a fifteen-week the mathematical sciences. program similar to the Research Experiences for Under­ The DMS has announced deadline dates for the fiscal graduates programs that are held each summer across the year 2005 competition for FRG grants. The deadline for United States. Math in Moscow draws on the Russian tra­ receipt of the required letters of intent to submit FRG dition of teaching mathematics, which emphasizes creative proposals is August 19, 2005. The deadline date for full approaches to problem solving. The focus is on develop­ proposals is September 16, 2005. The FRG solicitation ing in-depth understanding of carefully selected material may be found on the Web at http: I /www. nsf. gov I rather than broad surveys of large quantities of material. funding/pgm_summ.jsp?pims_id=5671&org=DMS. Discovering mathematics under the guidance of an expe­ rienced teacher is the central principle of Math in Moscow. -From an NSF announcement Most of the program's teachers are internationally recog­ nized research mathematicians, and all of them have considerable teaching experience in English, typically in NSF Mathematical Sdences the United States or Canada. All instruction is in English. With funding from the National Science Foundation, Postdoctoral Research the AMS awards five US$5,000 scholarships each semes­ Fellowships ter to U.S . students to attend the Math in Moscow program. To be eligible for the scholarships, students must submit The Mathematical Sciences Postdoctoral Research Fellow­ applications to both the Math in Moscow program and to ship program of the Division of Mathematical Sciences (DMS) the AMS. An applicant should be an undergraduate math­ of theNational Science Foundation (NSF) awards fellowships ematics or computer science major enrolled at a U.S. each year for research in pure mathematics, applied math­ institution. April 15 is the deadline for scholarship ap­ ematics and operations research, and statistics. The plications for the fall semester immediately following that deadline for this year's applications is October 19, 2005. date; September 30 is the deadline for the spring Applications must b e submitted via FastLane on the semester. World Wide Web. For more information see the website Information and application forms for Math in Moscow http://www.nsf.gov/funding/pgm_summ.jsp?pims_id= are available on the Web at http: I /www. mccme. ru/ 5 301&o rg=DMS. mat hi nmoscow or by writing to: Math in Moscow, P.O. Box 524, Wynnewood, PA 19096; fax +7095-291-65-01; - From an NSF announcement email: mi m@mccme. ru. Information and application forms for the AMS scholarships are available on the Web at http://www . ams.org/outreach/mimoscow.html orby AMS Scholarships writing to: Math in Moscow Program, Membership and Programs Department, American Mathematical Society, for Math in Moscow 201 Charles Street, Providence RI 02904-2294; email: The Independent University of Moscow has created a pro­ [email protected]. gram called Math in Moscow, which offers foreign students (undergraduate or graduate students specializing in - Allyn jackson

766 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Mathematics Opportunities

Call for Submissions for Sunyer i Balaguer Prize Crossword Puzzle Ferran Sunyer i Balaguer (1912-67) was a self-taught Catalan mathematician who, despite a serious physical To--thtvNflvVegt'l!b(page 761) disability, was very active in research in classical analysis, an area in which he acquired international recognition. Answers Each year, in honor of the memory of Ferran Sunyer i Balaguer, the Institut d'Estudis Catalans awards an inter­ national research prize bearing his name. The prize is awarded for a mathematical monograph of an expository nature presenting the latest developments in an active area of research in mathematics in which the author has made important contributions. The monograph should be written in English and should be at least 150 pages long. The prize, amounting to EUR 10,000 (about US$13,000), is provided by the Ferran Sunyer i Balaguer Foundation. The winning monograph will be published in Birkhauser Verlag's series Progress in Mathematics, subject to the usual regulations concerning copyright and author's rights. Submissions should be sent before December 2, 2005, to: Fundaci6 Ferran Sunyer i Balaguer, Carrer del Carme, 47, E-08001 Barcelona, Spain. For further infor­ mation, visit the website http: I /www. crm. es/FSBPri ze/ fsb2005prize.htm.

- From an Institut d'Estudis Catalans announcement Nominations Sought for 2005 IBC Young Researcher Award Nominations are sought for the 2005 Information-Based Complexity Young Researcher Award. This annual award is for significant contributions to information-based com­ plexity by a young researcher. The prize will consist of US$1,000 and a plaque and will be awarded at a suitable location. Any researcher who has not reached his or her thirty­ fifth birthday by September 30 of the year of the award is eligible. The members of the Award Committee (Josef Dick, Uni­ versity of New South Wales; Frances Kuo, University of New South Wales; Christiane Lemieux, University of Calgary; Peter Mathe, Weierstrass Institute for Applied Analysis and Stochastics; Joseph F. Traub, Columbia University; and Henryk Wozniakowski, Columbia University and Uni­ versity of Warsaw) would appreciate nominations. However, a person does not have to be nominated to win the award. The deadline for nominations for the award is Sep­ tember 30, 2005. Nominations should be sent to Joseph Traub. The award can be for work done in a single year or a number of years. The work can be published in any jour­ nal, number of journals, or monographs.

- joseph Traub, Columbia University

AUGUST 2005 NOTICES OF THE AMS 767 Inside the AMS

Dartmouth College; NoAH ]ACOB GIANSIRACUSA, University of AMS Announces Congressional Washington, Seattle; IGOR KoNFISAKHAR, Washington Univer­ Fellow sity in St. Louis; and RoDRIGO TREVINO , University of Texas at Austin. The AMS is pleased to announce that DAVID WEINREICH has Math in Moscow is a program of the Independent Univer­ been chosen as the AMS Congressional Fellow for 2005-06. sity of Moscow that offers foreign students (undergraduate The AMS will sponsor Weimeich's fellowship through or graduate students specializing in mathematics and/or the Congressional Fellowship program administered by the computer science) the opportunity to spend a semester in American Association for the Advancement of Science Moscow studying mathematics. The fifteen-week program (AAAS). The fellowship is designed to provide a unique pub­ is similar to the Research Experiences for Undergraduates lic policy learning experience, to demonstrate the value of programs that are held each summer across the United States. science-government interaction, and to bring a technical Since 2001, each semester the AMS has awarded background and external perspective to the decision­ several scholarships of approximately US$ 5,000 each making process in Congress. for U.S . students to attend the Math in Moscow program. Fellows spend a year working on the staff of a member The scholarships are made possible through a grant from of Congress or a congressional committee, working as a the National Science Foundation. Information about how special legislative assistant in legislative and policy areas to apply may be found in the "Mathematics Opportunities" requiring scientific and technical input. The fellowship section of this issue of the Notices. For more information program includes an orientation on congressional and about Math in Moscow, consult http: I /www. mccme. ru/ executive branch operations and a year-long seminar rna t hi nmo scow and the article "Bringing Eastern European series on issues involving science, technology, and public mathematical traditions to North American students," policy. Notices, November 2003, pages 1250-4. David Weimeich was chosen from a field of outstand­ ing candidates. He has a Ph.D. in mathematics from the -Allyn jackson University of Memphis and has worked as an assistant professor in the mathematical sciences at Gettysburg College and the University of Wisconsin, La Crosse. He is Deaths of AMS Members currently a Science and Technology Policy Fellow at the GEORGE B. DANTZIG, professor emeritus, Stanford, CA, died National Science Foundation. Weimeich will bring exper­ on May 13, 2005. Born on November 8, 1914, he was a tise in the mathematical sciences to this fellowship, as well as a demonstrated interest in public policy issues and the member of the Society for 64 years. role of science in addressing societal problems. ]IMMIE D. GILBERT, retired, University of South Carolina Upstate, Spartanburg, died on April 11, 2005. Born on - AMS Washington Office announcement July 12, 1934, he was a member of the Society for 46 years. H. ]. GoDwiN, professor emeritus, University of London, died on April4, 2005. Born on November 7, 1922, he was Math in Moscow Scholarships a member of the Society for 28 years. Awarded DIMITRIJE UGRIN-SPARAC, professor, University of Zagreb, Croatia, died on December 24, 2004. Born on October 26, The AMS has made awards to five undergraduate students 1933, he was a member of the Society for 13 years. to attend the Math in Moscow program in the fall of 2005. E. M. WRIGHT, retired, from Reading, England, died in The names of the students and their institutions are THOMAS February 2005. Born on February 13, 1906, he was a FRANKLIN CHURCH, Cornell University; HENRY F. DANAHER, member of the Society for 52 years.

768 NoTICEs oF THE AMS VOLUME 52, NUMBER 7 Reference and Book List

The Reference section of the Notices Upcoming Deadlines website http: llwww.ns f .govl is intended to provide the reader with July 15, 2005: Proposals for Leader­ fundingl pgm_summ.jsp?pims_id= frequently sought information in ship Awards of the NSF ADVANCE 5383. an easily accessible manner . New Program. See the website http: I I July 31,2005: Nominations for the information is printed as it becomes www.nsf.govl fundingl pgm_ summ. Ramanujan Prize of the Abdus Salam available and is referenced after the jsp?pims_id=5383. International Centre for Theoretical July 21, 2005: Proposals for NSF first printing. As soon as information Physics (ICTP). See the web site CAREER Program. See http: I lwww. is updated or otherwise changed, it nsf.govl pubsysl odsl getpub. http: llwww.ictp.trieste.itl will be noted in this section. cfm?nsf05 5 79. ~sci_infolawards i Ramanujan l July 22, 2005: Proposals for Insti­ Ramanuj an. html . Contacting the Notices tutional Transformation Awards of July 31,2005: Nominations for the The preferred method for contacting the NSF ADVANCE Program. See the SASTRA Ramanujan Prize. See the the Notices is electronic mail. The editor is the person to whom to send Where to Find It articles and letters for consideration. A brief index to information that appears in this and previous issues of the Articles include feature articles, Notices. memorial articles, communications, AMS Bylaws-November 2003, p. 1283 opinion pieces, and book reviews. The - December 2004, p. 1365 editor is also the person to whom to AMS E-mail Addresses send news of unusual interest about AMS Ethical Guidelines- June/July 2004, p. 675 other people's mathematics research. AMS Officers 2004 and 2005 (Council, Executive Committee Publications Committees, Board of Trustees)- May 2005, p. 564 ' The managing editor is the person to whom to send items for "Mathe­ AMS Officers and Committee Members- October 2004, p. 1082 matics People", "Mathematics Op­ Conference Board of the Mathematical Sciences-September 2004 p. 921 ' portunities", "For Your Information", 2005, p. 660 "Reference and Book List", and "Math­ Information for Notices Authors- June/ July ematics Calendar". Requests for Mathematics Research Institutes Contact Information-August 2005 p. 770 ' permissions, as well as all other National Science Board- January 2005, p. 76 inquiries, go to the managing editor. The electronic-mail addresses are New journals for 2004- June/ July 2005, p. 662 noti ces@math. ou. edu in the case of NRC Board on Mathematical Sciences and Their Applications- March 2005 p. 361 ' the editor and noti ces@ams. org in - April 2005, p. 465 the case of the managing editor. The NRC Mathematical Sciences Education Board fax numbers are 405-325-7484 for NSF Mathematical and Physical Sciences Advisory Committee- February 2005, p. 261 the editor and 401 -331-3842 for the Agencies-October 2004, Postal addresses Program Officers for Federal Funding managing editor. p. 1078 (DoD, DoE); December 2004, p. 1368 (NSF) may be found in the masthead.

AUGUST 2005 N OTICES OF THE AMS 769 Reference and Book list website http://www.math.ufl. nsf.gov/pubsys/ods.getpub. Banff International Research edu/sastra-prize. cfm?nsf05 510. Station July 31, 2005: Nominations and December 2, 2005: Submissions c/o PIMS Central Office applications for the Monroe H. Martin for Ferran Sunyer i Balaguer Prize. University of British Columbia Prize. Contact R. Roy, Director, Insti­ See "Mathematics Opportunities" in 1933 West Mall tute for Physical Science and Tech­ this issue. Vancouver, BC V6T 1Z2, Canada nology, University of Maryland, Col­ January 1, 2006: Submissions for Telephone: 403-762-6100 lege Park, MD 20742-2431. Competition 2006 of the European Fax: 403-763-6990 August 1, 2005: Submissions for Mathematical Society. See the website email: [email protected] Competition 2005 of the European http://www.mat.dtu.dk/people/ Website: http: I /www. pi ms. math. Mathematical Society. See the website V.L.Hansen/rpa/secondartcomp. ca/birs/ http://www.mat.dtu.dk/people/ html. V.L.Hansen/rpa/secondartcomp. January 1, 2006: Applications for Center for Discrete Mathematics html. ICM 2006 Travel Grants. See http: I I and Theoretical Computer Science August 19, 2005: Letters of intent www. i cm2006. org or email: grants@ (DIMACS) for NSF Focused Research Groups. See i cm2006. org. CoRE Building, 4th Floor "Mathematics Opportunities" in this January 27, 2006: Proposals for Rutgers University issue. Partnerships for Adaptation, Imple­ 96 Frelinghuysen Road September 15, 2005: Nominations mentation, and Dissemination Awards Piscataway, NJ 08854-8018 of the NSF ADVANCE Program. See for Sloan Research Fellowships. See Telephone: 732-445-5930 the website http: I /www. nsf. gov I http://www.sloan.org/programs/ Fax: 732-445-5932 funding/pgm_summ.jsp?pims_id= fellowship_brochure.shtml. email: cente radmi n@di macs. 5383. rutgers.edu September 16, 2005: Full propos­ April 15, 2006: Applications for als for NSF Focused Research Groups. Website: http: I I di macs. rutgers. AMS Math in Moscow Scholarships edu See "Mathematics Opportunities" in for fall 2006. See "Mathematics Op­ this issue. portunities" in this issue. September 16, 2005: Proposals for Center for Scientific Computation NSF program on Enhancing the Math­ and Mathematical Modeling Contact Information for (CSCAMM) ematical Sciences Workforce in the Mathematics Institutes University of Maryland Twenty-First Century. See the website 4146 CSIC Building #406 http://www.nsf.gov/pubs/2003/ American Institute of Mathematics Paint Branch Drive nsf03575/nsf03575.htm. 360 Portage Avenue College Park, MD 20742-3289 September 30, 2005: Applications Palo Alto, CA 94306-2244 Telephone: 301-405-0662 for AMS Math in Moscow Scholarships Telephone: 650-845-2071 Fax: 301-314-6674 for spring 2006. See "Mathematics Fax: 650-845-2074 email: i nfo@cscamm. umd. edu Opportunities" in this issue. email: [email protected] Website: http: I jwww. cscamm. umd. September 30, 2005: Nominations Website: http: I /www. ai math. org edu/ for 2005 Information-Based Com­ AIM Research Conference Center plexity Young Researcher Award. See (ARCC) Centre International de Rencontres "Mathematics Opportunities" in this 360 Portage Avenue Mathematiques (CIRM) issue. Palo Alto, CA 94306-2244 163, avenue de Luminy Case 916 October 1, 2005: Nominations for Telephone: 650-845-2071 F-13288 Marseille Cedex 09, France Lucien Godeaux Prize. Contact J. Fax: 650-845-2074 Telephone: +33 04 91 83 30 00 Aghion, c/ o Secretariat of the Royal So­ email: [email protected] Fax: +33 04 91 83 30 OS ciety of Sciences of Liege, Institute of Website: http: I /www. a i math. o rg/ email: Robert. Coque reaux@ Mathematics of the University of Liege, ARCC/ cirm.univ-mrs.fr 12 Grande Traverse, Sart Tilman Bat. Website: http: I /www. ci rm. B 37, B-4000 Liege l, Belgium; email: Stefan Banach International univmrs.fr [email protected]. Mathematical Center October 18, 2005: Proposals for 8 Sniadeckich str., P.O. Box 21 Centre de Recerca Matematica NSF Conferences, Workshops, and 00-950 Warszawa, Poland (CRM) Special Meetings in the Mathematical Telephone: +48-22 522-82-32; Apartat 50 Sciences. See http: I jwww. nsf. gov I 628-01-92 E 08193 Bellaterra, Spain funding/pgm_summ.jsp?pims_id= Fax: +48-22 622-57-50; 629-39-97 Telephone: +34 935 811 081 11701&org=DMS. email: banach@i mpan. gov. p l Fax: +34 935 812 202 October 19, 2005: Applications for Website: http: I /www. i mpan. gov. email: c rm@c rm . e s NSF Postdoctoral Research Fellow­ pl/BC Website: http://crm.es ships (MSPRF). See http: I jwww.

770 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Reference and Book list

Centre for Mathematics and Its The Erwin Schrodinger email: math@math. i as. edu Applications International Institute for Website: http: I jwww. math. i as. Mathematical Sciences Institute Mathematical Physics edu/ Building 27 Boltzmanngasse 9 Australian National University A-1090 Vienna, Austria Institute for Mathematical Sciences Canberra ACT 0200, Australia Telephone+ 43 1 4277 28282 National University of Singapore Telephone: +612 612 52897 Fax: + 43 1 4277 28299 3 Prince George's Park Fax: +612 612 55549 email: secr@esi. ac. at Singapore 118402, Republic of Sin­ email: CMAadmi n@maths. anu. Website: http: I jwww. es i . ac. at/ gapore edu.au Telephone: 65 6874 1897 Website: http : I lwww. maths . anu. Euler International Mathematical Fax: 65 6873 8292 edu. a ui CMAI Institute email: i ms@nus. edu. sg nab. Fontanka, 27 Website: http: I / www. i ms . nus . Centre de Recherches St. Petersburg 197023, Russia edu.sg Mathematiques (CRM) Telephone: 7 812 312-40-58 Universite de Montreal Fax: 7 812 310-5 3-77 Institute for Mathematics and its C.P. 6128, Succ. Centre ville email: admi n@eul er. pdmi. ras. ru Applications (IMA) Montreal, Quebec, Canada H3C 3]7 Website: http: I j www. pdmi . ras. University of Minnesota Telephone: 514-343-7501 ru/EIMI/index.html 400 Lind Hall Fax: 514-343-2254 207 Church Street, SE email: acti vi tes@ The Fields Institute for Research Minneapolis, MN 55455-0436 crm.umontreal . ca in Mathematical Sciences Telephone: 612-624-6066 Website: http: I l www. c rm. 222 College Street, 2nd Floor Fax: 612-626-7370 umontreal .ca Toronto, Ontario, Canada M5T 3]1 email: staff@i ma. umn. edu Telephone: 416-348-9710 Website: http: I / www. i ma. umn. Centro de Investigacion en Fax: 416-348-9714 edu/ Matemciticas (CIMAT) email: geni nfo@fi e l ds. A. P. 402, Guanajuato, Gto. utoronto.ca Institut Henri Poincare C.P. 36000, Mexico Website: http: I / www. fields . 11, rue Pierre et Marie Curie Telephone: 473 73 271-55; utoronto.ca/ 75231 Paris Cedex 05, France 73 508-00 Telephone : 01 44 27 67 89 Fax: 473 73 257-49 Forschungsinstitut fiir Mathematik Fax : 0144 07 09 37 email:cimat@ci mat .mx (FIM) Website: http: I / www. i hp. Website: http : I jwww. ci mat . mx Eidgenbssische Technische j ussieu.fr/ Hochschule Zentrum Chennai Mathematical Institute Ramistrasse 101 Institut Mittag Leffler 92 G. N. Chetty Road 8092 Zurich, Switzerland Auravagen 17 Chennai 600 01 7, India Telephone: +41-1-632-3475 S 182 60 Djursholm, Sweden Telephone: +91 -44-28157854, email: marcel a.kr aemer@ Telephone: +46-8-622 05 60 28157855 fim.math.ethz.ch Fax: +46-8-622 05 89 Fax: +91-44-281 57671 Website: http: I /www. fi m. math. email: wi dman@ml. kva. se email: offi ce@cmi . ac . in ethz.ch/ Website: http: I / www. ml . kva . se/ Website: http: I / www. cmi . ac. in Institut des Hautes Etudes Institute for Pure and Applied Danish National Research Scientifiques (IHES) Mathematics (IP AM) Foundation Network in Le Bois Marie 35, route de Chartres IP AM Building Mathematical Physics F 91440 Bures sur Yvette, France 460 Portola Plaza, Box 957121 and Stochastics (MaPhySto) Telephone: +33 1 60 92 66 00 Los Angeles, CA 90095-71 21 Department of Mathematical Fax: +33 1 60 92 66 69 Telephone: 310-825-4755 Sciences Website: http: I l www. i hes. fr Fax: 310-825-4756 University of Aarhus email: i pam@ucl a. edu Ny Munkegade, DK -8000 Aarhus C, Institute for Advanced Study (lAS) Website: http: I / www. i pam. Denmark School of Mathematics ucl a.edu Telephone: +45 8942 3515 Einstein Drive Fax: +45 8613 1769 Princeton, NJ 08540 Institute of Mathematical Sciences email: maphysto@i mf . au . dk Telephone: 609-734-8100 Chinese University of Hong Kong Website: http : I /www. maphysto. dk Fax: 609-951-4459 Unit 601, 6/ F Academic Building No. 1 Shatin, Hong Kong

AUGUST 2005 NOTICES OF THE AMS 771 Reference and Book List

Telephone: 852 2609-8038 Korea Institute for Advanced D-04103 Leipzig, Germany Fax: 852 2603-7636 Study (KIAS) Telephone: +49 341 9959 50 email: i ms@i ms. cuhk. edu. hk 207-43 Cheongnyangni 2-dong Fax: +49 341 9959 658 Website: http: I /www. i ms. cuhk. Dongdaemun-gu Website: http: I /www. mi s. mpg. de/ edu.hk Seoul130-722, Korea Telephone: +82-2-958-3711 Nankai Institute of Mathematics Instituto Nacional de Matematica Fax: +82-2-958-3770 Nankai University Pura e Aplicada (IMP A) Website: http: I /www. ki as. re. kr Weijin Road 94 Estrada Dona Castorina, 110 Tianjin 300071, China Jardim Botanico Mathematical Biosciences Institute Fax: +86-22-23501532 CEP 22460-320 The Ohio State University Website: http: I /202 .113. 29. 3/ Rio de Janeiro, R], Brazil 231 W. 18th Avenue english/2.htm Telephone: +55 21 2529 5000 Columbus, Ohio 43210 Fax: +55 21 2512 4115 Telephone: 614-292-3648 New Zealand Institute of email: i nfo@i mpa. b r Fax: 614-247-6643 Mathematics and Its Applications Website: http : I /www. i mpa. br email: rebecca@mbi . osu. edu (NZIMA) Website: http: I /www. mbi . osu. edu University of Auckland International Center for Private Bag 92019 Theoretical Physics (ICTP) Mathematical Sciences Research Auckland, New Zealand Strada Costiera 11 Institute (MSRI) Telephone: +64-9-373 7599 34014 Trieste, Italy 17 Gauss Way Fax: +64-9-373 7457 Telephone: +39 040 2240111 Berkeley, CA 94720-5070 email: nzi rna -admi n@ Fax: +39 040 224163 Telephone: 510-642-0143 nzima.auckland.ac.nz email: sci_i nfo@i ctp. it Fax: 510-642-8609 Website: http: I /www. nzi rna. Website: http : I /www. i ctp. it email:msri-inquiries@msri .org auckland.ac.nz Website: http: I /www. ms ri . o rg/ International Centre for Pacific Institute for the Mathematical Sciences (ICMS) Mathematics Institute Mathematical Sciences (PIMS) 14 India Street University of Warwick University of British Columbia Edinburgh EH3 6EZ, UK Coventry CV4 7AL, UK 1933 West Mall, Room 200 Telephone: +44 (0)131 220 1777 Telephone: +44 (0)24 7652 4661 Vancouver, BC, V6T 1Z2, Canada Fax: +44 (0)131 220 1053 Fax: +44 (0)24 7652 4182 Telephone: 604-822-3922 email: [email protected] Website: http : I /www. maths. Fax: 604-822-0883 Website: http: I /www. rna. hwac. uk/ warwick.ac.uk/ email: pi ms@pi ms. math. ca i ems Website: http: I /www. pi ms. Mathematics Research Institute math.ca Isaac Newton Institute for (Oberwolfach) Mathematical Sciences Schwarzwaldstr. 9-11 (Lorenzenhof) Alfred Renyi Institute of 20 Clarkson Road D 77709 Oberwolfach Walke, Mathematics Cambridge CB3 OEH, UK Germany Hungarian Academy of Sciences Telephone: +44 1223 335999 Telephone: +49 7834 979 0 POE 127 Fax: +44 1223 330508 Fax: +49 7834 979 55 H-1364 Budapest, Hungary email: i nfo@newton. cam. ac. uk email: admi n@mfo. de Telephone: +361-483-8302 World Wide Web: http: I /www. Website: www. mfo. de Fax: +361-483-8333 newton.cam.ac.uk/ email: math@renyi . hu Max Planck Institut Website: http: I /www. renyi . hu Istituto Nazionale di Alta fur Mathematik Matematica "F. Severi" (INDAM) P.O. Box 7280 Research Institute for Citta Universitaria D-53072 Bonn, Germany Mathematical Sciences (RIMS) P. le Aldo Moro 5 Telephone: +49 228 402 0 Kyoto University 00185 Rome, Italy Fax: +49 228 402277 Kyoto, 606 8502, Japan Telephone: 39 06490320 email: admin@mp i m-bonn.mpg.de Fax: +81 75 753 7272 Fax: 39 064462293 Website: http: I /www. mpi m-bonn. Website: http: I /www. ku rims. email: i ndam@a l tamatemati ca. it mpg.de kyotou. ac. j p/ Website: http: I /www. altamatematica.it Max Planck Institut fiir Statistical and Applied Mathematik in den Mathematical Sciences Institute Naturwissenschaften (SAMSI) Inselstrasse 22 19 T. W. Alexander Drive

772 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Reference and Book List

P.O. Box 14006 Book List 1-568-58316-8. (Reviewed in this is­ Research Triangle Park, The Book List highlights books that sue.) NC 27709-4006 have mathematical themes and are The Colours ofInfinity: The Beauty Telephone: 919-685-9350 aimed at a broad audience potentially and Power of Fractals, by Michael Fax: 919-685-9360 including mathematicians, students, Barnsley, Nigel Lesmoir-Gordon, email: i nfo@samsi . info and the general public. When a book Benoit B. Mandelbrot, Ian Stewart, Website: http: I lwww. samsi . i nfol has been reviewed in the Notices, a Gary Flake, Robert Prechter, and reference is given to the review. Gen­ Arthur C. Clarke. Clear Press, March Steklov Institute of Mathematics erally the list will contain only books 2004. ISBN 1-904-55505-5. Russian Academy of Sciences published within the last two years, Complexities: Women in Mathe­ Gubkina str. 8 though exceptions may be made in matics, edited by Bettye Anne Case 119991, Moscow, Russia cases where current events (e.g., the and Anne M. Leggett. Princeton Uni­ Telephone: +7 095 135-22-91 death of a prominent mathematician, versity Press, January 2005. ISBN Fax: +7 095 135-05-55 coverage of a certain piece of mathe­ 0-691 -11462-5. email: stekl ov@mi . ras. ru Constantin Caratheodory: Mathe­ matics in the news) warrant drawing Website: http: I lwww. mi . ras. rul readers' attention to older books. Sug­ matics and Politics in Turbulent Times, index_e.html by M. Georgiadou. Springer, Septem­ gestions for books to include on the list ber 2004. ISBN 3-540-44258-8. may be sent to noti ces-bookl i st@ Steklov Institute of Mathematics The Constants of Nature: From ams .org. 27, Fontanka Alpha to Omega-The Numbers That 1'Added to "Book List" since the St. Petersburg 191023, Russia Encode the Deepest Secrets of the Uni­ list's last appearance. Telephone: 7 812 312-4 0-58 verse, by John D. Barrow. Jonathan Fax: 7 812 310-53-77 Cape, September 2002. Pantheon 13: The Story of the World's Most email: admi n@pdmi . ras. ru Books, January 2003. ISBN 0-375- Popular Superstition, by Nathaniel Website: http: I lwww. pdmi . ras. ru 42221-8. (Reviewed November 2004.) Lachenmeyer. Thunder's Mouth Press, Converging Realities: Toward a Tata Institute of Fundamental October 2004. ISBN 1-568-58306-0. Common Philosophy of Physics and Research 1089 and All That. A journey into Mathematics, by Roland Omnes. School of Mathematics Mathematics, by David Acheson. Ox­ Princeton University Press, November Dr. Homi Bhabha Road ford University Press, July 2002. ISBN 2004. ISBN 0-691 -11530-3. Mumbai 400 005, India 0-19-8 5162 3-l. (Reviewed February The Curious Incident of the Dog in Telephone: +91 22 22804545 2005.) the Nighttime, by Mark Haddon. Vin­ Fax: +91 22 22804610; Action This Day, edited by Michael tage, May 2004. ISBN 1-400-03271-7. 91 22 22804611 Smith and Ralph Erskine. Random Dark Hero of the Information Age: email: regi stra@ti fr. res. in House of Canada, February 2003. In Search of Norbert Wiener, by Flo Website: http: I lwww. math. ti fr. ISBN 0-593-04910-l. Conway and Jim Siegelman. Basic res . in Alfred Tarski: Life and Logic, by Books, December 2004. ISBN 0-738- Anita Burdman Feferman and 20368-8. T. N. Thiele Centre for Applied Solomon Feferman. Cambridge Uni­ The Essential Turing, edited by Mathematics in Natural Science versity Press, October 2004. ISBN B. Jack Copeland. Oxford University University of Aarhus 0-521-80240-7. Press, September 2004. ISBN 0-198- Department of Mathematical Beyond Coincidence, by Martin 25080-0. Sciences Plimmer and Brian King. Icon Books, From Eudoxus to Einstein: A His­ Ny Munkegade, Building 530 March 2004. ISBN 1-840-4 6534-4. tory of Mathematical Astronomy, by 8000 Aarhus C, Denmark Beyond Reason: Eight Great Prob­ C. M. Linton. Cambridge University Telephone: +45 8942 3515 lems That Reveal the Limits of Science, Press, August 2004. ISBN 0-521- Fax: +45 8613 1769 by A. K. Dewdney. Wiley, April 2004. 82750-7. email: thi e l e@i mf. au. dk ISBN 0-471-01398-6. Geometry and Meaning, by Do­ Website: http: I lww. thi e l e. au. dk A Brief History of Infinity, by Paolo minic Widdows. Center for the Study Zellini. Penguin Books (paperback), of Language and Information, No­ Weierstrass Institute for Applied March 2005. ISBN 0-141-00762-l. vember 2004. ISBN 1-575-86448-7. Analysis and Stochastics The Calculus Gallery: Masterpieces The Golden Ratio: The Story of Phi, Mohrenstrasse 39 from Newton to Lebesgue, by William the World's Most Astonishing Number, 10117 Berlin, Germany Dunham. Princeton University Press, by Mario Livio. Broadway Books, Telephone: +49-30-203 720 December 2004. ISBN 0-691-09565-5. October 2002. ISBN 0-767-90815-5. Fax: +49-30-2044975 Chance: A Guide to Gambling, Love, (Reviewed March 2005.) email: contact@wi as-berlin. de the Stock Market and just About Every­ Graphic Discovery: A Trout in the Website: http: I lwww . thing Else, by Amir D. Aczel. Four Walls Milk and Other Visual Adventures, by wias-berlin.del Eight Windows, October 2004. ISBN Howard Wainer. Princeton University

AUGUST 2005 NOTICES OF THE AMS 773 Reference and Book list

Press, October 2004. ISBN 0-691- ,,. The Math Instinct: Why You're a Mathematical Association of Amer­ 10301-1. Mathematical Genius (Along with Lob­ ica, 2004. ISBN 0-88385-549-6. A Handbook of Mathematical Dis­ sters, Birds, Cats, and Dogs), by Keith '' The Newtonian Moment: Isaac course, by Charles Wells. Infinity Devlin. Thunder's Mouth Press, March Newton and the Making of Modern Publishing Company, 2003 . ISBN 2005. ISBN 1-560-25672-9. Culture, by Mordechai Feingold. New 0-7 414-168 5-9. (Reviewed September Math Magic: How to Master Every­ York Library and Oxford University 2004.) day Math Problems, by Scott Flansburg. Press, December 2004. ISBN 0-195- The Heart of Mathematics: An Perennial Currents, revised edition, 17735-5. Invitation to Effective Thinking, by August 2004. ISBN 0-060-72635-0. Number Theory from an Analytic Edward B. Burger and Michael Math through the Ages: A Gentle Point of View, by Badih Ghusayni. Starbird. Key College Publishing History for Teachers and Others, by Komati, December 2003. ISBN 9953- (Springer-Verlag), April 2000. ISBN WilliamP. Berlinghoff and Fernando Q. 0-0282-7. 0-555953-407-9. (Reviewed February Gouvea. Oxton House, 2002. ISBN Numbers, The Language ofScience, 1-881929-21-3. (Reviewed October 2005 .) by Tobias Dantzig. Pi Press, fifth edi­ 2004.) Incompleteness: The Proof and tion, March2005. ISBN 0-131-85627-8. The Mathematical Century: The 30 Paradox of Kurt Godel, by Rebecca The Oxford Murders, by Guillermo Goldstein. W. W. Norton & Company, Greatest Problems of the Last 100 Years, by Piergiorgio Odifreddi and Martinez. Abacus, January 2005. ISBN February 2005. ISBN 0-393-05169-2. 0-349-11721-7. The Infinite Book: Where Things Arturo Sangalli. Princeton University Press, May 2004. ISBN 0-691-09294-X. R. L. Moore: Mathematician and Happen That Don't, by John D. Barrow. Teacher, by John Parker. Mathemati­ Jonathan Cape, February 2005. ISBN 0- Mathematical Illustrations: A Man­ ual of Geometry and PostScript, by Bill cal Association of America, 2004. ISBN 224-06917-9. 0-88385-5 50-X. john Pell (1611-1685) and His Casselman. Cambridge University Press, December 2004. ISBN 0-521- The Reader of Gentlemen's Mail: Correspondence with Sir Charles Herbert 0 . Yardley and the Birth of Cavendish: The Mental World of an 54788-1. American Codebreaking, by David Early Modern Mathematician, by Noel A Mathematician at the Ballpark: Kahn. Yale University Press, March Malcolm and Jacqueline Stedall. Ox­ Odds and Probabilities for Baseball 2004. ISBN 0-300-09846-4. ford University Press, second edition, Fans, by Ken Ross. Pi Press, July 2004. ISBN 0-131-4 7990-3. The Road to Reality: A Complete January 2005. ISBN 0-198-56484-8. Mathematicians under the Nazis, by Guide to the Laws of the Universe, by Karl Pearson: The Scientific Life in Sanford L. Segal. Princeton University a Statistical Age, by Theodore M. Roger Penrose. Knopf, February 2005. Press, July 2003. ISBN 0-691-00451-X. Porter. Princeton University Press, ISBN 0-679-45443-8. (Reviewed April2005.) February 2004. ISBN 0-691-11445-5. Sneaking a Look at God's Cards: Mathematics: A Very Short Intro­ Kepler's Conjecture: How Some of Unraveling the Mysteries of Quantum duction, by Timothy Gowers. Oxford the Greatest Minds in History Helped Mechanics, by Giancarlo Ghirardi, University Press, October 2002. ISBN translated by Gerald Malsbary. Prince­ Solve One of the Oldest Math Prob­ 0-192-85361-9. (Reviewed February lems in the World, by George G. Szpiro. ton University Press, revised edition, 2005 .) January 2005. ISBN 0-691-12139-7. Wiley, January 2003. ISBN 0-471- Mathematics in Nature: Modeling 08601-0. (Reviewed January 2005.) '' Space/and, by Rudy Rucker. Tor Patterns in the Natural World, by John Books, June 2002. ISBN 0-765-30366- The Knot Book: An Elementary In­ Adam. Princeton University Press, No­ troduction to the Mathematical Theory 3. (Reviewed in this issue.) vember 2003. ISBN 0-691-11429-3. Stalking the Riemann Hypothesis: of Knots, Colin C. Adams. AMS, Sep­ (Reviewed June/July 2005.) tember 2004. ISBN 0-8218-3678-1. The Quest to Find the Hidden Law of The (Mis)Behavior of Markets: A Knots and Links, by Peter R. Prime Numbers, by Dan Rockmore. Fractal View of Risk, Ruin and Reward, Cromwell. Cambridge University Press, Pantheon, April 2005. ISBN 0-375- by Benoit Mandelbrot and Richard October 2004. ISBN 0-691-10301-1. 42136-X. Hudson. Basic Books, August 2004. Strange Curves, Counting Rabbits, The Liar Paradox and the Towers of ISBN 0-465-043 5 5-0. Hanoi: The Ten Greatest Math Puzzles and Other Mathematical Explorations, of A ll Time, by Marcel Danesi. Wiley, More Damned Lies and Statistics: by Keith Ball. Princeton University August 2004. ISBN 0-471-64816-7. How Numbers Confuse Public Issues, Press, November 2003. ISBN 0-691- Luck, Logic, and White Lies: The by Joel Best. University of California 11321-1. (Reviewed in December 2004.) Mathematics of Games, by Jorg Bew­ Press, August 2004. ISBN 0-520- A Tour Through Mathematical ersdorff. Translated by David Kramer. 23830-3. Logic, by Robert S. Wolf. Mathemati­ A K Peters, November 2004. ISBN 1- More Mathematical Astronomy cal Association of America, January 568-81210-8. Morsels, by Jean Meeus. Willmann-Bell 2005. ISBN 0-88385-036-2. Math and the Mona Lisa: The Art Inc., 2002. ISBN 0-943396-743. Towards a Philosophy ofReal Math­ and Science of Leonardo da Vinci, by Musings of the Masters: An An­ ematics, by David Corfield. Oxford Bulent Atalay. Smithsonian Books, thology of Miscellaneous Reflections, University Press, April 2003. ISBN April 2004. ISBN 1-588-34171-2. edited by Raymond G. Ayoub. 0-521-81722-6.

774 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Reference and Book List

The Transformation of Mathemat­ AMS SHORT COURSE ics in the Early Mediterranean World: From Problems to Equations, by Reviel Modeling and Simulation of Biological Networks Netz. Cambridge University Press, June 2004. ISBN 0-521-82996-8. january 1 0-11, 2006 The Universal Book ofMathematics: San Antonio, Texas From Abracadabra to Zeno's Para­ doxes, by David Darling. Wiley, July 2004. ISBN 0-471-27047-4. The Works of Archimedes: Trans­ Organizers lation and Commentary. Volume I: Reinhard Laubenbacher The Two Books on the Sphere and the Virginia Bioinformatics Institute and Mathematics Department Cylinder. Translated by Reviel Netz. Virginia Polytechnic Institute and State University Cambridge University Press, April 2004. ISBN 0-521-66160-9. (Reviewed Speakers May 2005.) Elizabeth Allman, University of Southern Maine A World without Time: The Forgot­ Suzanne Len hart, University of Tennessee ten Legacy of Godel and Einstein, by Pedro Mendes, Virginia Bioinformatics Institute Palle Yourgrau. Basic Books, January Madhav Marathe, Virginia Bioinformatics Institute 2005. ISBN 0-465-09293-4. You Can Do the Math: Overcome Liar Pachter, University of California Berkeley Your Math Phobia and Make Better Brandilyn Stigler, Mathematical Biosciences Institute Financial Decisions, by Ron Lipsman. Praeger Publishers, November 2004. One of the major challenges for biology in the 21 " century is an ISBN 0-275-98341-2. understand ing of the organizational principles of biological systems. Mathematics, statistics, computer science, and engineering w ill play key roles in meeting this c hall enge. Recent years have seen tremendous progress in our understanding of genetic information in organisms, and its fundamental role in cell metabolism. Mathematical and statistica l tools have been instrumental in this progress. Beyond an understanding of th e processes at th ese sca les, integrating them with the o rga nism and ecosystem sca les presents many mathematical cha llenges. Thus, biology wi ll be one of the major drivers of th e development of new mathematics. The aim of this Short Course is to present the state of the mathematical challenges at these different scales, from ..,.,"r r.rto genomic information all the way to the ecosystem leve l. emphasis will be placed on "nontrad itiona l" mathematica l a Two panel discussions w ill exp lore the rol e mathematics an mathematicians ca n play in life sciences and biomedical research.

Registration for this course will be available sta Advance fees are: member of the AMS US$87 nonmember US$115 student, unemployed, emeritus US$38 On-site fees are: member of the AMS US$118 nonmember US$148 student, unemployed, emeritus US$57

AUGUST 2005 NOTICES OF THE AMS 775 From the AMS Secretary

by nearly every mem­ ReportoftlleExeoutive ber. Our member publi­ Director, State of AMS, 2005 cations, the Notices and the Bulletin, are circu­ When I report on the AMS each spring, I try to examine the lated to more mathe­ Society from one particular perspective: publishing, pub­ maticians than any lic awareness, Mathematical Reviews, etc. This year, I want other mathematics jour­ to look at the Society from several perspectives at once to nal in the world. They understand how various groups of members see the AMS, communicate mathe­ each in a slightly different way. In many respects, seeing matical news, profes­ the Society through different eyes is the very best way to sional information, see it. high-level exposition, as well as a record of the Overview Society's governance. It is easy to forget that the AMS is a complicated mosaic. They tie together all In 2004 there were 29,538 members of the AMS . But only parts of the Society and 10,300 of these were more broadly the math­ "regular" members ematical community it­ AMS Membership (we used to call them self. Almost all mem­ "ordinary" members, bers view the Society as Affiliate but renamed them a publisher. The AMS 10% this year). More than publishes a dozen of its 3,200 were reciproc­ own journals and distributes others. It has more than ity members; nearly 3,000 books in print, including research monographs, pro­ 3,100 were affiliate ceedings, history, and textbooks. And the AMS maintains Nominee ("Category-S" from the Mathematical Reviews Database, along with sophisti­ 35% developing coun­ cated software for accessing that database online. In 2004 tries); over 10,300 we added more than 85,000 new items to that database, were nominee or stu­ compiled and selected by more than seventy staff in our Emeritus dent members; and Ann Arbor office. 9% 2,600 were emeritus As part of its publishing program, the Society maintains or life. its own warehouse and printing plant. It has a large staff Our members to develop electronic products (and to maintain them!). It come from all over the world; 31% are from outside the has editors and graphics specialists and bibliographic U.S. They hold many different types of jobs (only 55% are experts and T[X specialists- all these to produce its many assistant, associate, or full professors). And the percent­ publications, both print and electronic. age of members who are women now exceeds 17%. Of our Producing the products is only half of publishing, how­ regular members, about 21 % are under forty, 49% are in ever. We have to market and promote our products, and the range of forty to sixty, and 30% are older than sixty. we have greatly expanded our efforts at every level in (In 1987 the corresponding percentages were 32%, 58%, and recent years. For Math Reviews, marketing MathSciNet to 10%-we are getting older!) consortia has been remarkably successful: In ten years, the People often ask questions about an "AMS member": number of institutions with access to Math Reviews has What does a member want? How does a member feel about more than doubled. We have greatly extended our mar­ some program? Why does a member react in some way? keting for books as well, and we reach more markets in There are no simple answers to these questions, because more parts of the world than ever before. In recent years there is no such thing as an "AMS member". about half of our publishing revenue has come from North America; the rest comes from Europe (20%), Asia (20%), and Common Views the rest of the world. How does an AMS member view the Society? While there Our publishing program makes a profit. We use that is no single answer, there are some views that are shared profit to fund our other programs-everything from

776 NOTICES OF THE AMS VOLUME 52, NUMBER 7 From the AMS Secretary

In addition to our regular research conferences, the AMS Operating Revenue Society holds larger and longer "institutes" from time to time. One that has become a tradition, in algebraic geom­ etry, will take place during the summer of 2005. Mise Regular members of the Society also may see the Soci­ Invest inc 1 O% ety through its Washington 5% I office, which is headed by Sam Rankin. Over the past Meetings ten years the AMS presence 4%----- in Washington has become Dues __.-.-- Publications more visible and more effec­ 6%~ --75% tive. The annual meetings of the Committee on Science Policy and the Committee on AMS president James Education have become fo­ Arthur and Senator rums in which policymakers Vernon Ehlers (R-MI). and mathematicians can support for mathematicians in the developing world to pub­ learn from each other. Many lic awareness. In that sense, even when members are not department chairs now attend one or the other of these using our publications, they are benefiting from them. meetings. We administer various programs through our Washington office, including the Chairs Workshop at the Regular Members Joint Meetings and the Mass Media Fellows Program (in How do regular members see the Society? Of course, for which we support a graduate student who works at a many members, meetings play a big role in their mathe­ media outlet for a summer). During the coming year we matical life. The 2005 Joint Meetings in Atlanta were the will also support a congressional fellow: a mathematician third largest in history (counting mathematicians in at- who will work for a year, most likely in a congressional office, learning about policy and helping others to learn about scientific research. Most importantly, our Wash­ ington presence allows mathematicians to be part of the policy discussions that take place regularly in Washington, not at the highest levels of government, but among the representatives of scientific societies. Public awareness is an area that is often important to regular members. In recent years the AMS has been much more active in public awareness. Our public awareness website (http: I / www. ams. org/ pub l i c-awareness) has tendance). The number of special sessions was unusually become a valuable resource for many, and the Math in the large. The general level of activity at the Joint Meetings continues to increase year by year. Our eight sectional meetings attract many attendees (almost 2,500), including many young mathematicians and graduate students. Few members attend meetings every year, but for nearly all, Media feature has much first-rate exposition. The one­ meetings have played a role in their professional lives. page fliers, Mathematical Moments, are widely distributed Summer research conferences, which are funded by and appear on many department walls, as well as in high the NSF and carried out jointly with the Society for schools. The game Who Wants to Be a Mathematician has Industrial and Applied engaged groups of high school students and their teach­ Mathematics and the In­ ers throughout the country. Increasingly, members seem stitute for Mathematical to comment about all these things and recognize the value Statistics, have also been ~TSUMMER CONFERENCES of public awareness in their own mathematical lives. That important for many mem­ ~ ~~~:EARCH is one of the main goals of the effort. bers. During the past five @AMS ~ s.ia.m. None of these things are exclusive to regular members, years there have been 28 of course, but they may be more important to regular conferences, each one or two weeks long, on everything members, and they seem to be the ways in which regular from string theory to fast algorithms to Radon transforms. members most often interact with the Society. These have attracted mathematicians from every part of mathematics, and many have focused on young mathe­ Reciprocity Members maticians at the beginning of their careers. There will Reciprocity members also value all the things mentioned be 6 more conferences in 2005 (but beyond this year, the above, but they are likely to interact with the Society's program of research conferences may end b ecause of a programs in slightly different ways as well. These are lack of funding).

AUGUST 2005 NOTICES OF THE AMS 777 From the AMS Secretary members who belong first to another society-one outside Of course, our publishing program is still the way in the U.S.-and they most likely have an international focus which members, international or not, interact with the So­ that is influenced by certain of our programs. ciety-and not merely by reading our publications. Dur­ Each year the ing the past five years more than half the papers published AMS holds a joint in­ in our journals had no U.S. author. That is a remarkable ternational meeting fact that those who debate the future of journals often ••••••• 'II.,•• Ct •• welcome with one or more ignore. Our books too come from authors throughout the e e • c•e mathematics soci­ world, and beginning next year we will have an acquisitions •e,"'· ~ ··--• ··• • • •. e• . eties outside the U.S. editor specializing in acquisitions in Europe. .•... • •• •<~ . In the past five years .':t·.··· we have held meet­ Affiliate Members • • blenvenldos ings in Denmark, Affiliate members (the name used to be "Category-S") are INTERNATIONAL benvlnguts CONGRESS OF ongl etorri Hong Kong, France, mathematicians in certain developing countries who are MATHEMAtiCIANS benvldos Italy, Spain, and eligible to join the Society at a special rate: US$16 per year. :-~MFR@Q~?QQ6 ~ India. We will have a They can subscribe to either the Notices or the Bulletin and joint meeting in Ger­ otherwise receive full benefits. Most of these members see many during the summer of 2005, and there will be a the AMS through the Notices (the choice of almost all), and meeting in Taiwan in December. In addition to these, the indeed the Notices is often their primary contact with the AMS holds joint meetings with the Mexican Mathematics broader mathematical world. Society every three years-events that have become a reg­ For many years the Society has supported the ular part of mathematical life for the two countries. International Mathematical Union by soliciting donations For many years the AMS has supported the International from members. In the past five years we have collected Mathematical Union and the nearly US$110,000. That money helps to support young quadrennial international mathematicians from the developing world to attend the congress in various ways. We International Congress, and it represents an important have administered a system commitment from thousands of AMS members. of travel grants, funded by the The AMS Book and Journal Donation Program is sup­ National Science Foundation ported by donations from the Alan and Katherine Stroock (NSF), for young American Fund. It matches donors of certain kinds of journals and mathematicians and invited books with recipient speakers to attend the con­ institutions or libraries Eligible Countries gress. We have indicated our in developing coun­ Albania, Algeria, Angola, Argentina, Armenia, Azerbaijan, Bangladesh, Be­ willingness to continue this practice for the next congress tries and then pays for larus, Bolivia, Bosnia-Hercegovina, (provided the NSF makes an award). The Society has recently shipping. In recent Botswana, Brazil, Bulgaria, Burkina Faso, become an affiliate member of another international years the Society has Burundi, Cameroon, Central African Re­ organization, the International Council for Industrial and brokered donations to public, Chad, Chile, Colombia, Comoros Applied Mathematics (ICIAM), in order to support interna­ Argentina, Armenia, Islands, Costa Rica, Croatia, Cuba, Czech Rep,, Djibouti, Dominica, Dominican tional mathematics of every kind. Bulgaria, China, Rep,, Ecuador, Egypt, El Salvador, Esto­ The international nature of many AMS programs can be Colombia, Cuba, the nia, Ethiopia, Gabon, Gambia, Ghana, seen by sampling just two. Our Math in Moscow program Czech Republic, Egypt, Greece, Guatemala, Guinea-Bissau, is funded by the NSF and each semester supports about Georgia, Hungary, Guyana, Honduras, Hungary, India, In­ donesia, Iran, Iraq, Ivory Coast, Jamaica, five undergraduates who spend the time at the Indepen­ India, Iran, Morocco, Jordan, Kazakhstan, Kenya, Korea, Kyr­ dent University of Moscow working in an intense mathe­ Romania, Russia, gyzstan, Laos, Latvia, Lebanon, Lesotho, matical environment (in English). This academic year we South Africa, Turkey, Liberia, Libya, Lithuania, Madagascar, were able to support thirteen students (four of them Uzbekistan, and Viet­ Malawi, Malaysia, Mali, Malta, Mauritania, female), who continue to rave about the experience. The Mauritius, Mexico, Moldova, Mongolia, nam. This is a modest Morocco, Mozambique, Namibia, Nepal, Ky Fan China program fosters exchanges between but extremely effective Nicaragua, Niger, Nigeria, Oman, Pak­ mathematics departments in China and the U.S. The ex- program. istan, Panama, Papua New Guinea, changes go both ways, bringing Chinese math­ The Society has Paraguay, Rep. of Benin, People's Rep. of ematicians (especially young ones) for visits recently considered China, Rep. of Congo, Peru, Philippines, Poland, Portugal, Rep. of Cape Verde, to the U.S. and funding trips for various programs for Georgia, Rep. of Macedonia, Rep. of American mathematicians making journals more Yemen, Romania, Russia, Rwanda, Sao to visit Chinese departments. available to mathe­ Tome & Principe, Saudi Arabia, Senegal, In 2004 there were four such maticians in the Serbia, Sierra Leone, Slovak Rep., Slove­ exchanges; for the coming year developing world. One nia, Rep. of So. Africa, Somalia, Sri­ Lanka, Sudan, Surinam, Swaziland, Syria, the number of applications of the most effective Tajikistan, Tanzania, Thailand, Trinidad has increased dramatically. of these programs is & Tobago, Tunisia, Turkey, Turk­ This is funded through a gift carried out through menistan, Uganda, Ukraine, Uruguay, Professor Ky Fan made to the the Abdus Salam In­ Uzbekistan, Venezuela, Vietnam, Zaire, Society in 1999. ternational Centre for Zambia, Zimbabwe

778 NOTICES OF THE AMS VOLUME 52, NUMBER 7 From the AMS Secretary

Theoretical Physics in Italy, making it possible for the past several years. This past year there were 50 individual mathematicians in developing countries to employers using MathJobs, with 3,881 applicants sub­ request specific journal articles and to receive them by mitting materials. This produces some impressive num­ email (which is the only feasible method of receipt in bers: 21,058 documents uploaded by applicants; 5,186 locales with minimal bandwidth). The AMS now participates letters ofreference uploaded by writers (and another 7,538 in this program along with several other societies. scanned in by departments); and a total of more than Perhaps the most important way for the AMS to reach 22GB of data now in the system. out to mathematicians in the developing world is through For many nominee members the annual survey from the Mathematical Reviews. Society is crucial. It The National Data provides information about Access program was the state of the profession, Mathematical established more than especially for young math­ Reviews five years ago. For each ematicians. And reading developing country the through reports from several years provides an accurate program establishes a fee that depends on various eco­ view of the profession that nominees very much need. nomic factors and makes it possible for institutions to gain Many of the programs carried out by the Society affect access to Mathematical Reviews in its various formats. students, often before they ever become nominee mem­ The National DAF is now in place for nearly one hundred bers. Our Young Scholars Program continues to provide institutions in some twenty-five countries around the grants to summer programs for talented high school world. Publicizing this program and establishing consor­ students. The goal of a US$2 million endowment is about tia in the developing world has taken time, but the pro­ 75 percent completed. The Arnold Ross Lectures provide gram is steadily growing. an opportunity for high school students to interact with a research mathematician each year, normally at a science Nominee Members museum. The Trjitzinsky scholarships (6-8 each year) There are more nominee members than regular, and in are awarded to undergraduate mathematics majors. And some ways that is a hopeful sign. Almost all are graduate most recently, the Society has begun an effort to help students, and they are potentially lifelong members of departments collect profiles of their mathematics majors the AMS. We should care how these future members and post them on the Web. So far twenty-five departments perceive the Society. are participating, supported by small awards from a Sloan We do. Foundation grant. The AMS will link together all sites Many nominee in a searchable database. These and many more programs members use the and resources are found at the employment website, Employment Center, http://www.ams.org/employment. which has changed dramatically in re­ Early Career Profiles: cent years. The old Recent bachelor's-level graduates in the mathematical sciences scheduling system is used by fewer than half those using the The ReaiAMS system. For many, the Employment Center is merely a News, exposition, journals, books, MathSciNet, advocacy, collection of services making it easier for applicants to awareness, exchanges, jobs, surveys, scholarships, prizes­ find employers and for institutions to carry out the which is most important? Of course, none is. Each is just difficult process of one perspective of a complicated organization; each interviewing. At the emphasizes some parts of the Society and values certain January 2005 Joint of its parts; each presents the Society in a special way to Meetings there were special people. Which is the real AMS? They all are, and 539 applicants and that is what makes the AMS a healthy organization­ 113 employers. the fact that it can be many things to many people. In addition to the Employment Center, -John Ewing the Society now runs Executive Director another service in cooperation with the mathematics de- Employment Center resource partment at Duke tables University. Math]obs is a computer service that allows applicants, departments, and referees to interact through the Web by exchanging documents and making them available to authorized people. The service has grown slowly but steadily over

AUGUST 2005 NoTICES OF THE AMS 779 From the AMS Secretary

an income statement in a for-profit organization), and in­ Report of the Treasurer (2004) formation regarding the Society's invested funds. The Society segregates its net assets and the activities I. Introduction that increase or decrease net assets into three types. Un­ One of the most important duties of the treasurer is to lead restricted net assets are those that have no requirements the Board of Trustees in the oversight of financial activi­ as to their use placed on them by donors outside the ties of the Society. This is done through close contact with Society. A substantial majority of the Society's net assets the executive staff of the Society, review of internally gen­ and activities are in this category. Temporarily restricted erated financial reports, review of audited financial state­ net assets are those with donor-imposed restrictions or ments, and direct contact with the Society's independent conditions that will lapse upon the passage of time or the auditors. Through these and other means, the Trustees gain accomplishment of a specified purpose. Examples of an understanding of the finances of the Society and the the Society's temporarily restricted net assets and related important issues surrounding its financial reporting. The activities include grant awards and the spendable income "Report of the Treasurer" is presented annually and dis­ from prizes and other income-restricted endowment funds. Permanently restricted net assets are those that cusses the financial condition of the Society as of the im­ must be invested in perpetuity and are commonly referred to as en­ mediately preceding fiscal year-end and the results of its dowment funds. The accompanying financial information operations for the year then It ended. contains summary principally relates to the unrestricted net assets, as this information regarding the operating results and financial category includes the operating activities of the Society. condition of the Society for 2004; a review of 2004 oper­ Unrestricted revenues in excess of unrestricted ex­ ations, containing more detailed information regarding penses for the year ended December 31, 2004, resulted in the Society's operations; and a discussion of the assets and an increase in unrestricted net assets of approximately liabilities of the Society. Finally, in the last part of the re­ US$6,302,000. Of this amount, net income on the unre­ port, there are financial statements derived principally stricted portion of the long-term investment portfolio to­ from the Society's audited financial statements that taled approximately US$4,364,000, and net income from present the balance sheet, statement of activities (akin to operations totaled approximately US$1,938,000. The re- covery in the domestic and international finan­ Key Operating Results cial markets that continued in 2004 resulted in a return on the long-term portfolio of approxi­ mately 11.2%. These and other matters are dis­ 20,000 cussed in more detail in the following sections. The Society's net assets totaled US$60,456,000 15,000 at December 31, 2004: US$3,286,000 is perma­ nently restricted, consisting of the original amount 10,000 of donor-restricted gifts and bequests received by

5,000 the Society; US $1, 794,000 is temporarily restricted by donor-imposed limitations that will lapse upon

0 the passage of time or the use of the asset for its intended purpose; and US$55,376,000 is unre­ stricted, of which US$45,374,000 has been des­ ignated by the Board of Trustees as reserved for future expenditure, principally in the form of the Operating Operating Operating Net Long-term Net Economic Stabilization Fund (ESF). The ESF's pur­ Revenues Expenses Income Investment Income Income pose is to provide a source of cash in the event of a financial crisis. The fund consists of two Operating Income As % of Revenue subfunds, known as the base and supplemental portions of the ESF. The Society's Board of Trustees set the minimum level at which to main­ tain the base portion of the ESF at the sum of 75% of annual operating expenses plus the current es­ timate of the postretirement health benefit oblig­ ation. As of the end of 2004 the value of the base portion of the ESF exceeds the established mini­ mum level. The supplemental portion of the ESF is used to provide operating income to the Soci­ -10.0% +--...... ::------ety via the use of a 5% spending rate. The re- : maining unrestricted net assets consist of I US$4,027,000 -20.0% -'------~------' invested in fixed assets and un­ designated net assets of US$5,975,000.

780 NOTICES OF THE AMS VOLUME 52, NUMBER 7 From the AMS Secretary

Sales Trends - Historical Dollars a percentage of revenue is 3.6%, with significant vari­ 10,000 ation. For the most recent 1 5-year period the average

9 ,000 rises to 5.8% with less variation. Since 1997 the mar­ .... gin achieved is consistently higher than either of 8 ,000 ____. these averages and shows even less variation. Taken 7 ,000 - -+-MR & related together, these are positive financial indicators. --Journals 6,000 _,._Books If the Board of Trustees had not appropriated --lf-lndividual dues 5 ,000 -*-Institutional dues investment income to support operations in 2002- .... 2004, the operating income margin percentage above 4,000 "'-.. .. would have been approximately 5. 5% in 2002, 7.1% in 3,000 2003, and 5.2% in 2004. These are both above the av­ 2 ,000 erage for the period shown above and remain

1,000 consistent for the period from 1991 forward.

0 Sales Trends 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 The graphs on this page show sales trends from 1994 through 2004, first in historical dollars and second in constant dollars (using 2004 as the base year and Sales Trends - Constant Dollars 12,000 adjusting other years for inflation). The trends shown in Sales Trends- Historical Dol­ lars in general are mildly upward, and this is partly 10,000 due to pricing strategies that counter the effects of inflation and attrition. Below this, the chart is re­

8,000 peated with the underlying data converted to constant ~ ~_,._JournalsMR&related dollars...... _Books ,I -;;-Individual dues --.-Institutional dues Mathematical Reviews. Total revenue from MR in 6,000 its various forms increased in 2004. This is due to price increases effective in 2004, net of attrition (which

4,000 was minor). Also, the value of the dollar in many overseas markets continued to be favorable from the perspective of the overseas markets, thus maintain­ 2 ,000 "' ing or lowering the effective cost of the products in many other countries. The Society continues to con­ centrate its marketing efforts on working with con- 0 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2 004 sortia, where costs can be spread over a larger num­ L__~~~~~~~~~~~~~~~~~~~~~~__j ber of institutions. This has the effect of providing the II. Review of 2004 Operations MR product line to a much wider audience than could af- As indicated in the graph Key Operating Results, the past ford it as individual institutions, as well as protecting the four years have been very good years financially for the current revenue stream for future years. MR is currently Society, apart from investment losses incurred in the first financially healthy; however, it is probably unrealistic to two of these years. Although the Society experienced in­ expect significant increases in sales from additional sub­ vestment losses from 2000 to 2002, a significant portion scribers. of those losses had been recouped by the end of 2004. Fur­ journals. Journal revenues are doing well, with some ther, in spite of these losses, long-term investments have improvement seen in the last three years, as attrition of generated high returns over a long period (an average an­ subscribers has been less than expected. The strength of nual return of 10.37% over the last ten years), and that in­ the Society's journal program is further illustrated by come has helped the endowment funds (and the income the fact that substantially all of the subscribers granted they produce) to keep pace with inflation. gratis subscriptions in 2003 due to the bankruptcy of a Since 2002 the Board of Trustees has appropriated subscription agent renewed their subscriptions with the investment income from those endowment funds with Society in 2004. The financial solvency of subscription income whose use is unrestricted and from a portion of agents continues to be a worry to scholarly publishers, as the Economic Stabilization Fund to support operations. The in 2004 a subscription agent with significant market share amounts of such appropriations that have been included required the infusion of additional capital from investors in operating revenue totaled US$792,870 in 2004, in order to meet its obligations to subscribers and pub­ US$865,696 in 2003, and US$760,811 in 2002. lishers. Ultimately, it is the choice of the subscriber to use When reflecting on years with good operating results, a subscription agent, but the scholarly publishers pay the it is instructive to review the Society's record for a some­ highest price should any financial difficulties arise. what longer period. The chart on the previous page shows There continue to be financial pressures on libraries operating income as a percentage of operating revenues. everywhere in the world, as their budgets lag behind the Over this 2 5-year period, the average operating income as cost of obtaining scholarly journals and books. This has

AUGUST 2005 NOTICES OF THE AMS 781 From the AMS Secretary

Major Expense Categories 2002 2003 2004 Personnel Costs $12,945 64% $13,388 67% $13,881 66% Building and equipment related 1,436 7% 1,387 7% 1,391 7% Postage 844 4% 815 4% 799 4% Outside printing and binding 848 4% 691 3% 669 3% Travel, staff and volunteers 957 5% 778 4% 796 4% All other expenses 3,133 16% 3,050 15% 3,294 16% TOTAL $20,1 63 100% $20,109 100% $20,830 100% been the case for many years now and is not likely to restricted net assets are supported by investments in the change. Accordingly, scholarly publishers are fighting over long-term investment portfolio, and the temporarily re­ an ever-dwindling slice of pie. The decline in the value of stricted net assets are supported by investments in the the dollar compared to many other currencies has helped long-term and short-term investment portfolios. The Mar­ the Society's retention efforts with respect to non-U.S. ket Value of Invested Funds shows the market value of each subscribers. The domestic economy continued to recover endowment and Board-designated (quasi-endowment) slowly in 2004, which likely helped domestic retention fund, including any reinvested earnings. efforts in 2004. The Society's fiscal year is the calendar year and thus The drop in 1996 resulted from decisions made by coincides with the period covered by dues and subscrip­ those in control of four Russian journals (Izvestiya, Sbornik, tions. Since dues and subscriptions are generally received Steklov, and Doklady) to use sources other than the in advance, the Society reports a large balance of cash and AMS for translation into English and distribution of the short-term investments on its financial statements at year­ resulting translation journals. end. This amounted to approximatelyUS$16,745,000 and Books. Book revenues increased in 2004 in historical US$15,893,000 at December 31, 2004 and 2003, respec­ dollars and slightly in constant dollars despite a shortfall tively. The corresponding liability for the revenues re­ of new titles produced (85 titles were published in 2004, ceived in advance was approximately US$11,933,000 and the lowest number since 1998). This may in part be due US$10,797,000 at December 31, 2004 and 2003, respec­ to the economic recovery, which continued in 2004, albeit tively. slowly. The Society continues to work with distributors The Society's property and equipment include land, and continues to improve marketing efforts in order to keep buildings and improvements, office furniture and equip­ the book program as healthy as possible in a difficult ment, and software. The Society also owns a small amount market. of transportation equipment. The land, buildings, and Dues. Dues, the sum of individual and institutional, has improvements include the Society's Rhode Island head­ shown a slight upward slope on the historical dollars chart quarters, with buildings in Providence and Pawtucket, and and a flat or slightly decreasing line in constant dollars. the Mathematical Reviews offices in Ann Arbor. The largest A flat constant dollar line is expected for institutional part of the Society's office equipment is its investment in dues, as the number of members varies little from year to computer equipment. year and the dues rates have been set so that dues will in­ The Society's endowment is managed under the "total crease at about the same level as inflation. There has been return concept". Under this management policy, income a slight decline in individual dues from their high in 1998. in excess of a reasonable amount (set by the Board of Major Expense Categories Trustees) is reinvested and increases the value of the fund. This allows for growth in income over time. As discussed The table above shows the major expenses for 2002, 2003, previously, in 2002 the Board of Trustees established a and 2004 in thousands of dollars. There has not been policy of annually appropriating investment income much change from year to year in how expense dollars are from those true endowment funds whose use of income allocated. is unrestricted and from the supplemental portion of the Ill. Assets and liabilities Economic Stabilization Fund to support operations. The amount of such appropriations included in operating So far this report has dealt with revenues and expenditures revenue is US$792,870 and US$865,696 in 2004 and 2003 that affect unrestricted net assets. Another aspect of the respectively. Society's finances is what it owns and owes, or its assets and liabilities, which are reported in the Balance Sheets on IV. Summary Financial Information the following page. As discussed previously, the Society's The following Balance Sheets and Statements of Activities net assets and activities that increase or decrease net as­ are from the audited annual financial statements of sets are classified as unrestricted, temporarily restricted, the Society, and the Statement of Invested Funds is from or permanently restricted. A majority of the assets and li­ the internal financial records of the Society. Each year abilities detailed on the accompanying balance sheets con­ the Audit Committee of the Board of Trustees meets with stitute the unrestricted net assets. The permanently the Society's auditors to review the conduct of the audit,

782 NOTICES OF THE AMS VOLUME 52, NUMBER 7 From the AMS Secretary the Society's financial statements, and the auditors' report STATEMENTS OF ACTIVITIES on the financial statements. Pursuant to the recommen­ Years Ended December 31, 2004 and 2003 dation of the Audit Committee, the Board of Trustees has Changes in unrestricted net assets: accepted the audited financial statements. A copy of the Society's audited financial statements, as submitted to Operating Revenue 2004 2003 the Trustees and the Council, will be sent from the Publication: Providence office to any member who requests it from Mathematical Reviews and the treasurer. The treasurer will be happy to answer any related activities $ 8,935,727 $ 8,658,388 questions members may have regarding the financial Journals (excluding MR) 4,199,508 4,043,300 affairs of the Society. Books 3,047,302 2,797,201 Sale of services 341,789 312,760 -Respectfully submitted, Other 142,114 141,322 Total publication revenue 16,666,440 15,952,971

john M. Franks Membership and professional services: Treasurer Dues, services, and outreach 3,299,211 3,323,900 Grants, prizes, and awards 669,036 790,011 BALANCE SHEETS Investment earnings available December 31, 2004 and 2003 for spending 754,116 790,700 Meetings 938,409 944,433 Total membership and Assets 2004 2003 professional services revenue 5,660,772 5,849,044 Cash and cash equivalents $ 360,398 $ 678,795 Short-term investment income 331,610 452,613 Short-term investments 16,384,598 15 ,2 13,816 Other 108,758 154,919 Receivables, less allowances of $185,089 and $1 15,354 Total operating revenue $22,767,580 $22,409,547 respectively 800,123 1 ,223,912 Deferred prepublication costs 575,040 686,279 Completed books 986,303 1 ' 165,507 Operating Expenses Prepaid expenses and deposits 1,021 ,248 1,044,717 Publication: Land , bldgs., and equipment, less Mathematical Reviews and accumulated depreciation 4,027,381 4,316,071 related activities $ 5,635,138 $ 5,488,300 Long-term investments 54,740,077 47,292,301 Journals (excluding MR) 1,323,861 1 ,267,824 Total assets $78,895,168 $71,621,398 Books 2,533,093 2,480,675 Publication-divisional indirect 808,173 689,493 Liabilities and Net Assets Warehousing and distribution 716,452 704,464 Customer services 675,595 759,530 Liabilities: Marketing and sales 229,373 104,653 Accounts payable $ $ 1 '198,389 1,271,481 Sale of services 226,930 224,353 Accrued expenses: Total publication expense 12,148,615 11 ,719,292 Severance and study leave pay 1 ,093,480 1,272,399 Membership and professional services: Payroll, benefits, and other 974,527 1,350,955 Dues, services, and outreach 2,940,084 2,851,239 Deferred revenue 11 ,633,462 10,796,619 Grants, prizes, and awards 732,548 844,852 Postretirement benefit Meetings 896,816 856,032 obligation 3,538,947 3,1 08,747 Governance 464,003 464,816 Total liabilities 18,438,805 17,800,201 Divisional indirect 488,888 438,360 Total membership and professional Net assets: services expense 5,522,339 5,455,299 Unrestricted 55,375,894 49,074,025 Temporarily restricted 1 ,794,111 1,591,000 Other 9,395 64,965 Permanently restricted 3,286,358 3,156,172 General and administrative 3,149,791 2,868,969 Total operating expenses $20,830,140 $20,1 08,52 5 Total net assets 60,456,363 53,821 '197 Total liabilities and net assets $78,895,168 $71,621,398 (continued)

AUGUST 2005 NOTICES OF THE AMS 783 From the AMS Secretary

STATEMENTS OF ACTIVITIES (continued) Dec. 31, 2004 Dec. 31, 2003

2004 2003 Original Market Market Gift(s) Value Value Excess of operating revenue over operating expenses $1,937,440 $2,301,022 Endowment 100,000 713,905 661,856 Morita Long-term investment return 100,000 127,395 118,107 Henderson 548,223 3,826,949 in excess of investment earnings 3,547,938 Schoenfeld/ available for spending 4,364,429 7,781,294 Mitchell 573,447 717,973 665,628 Change in unrestricted Laha 189,309 242,1 53 224,498 net assets 6,301,869 10,082,316 Ritt 51,347 228,004 211,380 Changes in temporarily Moore 2,575 21,492 19,925 restricted net assets: Total Income Contributions and grants 148,873 86,158 Unrestricted Long-term investment Funds 1,564,901 5,877,871 5,449,332 income (loss) 301,818 439,822 Net assets released from Total Endowment restrictions (247,580) (296,01 7) Funds $3,286,358 $8,638,063 $7,959,182 Change in temporarily restricted net assets 203,111 229,963 Board-Restricted Funds: Change in permanently restricted net assets­ Friends of Math 123,572 123,572 Contributions 130,186 465,784 Russian Royalties 17,829 17,829 journal Archive 415,607 334,714 Change in net assets 6,635,166 10,778,063 Economic Stabilization (total) Net assets, beginning of year 53,821,197 43,043,1 34 44,277,514 37,476,366 Young Scholars 539,561 485,162 Net assets, end of year $60,456,363 $53,821,197 Total Board-Restricted Funds 45,374,083 38,437,643 Total Funds $54,012,146 $46,396,825 STATEMENTS OF INVESTED FUNDS As of Dece mber 3 7, 2004 and 2003

Dec. 31, 2004 Dec. 31, 2003 Original Market Market Gift(s) Value Value

Endowment Funds : Prize Fund s: Steele $145,009 $ 581,243 $ 547,113 Birkhoff 10,076 35,163 33,098 Veblen 2,000 11 ,875 11 ,178 Wiener 2,000 11,875 11 ,178 Bacher 1,450 8,636 8,129 Conant 9,477 38,764 36,488 Cole 5,550 20,394 19,196 Satter 15 ,000 30,872 29,059 Morgan 25,000 42,185 39,707 Whiteman 42,438 43,257 37,438 AMS Book Prize 10,000 10,996 10,350 Arnold Ross Lectures 50,000 50,949 50,000 Trjitzinsky Scholarships 196,030 467,333 439,892 C. V. Newsom 100,000 217,472 204,702 Centennial Fellowship 56,100 111 ,505 104,958 Menger 9,250 10,9 13 10,272 Ky Fan (China) 366,757 366,757 366,757 Epsilon 675,320 700,003 550,335 Total Income Restricted Funds $1,721,457 $2,760,192 $2,509,850

784 NOTICES OF THE AMS VOLUME 52, NUMBER 7 published by the London Mathematical Society on behalf of Foundation Compositio Mathematica COMPOSITIO MATHEMATICA produced marketed & Compositio Mathematica is a prestigious well­ distributed for the established journal publishing first-class research London Mathematical papers that traditionally focus on the mainstream Society

of pure mathematics. Compositio Mathematica Editors: has a wide scope which includes the fields of: Bas Edixhoven algebra, number theory, topology, algebraic and Leiden University The Netherlands analytic geometry and (geometric) analysis. Ben Moonen Papers on other topics are welcome if they University of Amsterdam The Netherlands are of broad interest. All contributions are required to meet high standards of quality and Gerard van der Geer University of Amsterdam originality. Publications in this journal benefit The Netherlands from the added value of careful reviewing and editing. 1COMPDSIT iiOMATM EMATICA.

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d44JA.!§M Journals journals marketing department CAMBRIDGE forty west twentieth· street new york, ny 10011-4211 online phone: 800.872.7423 UNIVERSITY PRESS fax: 845.353.4141 http: I lwww .j o urn a Is. cambridge. o rg/j i d_ C 0 M ~ Whether they become Please give generously. {.!!!!~ scientists, engineers, or entrepreneurs, young people Learn about giving opportunities and estate planning www.ams.org/giving-to-ams with mathematical talent need to be nurtured. Income from this Contact the AMS Development Office fund supports the Young Scholars 1.800.321.4267 ,::~.:=:~,~" AM S i ~ ~ ~ (U.S. and Canada) or ~~ ~ Program, which provides grants to , houNDEm \"'q,'+> , 1.401.455.4000 AMERICAN MATHEMATICAL SOCIETY summer programs for talented high (worldwide) school students. email: [email protected] I www.ams.org I 09/04 Mathematics Calendar

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

August 2005 '' 1 7-1 9 Workshop on Profinite Groups and Applications, The Fields Institute for Research in Mathematical Sciences, Carleton ,., 1 0-1 2 17th Canadian Conference on Computational Geome­ University, Ottawa, Ontario, Canada. try, The Fields Institute for Research in Mathematical Sciences, Overview: The workshop will consist of a series of mini-courses by University of Windsor, Windsor, Ontario, Canada. renowned specialists in profinite groups that should be accessible Information: email: gensci@fields. utoronto. ca. to graduate students and of use to researchers in group theory, number theory, algebraic geometry and related areas. There will '' 1 7- 1 9 Spatial/Temporal Modelling for Marine Ecological Sys­ also b e some more sp ecialized talks by invited speakers. tems, The Fields Institute for Research in Mathematical Sciences, Information: For further information please see the website Dalhousie University, Halifax, Nova Scotia, Canada. at: http ://www. fields.utoronto.ca/ programs/scientific/05- Description: The purpose of the workshop is to bring together 06/profini te/; email: gensci©fields. utor onto. ca. researchers in statistics and marine ecology interested in the devel­ opment of models for the analysis of the complex temporal/spatial September 2005 data now becoming available. These data include, for example, animal tracking data as well as time series of biological variables ,., 21-24 Workshop on Jordan Algebras and Related Fields, The from ocean observing system s. Advancements in marine ecology Fields Institute for Research in Mathematical Sciences, University will be reali zed using these new observations, but not without the of Ottawa, Ottawa, Ontario, Canada. development and application of new statistical analysis techniques. Description: The workshop will bring together the leading experts Our over-riding goal is to review and further fa ciliate the identifica­ in the theory of Jordan structures (Jordan algebras, Jordan triple tion of appropriate statistical m ethods and modeling approaches system s and Jordan pairs) and researchers from other areas for to address outstanding research questions. which Jordan structures play a pivotal role. Its aim is to present Call for Papers: We invite participants to submit poster presenta­ some of the many recent advances in the theory of Jordan structures tions. There will also be a limited number of oral presentations and their applications, to stimulate future work on the outstanding possible. Submitted abstracts should address one of the major problems in Jordan structures and to foster the interaction between conference themes. all researchers interested in Jordan theory. Information: For Registration and Abstract Submission please Speakers: The workshop will feature a lecture series by Efim contact Joanna Mills Flemming. Zelmanov and, in addition, talks by invited speakers. The number Important dates: Abstract Submission deadline: May 31, 2005. of talks is limited, in order to give enough time for informal Registration deadline: June 15, 2005. discu ssions. Information: email: gensci@f ields . utoronto . ca; http: I /www. Invited Speakers: T. Cortes (Oviedo), A. Elduque (Zaragoza), ]. mathstat. dal. ca/. Faulkner (Virginia), E. Garcia (Madrid), S. Garibaldi (Emory), S.

respect to participation in the meeting, tllis fact should be noted. This section contains announcements of meetings and conferences All communications on meetings and conferences in the mathematical of interest to some segment of the mathematical public, including ad sciences should be sent to the Editor of the No tices in care of the American hoc, local, or regional mee tings, and meetings and symposia devoted Mathematical Society in Providence or electronically to notices©ams. org to specialized topics, as well as announcements of regularly scheduled or mathcal ©ams . or g. mee tings of national or international mathematical organizations. A In order to allow participants to arrange their travel plans, organizers of complete list of meetings of the Society can be found on the last page of meetings are urged to subnlit information for these listings early enough each issue. to allow them to appear in more than one issue of the No tices prior to An announcement will be published in the Notices if it contains a call the meeting in question. To achieve this, listings should be received in for papers and specifies the place, date, subject (when applicable), and Providence eight months prior to the scheduled date of the meeting. the speakers; a second announcement will be published only if there The complete listing of the Mathematics Calendar will be published are changes or necessary additional information. Once an announcement only in the September issue of the Notices. The March, June/July, and has appeared, the event will be briefl y noted in every third issue until December issues will include, along with new announcements, references it has been held and a reference will be given in parentheses to the to any previously announced meetings and conferences occurring within month, year, and page of the issue in which the complete information the twelve-month period following the month of those issues. New appeared. Asterisks ("') mark those announcements containing new or information about meetings and conferences that will occur later than revised information. the twelve-month period will be announced once in full and will not be In general, announcements of meetings and conferences held in North repeated until the date of the conference or meeting falls within th e America carry only the date, title of meeting, place of meeting, names of twelve-month period. speakers (or sometimes a general statement on the program), deadlines The Mathematics Calendar, as well as Meetings and Conferences of for abstracts or contributed papers, and source of further information. the AMS, is now available electronically through the AMS website on the Meetings held outside the North American area may carry more detailed World Wide Web. To access the AMS website, use the URL: http: I /www . information. In any case, if there is any application deadline wi th ams. org/.

AUGUST 2005 NOTICES OF THE AMS 787 Mathematics Calendar

Krutelevich (Ottawa), 0. Loos (Innsbruck), C. Martinez (Oviedo), Local Arrangements: Maria Mercado, DIMACS Center, email: K. McCrimmon (Virginia), H. Petersson (Hagen), I. Shestakov (Sao mercadol!ldimacs. rutgers. edu, 732-445-5928. Paulo), U. Stenger (Hagen), Y. Yoshii (North Dakota State), E. Information: See http: I /dimacs. rutgers . edu/Workshops/ Zelmanov (UC, San Diego). Clusters/. Funding: Support for graduate students and postdoctoral fellows: There are limited funds available for graduate students and ,., 28-30 Applications of Methods of Stochastic Systems and postdoctoral fellows. If interested please submit an application by Statistical Physics in Biology, University of Notre Dame, Notre June 15, 2005 through the student support application form. Dame, Indiana. Information: http: I /www. fields. utoronto. ca/programs/ Goals of the Workshop: Discussion of different applications of scientific/05-06/ jordanalg/;email:gensci@fields. utoronto. methods of stochastic analysis and statistical physics for study­ ca. ing biological systems and stimulation of new interdisciplinary collaborations. Some of the specific topics to be covered include pattern formation in development, aggregation in bacteria October 2005 colonies, protein folding, regulation of gene expression, immunology, cy­ '' 13-1 5 Workshop on Current Issues in the Analysis of Incomplete toskeleton, biological networks, and genetic drift. This workshop Longitudinal Data, The Fields Institute, Toronto, Ontario, Canada. is organized in cooperation with SIAM (Society for Industrial and Description: This workshop will focus on four main themes: (1) Applied Mathematics). longitudinal data analysis with missing values, (2) measurement Organizers: Mark Alber (Notre Dame), email: alber. 111lnd. edu; errors models, (3) joint modeling of survival and longitudinal data, Albert-Laszlo Barabasi (Notre Dame), email: alb@nd . edu; Yi ]iang and (4) models for multi-state data. (Los Alamos), email: j iangl!llanl. gov; James Glazier (IU Blooming­ For each theme, the workshop will feature an invited overview talk ton), email: glazier@indiana. edu. and a few invited talks on some specific topics of current interest. This workshop will be appropriate for university facuity, research Information: Limited funding may be available to support atten­ staff, data analysts, post-doctoral fellows, and graduate students. dance by graduate students, postdocs and junior faculty. Poster Funding: Send the required information to Professor Peter Song presentations are encouraged and a limited number of contrib­ email: song@math . uwaterloo. ca by September 15, 2005. uted talks will also be accepted. For more information visit our Information: Registration: The registration fee is $100 for regular website: http: I /www. nd. edu;-icsb/wrkshp2005. html; or contact participants, $25 for graduate students and post-docs. For fur­ Betsy Karnes, email: ekarnes@nd. edu; Dr. Mark Alber, email: ther information please visit our website at: http: I /www. fields. malber@nd. edu. utoronto.ca/programs/scientific/NPCDS/05-06/incomplete/; email: genscil!lfields. utoronto. ca. November 2005

'' 1 5-1 7 The 26th Midwest-Pacific Differential Equations Confer­ '' 1 3-16 INFORMS Annual 2005 Meeting, New Orleans Marriott & ence, University of Alberta, Edmonton, Alberta, Canada. Sheraton New Orleans, New Orleans, Louisiana. Description: This conference is the continuation of the Midwest Description: The theme of the 2005 Annual Meeting comprises Differential Equations Conference series, and it strives to represent a broad area of application in which our discipline's strengths in a broader participation from across and beyond Midwest and Pacific modeling, analysis and algorithm design can be utilized to make regions. The conference is dedicated to Professors Jack W. Macki vital contributions. We focus on the role operations research can and James S. Muldowney for the occasion of their retirement from play in the interaction between ecological concerns and economic the University of Alberta. It celebrates their distinguished academic growth. As a natural outgrowth of this theme, the conference careers and their contributions to research and education in the program will also emphasize the importance of the relationship area of differential equations. between basic research and the practice of operations research. Plenary Lectures: One hour plenary lectures will be given by: Lynn Information: S. Owens; email: meetingsillin forms. org. Erbe (University of Nebraska-Lincoln), John Mallet-Paret (Brown '' 1 7-20 Analysis and related topics, Lviv Ivan Franko National University), Michael Y. Li (University of Alberta), Robert O'Malley, Jr. University, Lviv, Ukraine. (University of Washington), George R. Sell (University of Minnesota), Description: The conference is devoted to the S. Mazur centennial, Pauiine van den Driessche (University of Victoria), James Wong W. Lyantse's 85th anniversary and A. Gol'dberg's 75th anniversary. (Hongkong City University), Jianhong Wu (York University), Pietro Topics: The following Zecca (University of Florence). topics will be presented at the conference: complex analysis; functional analysis; topological algebra; history Contributed Talks: There will also be sessions of contributed of Lviv mathematics. talks. A r efereed Conference Proceedings will be published by Organizers: The Lviv Mathematical Society and Lviv Ivan Franko the Canadian Applied Mathematics Quarterly (CAMQ). Depending National University. on funding, partial support may be provided for students and postdocs. Organizing and Program Committee: T. 0 . Banakh, Eu. V. Cherem­ nyh, I. E. Chyzhykov (secretary), S. Yu. Favorov, S. Yu. Grishyn, I. Information: To register online and for further information, please Yo. Guran, M. L. Gorbachuk, R. 0 . Hryniv, B. N. Khabibullin, A. A. visit the conference website at http: I /www. math. ualberta. ca/ Kondratyuk, V. M. Kyrylych, 0. V. Lopushanky, I. I. Marchenko, V. ami/mwpde. html. K. Maslyuchenko, A. Z. Mokhon'ko, Ya. V. Mykytyuk, A. M. Plichko, I. V. Protasov, Ya. G. Prytula, '' 27-28 DIMACS Workshop on Disease Clusters, DIMACS Center, F. S. Rofe-Beketov, M. M. Sheremeta, I. CoRE Bldg, Rutgers University, Piscataway, New Jersey. 0. Shevchuk, 0. B. Skaskiv, 0. G. Storozh, M. V. Zabolotskyi, M. M. Zarichnyi, Yu. B. Zelins'kyi. Description: Disease clusters, defined as local excesses of disease Information: http: I /www. franko .lvi v. ua/facul ty /mechmat/ in space, time or space and time, represent an important but Conference/ conf2005. htm;email: analysis05@franko .l vi v . ua. vexing problem in public health. The workshop will bring together mathematicians, biostatisticians, epidemiologists and public health officials to develop an approach that, while statistically rigorous, January 2006 is able to address the concerns of the public. '' 2-5 Mathematics in the Twentieth Century: In Commemoration Organizers: Andrew Lawson, University of South Carolina, email: of the Birth Centenary of Andre Weil, Delhi, India. alawsonillgwm. sc. edu; Daniel Wartenberg, Robert Wood Johnson Organizer: Mathematical Sciences Foundation, St. Stephen's Col­ Medical School, email: dew@eohsi. rutgers. edu. lege, Delhi.

788 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Mathematics Calendar

Featured Speakers/Scientific Organizing Committee: Henry Hel­ son,]. P. Kahane,]. P. Pier, Kenneth Ross, Norbert Schlowniuk, Ram Murty, B.S. Yadav, Dinesh Singh. Information: email: conference .msf@gmail. com, indusahu612@ gmail. com; http: I /www. mathscifound. org;MathematicalSciences Foundation, St. Stephen's College, University of Delhi, Delhi-11000 7, India; Telephone/Fax: +91- 011-27666300.

'' 1 6-20 Random analytic functions, AIM Research Conference Center, Palo Alto, California. Workshop topics: This workshop, sponsored by AlMand the NSF, will be devoted to advancing the theory of random functions and surfaces. The main topics for the workshop are the distribution of zeroes of random analytic functions, discrete random analytic functions, the topology of random real zero sets. Organizers: Arnir Dembo, .T. Maurice Rojas, Bernard Shiffman, and Steve Zelditch. Application deadline: October 15, 2005. lnformation:http: I I aimath. orgl ARCCiworkshopslrandomzeros. html.

'' 22-24 ACM-SIAM Symposium on Discrete Algorithms (SODA), Radisson Hotel Miami, Miami, Florida. Description: This symposium focuses on research topics related to efficient algorithms and data structures for discrete problems. In addition to the design of such methods and structures, the scope also includes their use, performance analysis, and the mathematical problems related to their development or limitations. Performance analyses may be analytical or experimental and may address worst­ case or expected-case performance. Studies can be theoretical or based on data sets that have arisen in practice and may address methodological issues involved in performance analysis. Information: http: I lwww. siam. orglmeetings1DA06/index. htm.

April 2006 ,., 20- May 2 INFORMS Practice Conference: Applying Science to the Art of Business, Hotel Intercontinental Miami, Florida. Description: Real-world applications, professional development, best practices and case studies, great networking- all in one in-depth conference.

june 2006 *25-28 INFORMS International Hong Kong 2006, Sheraton Hotel & Towers Hong Kong, Hong Kong, China. Description: Join your colleagues for this international event, , bringing O.R. professionals together to present the latest research, introduce methodologies, and share new developments in the field. We are proud to partner with the Hong Kong Operational Research Society and the Operations Research Society of China in organizing this important conference. Information: http: I lwww. informs. orgiConf 1Hongkong06.

july 2006 * 1 0-14 Ninth International Conference on p-adic functional - analysis, University of Concepcion, Concepcion, Chile. Scientific Committee: A. Escassut, H. Ochsenius, ]. Araujo, ]. Rivera-Lerelier,]. Aguayo. Organizing Committee:]. Aguayo (jaguayo@udec. cl); H. Ochse­ nius (hochsen@mat. puc. cl); X. Vidaux (xvidaux@udec. cl; M. Saavedra (mariansa@udec . cl) . -- .,, 23-2 7 The Ninth International Conference on Integral Methods in Science and Engineering (IMSE-2006), Sheraton Fallsview Hotel and Conference Centre, Niagara Falls, Ontario, Canada. Information: email: spotapenko@uwaterloo. ca.

AUGUST 2005 NOTICES OF THE AMS 789 New Publications Offered by the AMS

Algebra and Algebraic Complex Tori and Geometry Abelian Varieties Olivier Debarre, Universite Louis Pasteur, Strasbourg, France Arithmetic Complex Tori and This graduate-level textbook Arithmetic Differential Abelian Varieties introduces the classical theory of Differential Equations Olivier Debarre complex tori and abelian varieties, Equations while presenting in parallel more Alexandru Buium, University modern aspects of complex algebraic Alexandru Buium of New Mexico, Albuquerque and analytic geometry. Beginning with complex elliptic curves, the book moves on to the higher­ This monograph contains exciting dimensional case, giving characterizations from different original mathematics that will inspire points of view of those complex tori which are abelian new directions of research in algebraic varieties, i.e., those that can be holomorphically embedded in geometry. Developed here is an a projective space. This allows, on the one hand, for arithmetic analog of the theory of illuminating the computations of nineteenth-century ordinary differential equations, where mathematicians, and on the other, familiarizing readers with functions are replaced by integer numbers, the derivative more recent theories. Complex tori are ideal in this respect: operator is replaced by a "Fermat quotient operator", and One can perform "hands-on" computations without the theory differential equations (viewed as functions on jet spaces) are being totally trivial. replaced by "arithmetic differential equations". The main application of this theory concerns the construction and study Standard theorems about abelian varieties are proved, and of quotients of algebraic curves by correspondence with moduli spaces are discussed. Recent results on the geometry infinite orbits. Any such quotient usually reduces to a point in and topology of some subvarieties of a complex torus are also algebraic geometry. But many of the above quotients cease to included. be trivial (and become quite interesting) if one enlarges The book contains numerous examples and exercises. It is a algebraic geometry by using arithmetic differential equations very good starting point for studying algebraic geometry, in place of algebraic equations. suitable for graduate students and researchers interested in This book, in part, follows a series of papers written by the algebra and algebraic geometry. author. However, a substantial amount of the material has SMF members are entitled to AMS member discounts. never been published before. For most of the book, the only Contents: Preface to the French edition; Preface to the English prerequisites are the basic facts of algebraic geometry and edition; Lattices and complex tori; Elliptic curves; Differential algebraic number theory. It is suitable for graduate students forms and de Rham cohomology; Theta functions and divisors; and researchers interested in algebraic geometry. Line bundles, sheaf cohomology, and first Chern class; Abelian Contents: Main concepts and results: Preliminaries from varieties; Moduli spaces; Subvarieties of a complex torus; algebraic geometry; Outline of 6 -geometry; General theory: Bibliography; Index. Global theory; Local theory; Birational theory; Applications: SMF/AMS Texts and Monographs, Volume ll Spherical correspondences; Flat correspondences; Hyperbolic correspondences; List of results; Bibliography; Index. August 2005, 109 pages, Softcover, ISBN 0-8218-3165-8, 2000 Mathematics Subject Classification: 14-01, 14K20, 14K25, All Mathematical Surveys and Monographs, Volume ll8 AMS members US$31, List US$39, Order code SMFAMS/ 11 September 2005, approximately 360 pages, Hardcover, ISBN 0- 8218-3862-8, 2000 Mathematics Subject Classification: 14G20, 14G35, 30Fl0; 53A55, 37F05, 14L24, All AMS members US$68, List US$85, Order code SURV / ll8

790 NOTICES OF THE AMS VOLUME 52, NUMBER 7 New Publications Offered by the AMS

Representation Type Mathematical Surveys and Monographs, Volume 117 ME~9IRS September 2005, 231 pages, Hardcover, ISBN 0-8218-3831-8, Amerlc~>.n MothemoUul Soe1ety of Commutative LC 2005048021, 2000 Mathematics Subject Classification: 20F65, 37B10; 37F20, 37Fl5, 20£08, 22A22, All AMS members Representa tion Type of Noetherian Rings III: Commutative Noetherian US$47, List US$ 59, Order code SURV/117 Rings Ill: Global Wildness Global Wildness and and Tameness Lt:e Klingler Tameness Lawrence S. Levy Lee Klingler and Lawrence S. Levy ArnorloonMothernntlcalSodety Analysis Contents: Introduction; Preliminaries; Dedekind-like rings; Wildness; Structure of a genus; Substitute for conductor squares; Isomorphism classes in a genus, idele group action; Web of Trace Ideals and class groups; Direct sums; Finite normalization; Appendix A; Appendix B; Bibliography. Their Applications Memoirs of the American Mathematical Society, Volume 176, Second Edition Number 832 Barry Simon, California June 2005, 170 pages, Softcover, ISBN 0-8218-3738-9, LC Institute of Technology, 2005044092, 2000 Mathematics Subject Classification: 13£05, Pasadena 16G60, Individual member US$38, List US$63, Institutional member US$ 50, Order code MEM0/ 176/ 832 From a review of the first edition: "Beautifully written and well organized ... indispensable for those Self-Similar Groups interested in certain areas of mathe­ matical physics ... for the expert and beginner alike. The author Volodymyr Nekrashevych, deserves to be congratulated both for his work in unifying a International University subject and for showing workers in the field new directions for Bremen, Germany, and Kyiv future development." Taras Shevchenko University, -Zentralblatt MATH Ukraine This is a second edition of a well-known book stemming from the author's lectures on the theory of trace ideals in the algebra Self-similar groups (groups generated of operators in a Hilbert space. Because of the theory's many by automata) initially appeared as different applications, the book was widely used and much in @ examples of groups that are easy to demand. define but have exotic properties like nontrivial torsion, intermediate For this edition, the author has added four chapters on the growth, etc. This book studies the self-similarity phenomenon closely related theory of rank one perturbations of self-adjoint in group theory and shows its intimate relationship with operators. He has also included a comprehensive index and an dynamical systems and more classical self-similar structures, addendum describing some developments since the original such as fractals, Julia sets, and self-affine tilings. This notes were published. connection is established through the central topics of the This book continues to be a vital source of information for book, which are the notions of the iterated monodromy group those interested in the theory of trace ideals and in its and limit space. applications to various areas of mathematical physics. A wide variety of examples and different applications of self­ This item will also be of interest to those working in similar groups to dynamical systems and vice versa are mathematical physics. discussed. In particular, it is shown that julia sets can be Contents: Preliminaries; Calkin's theory of operator ideals and reconstructed from the respective iterated monodromy groups symmetrically normed ideals; convergence theorems for Jp; and that groups with exotic properties can appear not just as Trace, determinant, and Lidskii's theorem; j(x)g( - i\7); isolated examples, but as naturally defined iterated Fredholm theory; Scattering with a trace condition; Bound state monodromy groups of rational functions. problems; Lots of inequalities; Regularized determinants and The book offers important, new mathematics that will open renormalization in quantum field theory; An introduction to the new avenues of research in group theory and dynamical theory on a Banach space; Borel transforms, the Krein spectral systems. It is intended to be accessible to a wide readership of shift, and all that; Spectral theory of rank one perturbations; professional mathematicians. Localization in the Anderson model following Aizenman­ This item will also be of interest to those working in differential Molchanov; The Xi function; Addenda; Bibliography; Index. equations. Mathematical Surveys and Monographs, Volume 120 Contents: Basic definitions and examples; Algebraic theory; September 2005, 150 pages, Hardcover, ISBN 0-8218-3581-5, Limit spaces; Orbispaces; Iterated monodromy groups; LC 2005048059, 2000 Mathematics Subject Classification: Examples and applications; Bibliography; Index. 47L30; 47A40, 8lU99, All AMS members US$39, List US$49, Order code SURV / 120

AUGUST 2005 NOTICES OF THE AMS 791 New Publications Offered by the AMS

Differential Equations Geometric Theory of Geometric Theory Incompressible of Incompressible Flows with Flows with The Complete Applications MEJY!9IRS ·to Fluid Dynamics Applications to Fluid American Mntbemallco.l Society Dimension Theory of Tian Ma Shouhong Wang Dynamics The Complete Dimension Partially Ordered Theory of Partially Tian Ma, Sichuan University, Ordered Systems Systems with Chengdu, China, and with Equivalence and Orthogonality Equivalence and Shouhong Wang, Indiana K. R. Goodearl University, Bloomington F. Wehnmg Orthogonality This monograph presents a geometric theory for K. R. Goodearl and F. incompressible flow and its applications to fluid dynamics. Amerlcnnl\f a tbcm~Ucal.Society Wehrung The main objective is to study the stability and transitions of the structure of incompressible flows and its applications to Contents: Introduction; Partial fluid dynamics and geophysical fluid dynamics. The commutative monoids; Continuous dimension scales; development of the theory and its applications goes well Espaliers; Classes of espaliers; Bibliography; Index. beyond its original motivation of the study of oceanic Memoirs of the American Mathematical Society, Volume 176, dynamics. Number 831 The authors present a substantial advance in the use of June 2005, 117 pages, Softcover, ISBN 0-8218-3716-8, LC geometric and topological methods to analyze and classify 2005044093, 2000 Mathematics Subject Classification: 06B15, incompressible fluid flows. The approach introduces genuinely 06C15, 06B23, 06B30,06E1 5,06C10, 08A55; 06B35,06C20, innovative ideas to the study of the partial differential 06A05 , 16D50, 16D70, 16D90, 16E20, 16E50, 18E10, 19A49, equations of fluid dynamics. One particularly useful 19K14, 28B10, 28A60, 46L51, Individual member US$35, List development is a rigorous theory for boundary layer US$ 58, Institutional member US$46, Order code separation of incompressible fluids. MEM0/176/831 The study of incompressible flows has two major interconnected parts. The first is the development of a global geometric theory of divergence-free fields on general two­ dimensional compact manifolds. The second is the study of Translations of Algebraic Analysis of • MATIIEMATICAL the structure of velocity fields for two-dimensional MONOGRAPHS Singular Perturbation incompressible fluid flows governed by the Navier-Stokes Takahiro Kawai, Kyoto equations or the Euler equations. Algebraic University, japan, and Motivated by the study of problems in geophysical fluid Analysis Yoshitsugu Takei, Kyoto, dynamics, the program of research in this book seeks to of Singular develop a new mathematical theory, maintaining close links to Perturbation japan physics along the way. In return, the theory is applied to Takahtro Kawai physical problems, with more problems yet to be explored. Yoshitsugu Takei The topic of this book is the study of singular perturbations of ordinary The material is suitable for researchers and advanced differential equations, i.e., graduate students interested in nonlinear PDEs and fluid perturbations that represent solutions dynamics. as asymptotic series rather than as This item will also be of interest to those working in analytic functions in a perturbation parameter. The main applications. method used is the so-called WKB (Wentzel-Kramers-Brillouin) method, originally invented for the study of quantum­ Contents: Introduction; Structure classification of divergence­ mechanical systems. The authors describe in detail the WKB free vector fields; Structural stability of divergence-free vector method and its applications to the study of monodromy fields; Block stability of divergence-free vector fields on problems for Fuchsian differential equations and to the manifolds with nonzero genus; Structural stability of solutions analysis of Painleve functions. The volume is suitable for of Navier-Stokes equations; Structural bifurcation for one­ graduate students and researchers interested in differential parameter family of divergence-free vector fields; Two equations and special functions. examples; Bibliography; Index. Contents: Borel resummation; WKB analysis of Schrtidinger Mathematical Surveys and Monographs, Volume 119 equations; Applications of WKB analysis to global problems; October 2005, approximately 288 pages, Hardcover, ISBN 0- WKB analysis of the Painleve function; Future directions and 8218-3693-5, LC 2005048120, 2000 Mathematics Subject projects; Appendix; Bibliography; Index. Classification: 35Q30, 35Q35, 76D05, 76D10, 37Cl0, 37C75, Translations of Mathematical Monographs (Iwanami Series in 86A10, 86A05; 46E25, 20C20, All AMS members US$ 55, List Modern Mathematics), Volume 227 US$69, Order code SURV/119 October 2005, approximately 136 pages, Softcover, ISBN 0-8218-3547-5, 2000 Mathematics Subject Classification: 34E15; 34E20, 34M40, All AMS members US$23, List US$29, Order code MMON0/227

792 NOTICES OF THE AMS VOLUME 52, NUMBER 7 New Publications Offered by the AMS

Fo• Classroom October 2005, approximately 224 pages, Hardcover, ISBN 0- On Finiteness Use 8218-2805-3, 2000 Mathematics Subject Classification: 34C07, c CRM R MONOGRAPH in Differential 34C08, 34M35, 14G25; 11]91, 11]82, 12H05, 32G10, 34C10, M SERIES 34M10, 34M50, 37C20, 37C27, 58K20, All AMS members Equations and US$47, List US$ 59, Order code CRMM/24 On Finiteness in Differentia l Equations Diophantine and Diophantine Geometry

DanaSehlomluk Andrel A.Dollbn1kh Geometry ~~~~.', ~~~~:~::~0 Alc.~"ndru Buh>m Dana Schlomiuk, Universite de Discrete Mathematics and Montreal, QC, Canada, Andrei A. Bolibrukh, Steklov Institute, Combinatorics Russian Academy of Sciences, Moscow, Russia, Sergei Yakovenko, Weizmann Institute of Science, A Generating MEMOIRS Rehovot, Israel, Vadim Kaloshin, California of the AmericanMat hematleaiSoclcty Function Approach Institute of Technology, Pasadena, CA, and A Genera ting Function to the Enumeration Alexandru Buium, University of New Mexico, Approach to the Enumeration of Matrices Albuquerque, NM in Classical Groups of Matrices in over Finite Field This book focuses on finiteness conjectures and results in Jason Fulrnan Classical Groups Peter M. Neumann ordinary differential equations (ODEs) and Diophantine Chery! E. Pracgcr geometry. During the past twenty-five years, much progress has over Finite Fields been achieved on finiteness conjectures, which are the offspring Jason Fulman, Peter M. of the second part of Hilbert's 16th problem. Even in its ""'•tiennMMhemu te oi Soetety Neumann, and Cheryl E. simplest case, this is one of the very few problems on Hilbert's list which remains unsolved. These results are about existence Praeger and estimation of finite bounds for the number of limit cycles This item will also be of interest to those working in algebra occurring in certain families of ODEs. The book describes this and algebraic geometry. progress, the methods used (bifurcation theory, asymptotic expansions, methods of differential algebra, or geometry) and Contents: Introduction, tables, and preliminaries; Separable the specific results obtained. The finiteness conjectures on limit and cyclic matrices in classical groups; Semisimple and regular cycles are part of a larger picture that also includes finiteness matrices in classical groups; Bibliography. problems in other areas of mathematics, in particular those in Memoirs of the American Mathematical Society, Volume 176, Diophantine geometry where remarkable results were proved Number 830 during the same period of time. There is a chapter devoted to June 2005, 90 pages, Softcover, ISBN 0-8218-3706-0, LC finiteness results in Diophantine geometry obtained by using 2005044094, 2000 Mathematics Subject Classification: 05E15; methods of differential algebra, which is a connecting element 20G40, Individual member US$34, List US $ 56, Institutional between these parallel developments in the book. member US$45, Order code MEM0/ 176/ 830 The volume can be used as an independent study text for advanced undergraduates and graduate students studying ODEs or applications of differential algebra to differential equations and Diophantine geometry. It is also a good entry point for researchers interested these areas, in particular, in Geometry and Topology limit cycles of ODEs, and in finiteness problems. Contributors to the volume include Andrei Bolibrukh and Alexandru Buium. Available from the AMS by A. Buium is Entropy Bounds and Arithmetic Differential Equations, as Volume 118 in the ME1Y191RS Mathematical Surveys and Monographs series. American Mathematical Sodety Isoperimetry This item will also be of interest to those working in algebra S. G. Bobkov and B. and algebraic geometry. Entropy Bounds Zegarlinski and Isoperimetry Contents: Finiteness problems in differential equations and This item will also be of interest to Diophantine geometry; Linear differential equations, Fuchsian S . G. Bobkov B. Zegarlinski those working in analysis. inequalities and multiplicities of zeros; Quantitative theory of ordinary differential equations and tangential Hilbert 16th Contents: Introduction and notations; problem; Around Hilbert-Arnol'd problem; Finiteness results in Poincare-type inequalities; Entropy differential algebraic geometry and Diophantine geometry; a­ ""'•rlcan MathemaUealSoelety and Orlicz spaces; LSq and Hardy-type minimal structures, real analytic geometry, and transseries; inequalities on the line; Probability List of lectures; List of participants; List of participants II. measures satisfying LSq-inequalities on the real line; Exponential integrability and perturbation of CRM Monograph Series, Volume 24 measures; LSq-inequalities for Gibbs measures with super Gaussian tails; LSq-inequalities and Markov semigroups; Isoperimetry; The localization argument; Infinitesimal version;

AUGUST 2005 NOTICES OF THE AMS 793 New Publications Offered by the AMS

Proof of Theorem 9.2; Euclidean distance (proof of Theorem Hyperbolic surfaces of constant mean curvature one with 9.1); Uniformly convex bodies; From isoperimetry to LSq· compact fundamental domains; ]. Choe, Isoperimetric inequalities; Isoperimetric functional inequalities; inequalities of minimal submanifolds; F. Martin, Complete Bibliography. nonorientable minimal surfaces in 1Pl. 3; F.]. Lopez, Some Memoirs of the American Mathematical Society, Volume 176, Picard-type results for properly immersed minimal surfaces in Number 829 1Pl.3; M. Ritore, Optimal isoperimetric inequalities for three­ dimensional Cartan-Hadamard manifolds; T. H. Colding and June 2005, 69 pages, Softcover, ISBN 0-8218-3858-X, LC W. P. Minicozzi II, Embedded minimal disks; M. Traizet, 2005045310, 2000 Mathematics Subject Classification: 46-XX; Construction of minimal surfaces by gluing Weierstrass 51-XX, 52-XX, Individual member US$32, List US$53, representations; W. H. Meeks III, Global problems in classical Institutional member US$42, Order code MEM0/ 176/ 829 minimal surface theory; W. H. Meeks III and H. Rosenberg, Minimal surfaces of finite topology; N. Kapouleas, Constructions of minimal surfaces by gluing minimal

Cl•y Mathem;ot.h:s immersions; R. Mazzeo, F. Pacard, and D. Pollack, The Ptoceo-dlngs Global Theory of """"' conformal theory of Alexandrov embedded constant mean Minimal Surfaces curvature surfaces in 1Pl. 3; W. Rossman, M. Umehara, and Global K. Yamada, Constructing mean curvature 1 surfaces in H 3 Theory ~, . David Hoffman, Mathematical with irregular ends; R. Kusner, Conformal structures and of Minimal· Sciences Research Institute necksizes of embedded constant mean curvature surfaces; Surfaces ~~-. ~ (MSRI), Berkeley, CA, Editor ]. Perez, W. H. Meeks III, and A. Ros, Uniqueness of the fl.~~ ', .. l David Hoffman t , · Riemann minimal surfaces; Y. Fang, The mathematical protein ' Editor In the Summer of 2001, the folding problem; K. Tenenblat, Minimal and CMC surfaces Mathematical Sciences Research obtained by Ribaucour transformations; R. Sa Earp and Institute (MSRI) hosted the Clay E. Toubiana, Meromorphic data for surfaces of mean Mathematics Institute Summer School curvature one in hyperbolic space, II; R. Schoen, Special on the Global Theory of Minimal Lagrangian submanifolds; D. Joyce, Lectures on special Surfaces. During that time, MSRI Lagrangian geometry; ]. Wolfson, Variational problems in became the world center for the study Lagrangian geometry: J:'z-currents; ]. Hass, Minimal surfaces of minimal surfaces: 150 mathematicians-undergraduates, and the topology of three-manifolds; J. H. Rubinstein, Minimal post-doctoral students, young researchers, and world surfaces in geometric 3-manifolds; K. GroSe-Brauckmann, experts-participated in the most extensive meeting ever held Cousins of constant mean curvature surfaces; P. Topping, An on the subject in its 250-year history. The unusual nature of approach to the Willmore conjecture; C. Mese, Minimal the meeting made it possible to put together this collection of surfaces and harmonic maps into singular geometry; expository lectures and specialized reports, giving a ]. H. Rubinstein, Shortest networks in 2 and 3 dimensions; panoramic view of a vital subject presented by leading List of participants. researchers in the field. Clay Mathematics Proceedings, Volume 2 The subjects covered include minimal and constant-mean­ curvature submanifolds, geometric measure theory and the September 2005, approximately 816 pages, Softcover, ISBN 0- double-bubble conjecture, Lagrangian geometry, numerical 8218-3587-4, 2000 Mathematics Subject Classification: 53Al0; simulation of geometric phenomena, applications of mean 49Q15, 53C25, 53C42, 53C43, 58E35, All AMS members curvature to general relativity and Riemannian geometry, the US$95, List US$119, Order code CMIP/2 isoperimetric problem, the geometry of fully nonlinear elliptic equations and applications to the topology of three­ dimensional manifolds. The wide variety of topics covered Curves and For make this volume suitable for graduate students and Clu,.ass room researchers interested in differential geometry. Surfaces This item will also be of interest to those working in analysis. Sebastian Montiel and Titles in this series are published by the AMS for the Clay Mathematics Antonio Ros, Universidad de Institute (Cambridge, MA). Granada, Spain Contents: F. Morgan and M. Ritore, Geometric measure theory and the proof of the double bubble conjecture; M. Weber, This introductory textbook puts forth Classical minimal surfaces in Euclidean space by examples: a clear and focused point of view on Geometric and computational aspects of the Weierstrass the differential geometry of curves representation; K. Polthier, Computational aspects of discrete and surfaces, emphasizing the global minimal surfaces; R. Schoen, Mean curvature in Riemannian aspects. The excellent collection of geometry and general relativity; H. Karcher, Introduction to examples and exercises (with hints) conjugate Plateau constructions; ]. Perez and F. ]. Lopez, will help students in learning the Parabolicity and minimal surfaces; A. Ros, The isoperimetric material. Advanced undergraduates and graduate students will problem; M. Wolf, Flat structures, Teichmuller theory and find this a nice entry point to differential geometry. handle addition for minimal surfaces; M. Weber, D. Hoffman, In order to study the global properties of curves and surfaces, and M. Wolf, The genus-one helicoid as a limit of screw­ it is necessary to have more sophisticated tools than are motion invariant helicoids with handles; D. Hoffman, usually found in textbooks on the topic. In particular, students Computing minimal surfaces; ]. Spruck, Geometric aspects of must have a firm grasp on certain topological theories. Indeed, the theory of fully nonlinear elliptic equations; H. Karcher, this monograph treats the Gauss-Bonnet theorem and

794 NOTICES OF THE AMS VOLUME 52, NUMBER 7 New Publications Offered by the AMS discusses the Euler characteristic. The authors also cover relations in non-elementary classes; 0. Lessmann, An Alexandrov's theorem on embedded compact surfaces in 18. 3 introduction to excellent classes; D. Mushtari, Ultrafilters and with constant mean curvature. The last chapter addresses the nuclear spaces; J. Steprans, Many quotient algebras of the global geometry of curves, including periodic space curves and integers modulo co-analytic ideals; V. Tolstykh, What does the the four vertices theorem for plane curves that are not automorphism group of a free abelian group A know about necessarily convex. A?; B. Zilber, A categoricity theorem for quasi-minimal This volume is suitable for advanced undergraduates, excellent classes. graduate students, and researchers interested in the Contemporary Mathematics, Volume 380 differential geometry of curves and surfaces. It can also be August 2005, 306 pages, Softcover, ISBN 0-8218-3474-6, LC used as an introduction to a more general study of differential 2005041239, 2000 Mathematics Subject Classification: 03-06; geometry. 03C35, 03C45, 03C60,03C95,03C98,03E05,03E15,03F30, This book is jointly published by the AMS and the Real Sociedad 03H15, All AMS members US$63, List US$79, Order code Matematica Espanola (RSME) . CONM/380 Contents: Plane and space curves; Surfaces in Euclidean space; The second fundamental form; Separation and orientability; Integration on surfaces; Global extrinsic geometry; Intrinsic geometry of surfaces; The Gauss-Bonnet theorem; Global geometry of curves; Bibliography; Index. Graduate Studies in Mathematics, Volume 69 Mathematical Physics October 2005, approximately 384 pages, Hardcover, ISBN 0- 8218-3815-6, 2000 Mathematics Subject Classification: 53A04, 53A05, 53C40, All AMS members US$47, List US$ 59, Order Mathematical Studies code GSM/ 69 in Nonlinear Wave

Mathematical Studies Propagation in Nonlinear Wave Propagation Dominic P. Clemence and Dominic P. Clemence Guoqing Tang, North Carolina Guoqing Tang Logic and Foundations Editors A & T University, Greensboro, Editors Lively discussions and stimulating Logic and Its research were part of a five-day Applications conference on Mathematical Methods in Nonlinear Wave Propagation sponsored by the NSF and Andreas Blass, University of CBMS. This volume is a collection of lectures and papers Logic and Michigan, Ann Arbor, and stemming from that event. Leading experts present dynamical its Applications Yi Zhang, Sun Yat-Sen systems and chaos, scattering and spectral theory, nonlinear Andreas Blass wave equations, optimal control, optical waveguide design, Yi Zhang University, Guangzhou, China, Editors and numerical simulation. Editors The book is suitable for a diverse audience of mathematical Two conferences, Logic and Its specialists interested in fiber optic communications and other Applications in Algebra and Geometry nonlinear phenomena. It is also suitable for engineers and and Combinatorial Set Theory, other scientists interested in the mathematics of nonlinear Excellent Classes, and Schanuel wave propagation. Conjecture, were held at the University of Michigan (Ann This item will also be of interest to those working in differential Arbor). These events brought together model theorists and set equations. theorists working in these areas. This volume is the result of those meetings. It is suitable for graduate students and Contents: R. E. Mickens, An introduction to wave equations; researchers working in mathematical logic. M. Klaus, On the Zakharov-Shabat eigenvalue problem; T. Aktosun, Solitons and inverse scattering transform; Contents: j. T. Baldwin, Ehrenfeucht-Mostowski models in j. Yang, A tail-matching method for the linear stability of abstract elementary classes; A. Blass, Unsplit families, multi-vector-soliton bound states; R. H. Goodman, dominating families, and ultrafilters; A. Bovykin, Several R. E. Slusher, M. I. Weinstein, and M. Klaus, Trapping light proofs of PA-unprovability; M. Di Nasso and M. Forti, with grating defects; B. N. Borah, Thermo-elastic-plastic Ultrafilter semirings and nonstandard submodels of the Stone­ transition; A. B. Srnirnova, Regularized quasi-Newton method ( ech compactification of the natural numbers; S. Gao, Unitary with continuous inversion ofF' + EI for monotone ill-posed group actions and Hilbertian polish metric spaces; operator equations; W. Huang, Transition layers for a R. Grossberg and 0. Lessmann, Abstract decomposition singularly perturbed neutral delay differential equation; theorem and applications; G. Hjorth, A dichotomy theorem for C. Y. Lob, Nonlinear aeroacoustics computations by the CE/SE being essentially countable; T. Huuskonen and Y. Zhang, Mad method; S. C. Chang, A. Himansu, C. Y. Lob, X. Y. Wang, and families are small; T. Hyttinen, Random logarithm and S. T. Yu, Robust and simple non-reflecting boundary homogeneity; j. Iovino, Definability, semidefinability, and conditions for the Euler equations-A new approach based on asymptotic structure in analysis; A. Kolesnikov, Dependence

AUGUST 2005 NOTICES OF THE AMS 795 New Publications Offered by the AMS the space-time CE/SE method; G. Tang, D. Clemence, theory of asymptotic functions"; Voronof's memoirs on C. Jackson, Q. Lin, and V. Burbach, Physical and numerical quadratic forms; Ivan Matveevich Vinogradov (1891-1983): modeling of seismic wave propagation. Ivan Matveevich Vinogradov; Works of Vinogradov from the Contemporary Mathematics, Volume 379 first period of his mathematical activity; Waring's problem; The Goldbach problem; Estimation of Weyl sums and the July 2005, 213 pages, Softcover, ISBN 0-8218-3349-9, LC problem of the fractional parts of a polynomial; Bibliography. 2005041238, 2000 Mathematics Subject Classification: OOB25, 35-06, 65-06, All AMS members US$47, List US$ 59, Order History of Mathematics, Volume 26 code CONM/3 79 September 2005, approximately 296 pages, Hardcover, ISBN 0- 8218-3457-6, 2000 Mathematics Subject Classification: 01A72, 11-03; 01A55, 01A60, All AMS members US$47, List US$ 59, Order code HMATH/ 26 Number Theory University Arithmetic LECTURE Senes Noncommutative The Sl Petersburg School The St. Petersburg Arithmetic Geometry of Number Theory School of Number Noncommutative Matilde Marcolli, Max-Planck­ Geometry B.N.Delone Theory Institut fur Mathematik, Bonn, Mattlde Marcolli Germany B. N. Delone Arithmetic noncommutative geometry For over two centuries, the work of uses ideas and tools from the St. Petersburg mathematicians in noncommutative geometry to address number theory has constituted a questions in a new way and to glorious contribution to mathematics. reinterpret results and constructions from number theory and The Russian book, The St. Petersburg arithmetic algebraic geometry. This general philosophy is School of Number Theory, is about the applied to the geometry and arithmetic of modular curves and life and work of prominent members to the fibers at Archimedean places of arithmetic surfaces and of this school, such as Chebyshev, Korkin, Zolotarev, Markov, varieties. Voronof, and Vinogradov. These mathematicians are indeed a very distinguished group, and their work in number theory is Noncommutative geometry can be expected to say something of the highest quality and continues to have lasting about topics of arithmetic interest because it provides the significance. right framework for which the tools of geometry continue to make sense on spaces that are very singular and apparently This English translation acquaints the reader with the most very far from the world of algebraic varieties. This provides a important works of these six eminent members of the St. way of refining the boundary structure of certain classes of Petersburg school. A short biography is given for each of spaces that arise in the context of arithmetic geometry. them, followed by an exposition of some of his most significant contributions. Each contribution features the With a foreword written by Yuri Manin and a brief author's original terminology and notation and is followed by introduction to noncommutative geometry, this book offers a commentary. Certain works receive relatively complete comprehensive account of the cross fertilization between two expositions, while others are dealt with more briefly. important areas, noncommutative geometry and number theory. It is suitable for graduate students and researchers With a Foreword written for the English edition, this volume interested in these areas will appeal to a broad mathematical audience, including mathematical historians. It is particularly suitable for graduate This item will also be of interest to those working in algebra students and researchers interested in number theory. and algebraic geometry. This item will also be of interest to those working in general Contents: Ouveture; Noncommutative modular curves; and interdisciplinary areas. Quantum statistical mechanics and Galois theory; Noncommutative geometry at arithmetic infinity; Vistas; Copublished with the London Mathematical Society. Members of the LMS may order directly from the AMS at the AMS member price. The Bibliography. LMS is registered with the Charity Commissioners. University Lecture Series, Volume 36 Contents: Pafnutir L'vovich Chebyshev (1821-1894): Pafnutif July 2005, approximately 144 pages, Softcover, ISBN 0-8218- L'vovich Chebyshev; Chebyshev's articles on prime numbers; 3833-4, 2000 Mathematics Subject Classification: 58B34, All Aleksandr Nikolaevich Korkin (1837-1908): Aleksandr AMS members US$23, List US$29, Order code ULECT/36 Nikolaevich Korkin; The articles by Korkin and Zolotarev on the minima of positive quadratic forms; Egor Ivanovich Zolotarev (1847-1878): Egor Ivanovich Zolotarev; Zolotarev's memoirs on the theory of ideal numbers; Andrer Andreevich Markov (1856-1922): Andrei' Andreevich Markov; On binary quadratic forms of positive determinant; Georgi( Fedoseevich Voronoif (1868-1908): Georgli Fedoseevich Voronof; Voronof's dissertations on algebraic numbers of the third degree; Voronof's memoir of 1903: "On a problem from the

796 NOTICES OF THE AMS VOLUME 52, NUMBER 7 New AMS-Distributed Publications

Cunent Developments Current New AMS-Distributed in Mathematics, 2002 Developments in Sponsored by Ediwdby IIJr.";l rdllniversily BarryMal ur Mathematics, 2002 Wilfrk'dSchmid Publications itWll S.T. Yau ~~ Barry Mazur, Wilfried Schmid, Mas...achusct1 s lnstitutc ofTechnology DavidJcrison and S.T. Yau, Harvard TomMrowka RichardStanky University, Cambridge, and David jerison, Tom Mrowka, and Richard Stanley, Massachusetts Institute of Algebra and Algebraic Technology, Cambridge, Geometry Editors These are the proceedings of the joint MIT -Harvard University (Cambridge, MA) seminar on current developments Current in mathematics held in 2002. Current Developments The organizing committee for the seminar consisted of in Mathematics, 2001 Developments in distinguished mathematicians from both institutions: B. Mazur, W. Schmid, and S.T. Yau from Harvard, and D. ]erison, Sponsored by Edited by Mathematics, 2001 Harvard University Barry Mawr T. Mrowka, and R. Stanley from MIT. This year, the seminar Wilfril::dSchmid lfliDI S.T. Yau Barry Mazur, Wilfried Schmid, was dedicated to Professor Wilfried Schmid and Professor -~~ and S.-T. Yau, Harvard George Lusztig. The 2002 speakers included Albert Bressan, Massachusetts institute Mark Haiman, Richard Hain, Stephen Kudla, Yair Minsky, John of Technology A.J.deJong University, Cambridge, MA, Oa\'idJcrison Morgan, Leslie Saper, Kari Vilonen, and David Vogan. George Lustig and A. J. de Jong, David Jerison, and George Lustig, This item will also be of interest to those working in mathematical physics, number theory, geometry and topology, Massachusetts Institute of and probability. Technology, Cambridge, A publication of International Press. Distributed worldwide by the Editors American Mathematical Society. This proceedings volume grew from the joint seminar by MIT Contents: A. Bressan, One dimensional hyperbolic systems of and Harvard on the developments in mathematics during the conservation laws; M. Haiman, Combinatorics, symmetric year 2001. functions and Hilbert schemes; R. Hain, Periods of limit mixed Hodge structures; S. S. Kudla, Modular forms and arithmetic The organizing committee for the seminar consisted of geometry; Y. N. Minsky, End invariants and the classification distinguished mathematicians from both institutions: Barry of hyperbolic 3-manifolds; L. Saper, On the cohomology of Mazur, Wilfried Schmid, and S.-T.Yau from Harvard, and A.]. locally symmetric spaces and of their compactifications. de Jong, David Jerison, and George Lustig from MIT. International Press The book is suitable for graduate students and researchers interested in algebra, algebraic geometry, analysis, December 2003, 289 pages, Hardcover, ISBN 1-57146-102-7, mathematical physics, number theory, geometry, topology, All AMS members US$52, List US$65, Order code INPR/57 and probability. A publication of International Press. Distributed worldwide by the American Mathematical Society. Analysis Contents: G. Carlsson, Recent developments in algebraic K­ theory; D. S. Freed, K-theory in quantum field theory; E. H. Ueb and J. Yngvason, The mathematical structure of the second law of thermodynamics; E. H. Lieb, ]. P. Solovej, Geometric Measure R. Seiringer, andY. Yngvason, The ground state of the Bose Theory- An gas; S.-W. Zhang, Elliptic curves, L -functions and CM-points. International Press Introduction December 2002, 219 pages, Hardcover, ISBN 1-57146-101-9, Lin Fanghua, New York All AMS members US$ 52, List US$65, Order code INPR/55 University, and Yang Xiaoping, Chinese Academy of Sciences, Beijing, China In the last three decades since the publication of the seminal work of H. Federer, which gives a rather complete and comprehensive discussion on the subject, geometric measure theory has

AUGUST 2005 NOTICES OF THE AMS 797 New AMS-Distributed Publications

developed into an even more cohesive body of basic hereoclinic orbits of Hamiltonian systems and symplectic knowledge with an ample structure of its own, establishing geometry. strong ties with many other areas of mathematics and making The book is suitable for graduate students and researchers numerous new striking applications. interested in differential equations. The present book is intended for graduate students and A publication of International Press. Distributed worldwide by the researchers in other fields of mathematics as a quick overview American Mathematical Society. on the subject of geometric measure theory, emphasizing Contents: A. Bahri and S. Chanillo, The difference of topology various basic ideas, techniques, and their applications in at infinity for the case of two masses in changing sign Yamabe problems arising in the calculus of variations, geometrical problems on S3; T. Bartsch, Linking, positive invariance and analysis and nonlinear partial differential equations. This localization of critical points; H. Brezis, Is there failure of the graduate-level treatment of geometric measure theory inverse function theorem?; C.-N. Chen, Blow-up of solutions of illustrates with concrete examples and emphasizes basic ideas nonlinear parabolic problems; D. G. Costa, Variational and techniques with applications to the calculus of variations, problems which are nonquadratic at infinity; Y. Ding, geometrical analysis, and non-linear PDEs . In addition to a full Homoclinic orbits of Hamiltonian systems; M.-Y. Jiang, Self­ index and bibliography, the book includes eight main adjointness of Hamiltonian operator and some problems in chapters. It is co-published by Science Press (Beijing/ New symplectic geometry; G. Li and H.-S. Zhou, Dirichlet problem York) and International Press (Boston). of p-Laplacian with nonlinear term j(x, u) ~ uP - 1 at infinity; The book is suitable for graduate students and researchers S. Li, Some advances in Morse theory and minimax theory; interested in analysis. Y. Li, On a class of elliptic eigenvalue problems with A publication of International Press. Distributed worldwide by the constraint; C. Liu, Iteration theory of Maslov-type index and its American Mathematical Society. applications; Z. Liu and J. Sun, Number of invariant sets of Contents: Hausdorff measure; Fine properties of functions descending flow with applications in critical point theory; and sets and their applications; Lipschitz functions and Y. Long, The Maslov-type index and its iteration theory and rectifiable sets; The area and co-area formulae; BV functions applications to Hamiltonian systems; R. Manasevich and and sets of finite perimeter; Theory of varifolds; Theory of J. Mawhin, The spectrum of p-Laplacian systems under currents; Mass minimizing currents; Bibliography; Index. Dirichlet, Neumann and periodic boundary conditions; P. H. Rabinowitz, A note on Hamiltonian systems of multiple International Press pendulum type; J. Su, Nontrivial critical points for December 2002, 247 pages, Hardcover, ISBN 1-57146-125-6, asymptotically quadratic functional at resonance; Z.-Q. Wang, All AMS members US$44, List US$ 55, Order code INPR/62 Positive solutions having prescribed symmetry for nonlinear elliptic problems; M. Willem, A decomposition lemma and critical minimization problems; S. Wu, The effect of sublinear term at origin in some elliptic problems; X. Zhang, Positive Differential Equations mass theorem for modified energy condition. International Press

lP New Studtes in December 2003, 286 pages, Hardcover, ISBN 1-57146-109-4, Advanced Morse Theory, 2000 Mathematics Subject Classification: 49]40, 34B15, 35120, Mathematics 35]25, 35]60, 37]45, All AMS members US$38, List US$48, S·T'fau SomasEd1lor Minimax Theory and Morse Theory, Order code INPR/58 Minimax Theory Their Applications to and their Applications to Nonlinear Differential Nonlinear Equations IP NeW Stud1es 1n l.ec!uresatlheMorningside Lectures on Partial Advanced Cent~ r o f Mathematics Differential MathematiC.<; HaimBrezis S T Y<~ll SencsB:mor Differential ShuJieli Equations JiaQuanliu Paul H. Rabinowitz Lectures at the Equations Morningside Center of Proceedings in Honor of Mathematics Louis Nirenberg's 75th Birthday Haim Brezis, University of Paris VI, France, Shujie li, Academia Sinica, Beijing, PRC, JiaQuan liu, Peking Sun-Yung Alice Chang, University, Beijing, PRC, and Paul H. Rabinowitz, Princeton University, N], University of Wisconsin, Madison, Editors Chang-Shou Lin, Chung Cheng University, Chia-Yi, Minghsiung, Taiwan, and Based on lectures held at the Morningside Center of Mathematics at the Chinese Academy of Sciences (Beijing), this Horng-Tzer Yau, Stanford University, CA, Editors volume contains both survey and expository papers on Morse Based on lectures held at the Center for Theoretical Sciences theory, minimax theory, iteration theory of Maslov-type index, (Taiwan) in honor of Louis Nirenberg's 75th birthday, this and critical minimization problems. volume contains research papers dealing with various The book particularly emphasizes applications to nonlinear problems in partial differential equations, such as wave maps, differential equations, including semilinear elliptic boundary the Navier-Stokes equations, and Lagrangian submanifolds. problems, p-Laplacian systems, periodic, homoclinic and Professor Nirenberg is particularly appreciated for his

798 NOTICES OF THE AMS VOLUME 52, NUMBER 7 New AMS-Distributed Publications generous encouragement of the development of mathematics and symbolic dynamics, and (6) shadowing lemma and in the Asia-Pacific region and the mixture of articles by symbolic dynamics. distinguished mathematicians from Asia and other parts of This monograph is suitable for graduate students and the world. researchers interested in differential equations, particularly in The book is suitable for graduate students and researchers chaos in high dimensions. interested in differential equations. A publication of International Press. Distributed worldwide by the A publication of International Press. Distributed worldwide by the American Mathematical Society. American Mathematical Society. Contents: General setup and concepts; Soliton equations as Contents: A. Bahri, Recent progress in conformal geometry integrable Hamiltonian PDEs; Figure-eight structures; Melnikov (with an emphasis on the use of configuration spaces); vectors; Invariant manifolds; Homoclinic orbits; Existence of H. Brezis, Homotopy classes in Sobolev spaces; S.-Y. A. Chang, chaos; Stabilities of soliton equations in lffi.n; Lax pairs of Euler M. j. Gursky, and P. C. Yang, Entire solutions of a fully equations of inviscid fluids; Linearized 2D Euler equation at a nonlinear equation; S.-Y. A. Chang, C.-C. Chen, and C.-S. Lin, fixed point; Arnold's Liapunov stability theory; Miscellaneous Extremal functions for a mean field equation in two topics; Bibliography; Index. dimension; Y. Giga, Shocks and very strong vertical diffusion; International Press M. G. Grillakis, The wave map problem; Q. jiu and Z. Xin, Some regularity criteria on suitable weak solutions of the 3-D December 2003, 119 pages, Softcover, ISBN 1-57146-151-5, All incompressible axisymmetric Navier-Stokes equations; AMS members US$38, List US$48, Order code INPR/60 j. J. Kohn, Multiplier ideals and microlocalization; Y. Li, Some recent work on elliptic systems from composite material; F. H. Lin, Bubbling and quantization in high dimensions; T.- P. Liu, T. Yang, and S.-H. Yu, Entropy pairs for conservation General and Interdisciplinary laws and H-theorem for the Boltzmann equation; Y. Martel and F. Merle, Qualitative results on the generalized critical KdV equation; R. Schoen and j. Wolfson, The volume The Founders of The Founders of functional for Lagrangian submanifolds; F. Treves, An Index Theory algebraic characterization of the modified Korteweg-De Vries Rcminisccnes of Atiyah, Boll Index Theory hierarchy; S. R. Varadhan, Particle systems and partial Hi rLcbruch, and Singer differential equations; S.-T. Yau, An estimate of the gap of the Reminiscences of first two eigenvalues in the Schrodinger operator; Appendix. ~· ~~, IU~ :~ q Atiyah, Bott, Hirzebruch, International Press and Singer "' . December 2003, 238 pages, Hardcover, ISBN 1-57146-111-6, S. T. Yau, Harvard University, 2000 Mathematics Subject Classification: 35]60, 35]50, 35P15, Edited by Cambridge, MA, Editor 35Q53, 35 L70, 82C22, 53Dl2, 53A30, 49Q20, 35H20, 46E35, S.T. Yau 76P05, All AMS members US$ 52, List US$65, Order code li' """""'''"'"' r"" This book tells the story of the four INPR/61 great mathematicians who uncovered index theory, one of the most exciting discoveries of twentieth-century mathematics. It contains historically important essays by Atiyah, Bott, Hirzebruch, and Chaos in Partial Singer, as well as articles by Donaldson, Witten, Yau, and Differential others. A large photo section is also included. All combined, these features make this book valuable to everyone interested in understanding mathematics and mathematicians. Chaos in Equations Partial Differential Equations Y. Charles Li, University of A publication of International Press. Distributed worldwide by the American Mathematical Society. Missouri, Columbia Y. Charles Li Contents: M. Atiyah, Personal History; N. Hitchin, Sir Michael ~~!ty of Missouri, Columbia This book presents a survey on Atiyah: A brief biography; P. Goddard, Sir Michael Atiyah and the existing results in the rapidly early days of the Newton Institute; R. Bott, A letter from Raoul developing area of chaos in partial Bott; S. Donaldson, Geometry in Oxford c.1980-85; G. Lusztig, differential equations (PDEs). Recollections about my teacher, Michael Atiyah; L. Nirenberg, Nonlinear wave equations are the Memories of Sir Michael Atiyah; G. B. Segal, Being a graduate most important class of PDEs in natural sciences. Among student of Michael Atiyah; E. Witten, Michael Atiyah and the these nonlinear wave equations, there is a class of equations physics/geometry interface; M. Atiyah, Mathematics: Queen and called soliton equations that describe a wide spectrum of servant of the sciences; M. Atiyah, The conscience of science; natural phenomena. The author and his collaborators have Interview with Raoul Bott; L. W. Tu, The life and works of Raoul established a systematic theory on chaos in nonlinear wave Bott; R. Forman, Lessons from graduate school; N. Hingston, The equations. It is a standard program for proving the existence beautiful vision of Raoul Bott; P. Landweber, Some reminiscences of chaos in perturbed soliton equations, using the following: about Raoul Bott; L. W. Tu, Reminiscences of working with Raoul (1) Darboux transformations for soliton equations, (2) Bott; E. Witten, Lessons from Raoul Bott; Correspondence isospectral theory for soliton equations under periodic between]. A Todd and F. Hirzebruch; F. Hirzebruch, Kunihiko boundary condition, (3) persistence of invariant manifolds and Kodaira: Mathematician, friend, and teacher; A. jackson, Bonn's Fenichel fibers, (4) Melnikov analysis, (5) Smale horseshoes Max Planck Institute: A new building and a new era; E. Brieskom, Singularities in the work of Friedrich Hirzebruch; K. Hulek,

AUGUST 2005 NOTICES OF THE AMS 799 New AMS-Distributed Publications

Friedrich Hirzebruch and mathematics in post-war Germany; M. Kreck, Hirzebruch-Flachen; I. Singer, A tribute to Warren Ambrose; K. Hoffman, Fifty years of friendship and collaboration with Singer; C. C. Moore, Iz Singer and the founding of MSRI; D. Freed and J. Lott, Singer's Berkeley seminar; R. V. Kadison, Which Singer is that?; H. Rossi, Reminiscences of a mathematics student, 40 years ago; D. Stroock, Is Singer; F. Warner, I. M. Singer; E. Witten, Is Singer's contributions to geometry and physics; S. T. Yau, My friendship with Singer; M. Atiyah, Letter to Raoul, Fritz, and Is; R. Bott, Letter to Fritz, Is and Michael; F. Hirzebruch, Letter to Michael, Raoul, and Iz; I. M. Singer, Letters to Michael, Raoul, and Fritz; R. G. Douglas, The evolution of modern analysis; L. Garding, A happy collaboration; A. Weinstein, Memories of the gang of four; Bibliographies. International Press December 2003, 290 pages, Hardcover, ISBN l-57146-120-5, 2000 Mathematics Subject Classification: 51-XX, 54-XX, 58-XX, 34- XX, 46- XX, 14-XX, 47-XX, All AMS members US$68, List US$85, Order code INPR/ 54

Geometry and Topology

tP New Studtes m Advanced Low-Dimensional Mathematics S I Yau ScnosEd,tor Topology Low-Dimensional Topology Lectures at the Lectures at the Morningside Center of Malhamatics Morningside Center of

Editors· Mathematics Benghe U Shicheng Wang, XuezhiZhaa Benghe Li, Science Academy, Beijing, China, Shicheng Wang, Beijing University, China, and Xuezhi Zhao, Capital Normal University, Beijing, China, Editors This volume contains most of the series of lectures presented during the half-year program of low-dimensional topology held at the Morningside Center of Mathematics at the Chinese Academy of Sciences (Beijing). The order of contents is based on the chronological order in which the lectures were presented. This book is the third volume in the International Press series, New Studies in Advanced Mathematics. Each lecture provides a brief introduction to important fields in current research in low-dimensional topology. The volume is suitable for graduate students and researchers interested in geometry and topology. A publication of International Press. Distributed worldwide by the American Mathematical Society. Contents: J. W. Morgan, Definition of the Seiberg-Witten (SW) invariants of 4-manifolds; J. W. Morgan, Computation of SW invariants for certain 4-manifolds; M. Scharlemann, Heegaard splittings of 3-manifolds; C. M. Gordon, Dehn filling; H. Rubinstein, Dehn's lemma and the Loop theorem; H. Rubinstein, Polyhedral geometry; H. Rubinstein, Triangulations of 3-manifolds. International Press December 2003, 80 pages, Softcover, ISBN l-57146-112-4, All AMS members US$38, List US $48, Order code INPR/ 56

800 NOTICES OF THE AMS VOLUME 52, NUMBER 7 International Press Publishing high-quality, peer-reviewed mathematics and physics journals at affordable prices since 1992

Quarterly Journal of Pure Communications in and Applied Mathematics Mathematical Sciences A new journal promoting Rapidly publishing results the most recent interests in modem applied math, in mathematics and intro­ including modeling, analy- --~:-~~;&.-. ~~ --,

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qualifications. The department seeks can­ didates whose research interests mesh MICHIGAN well with current faculty. The department has research groups in the areas of analy­ MICHIGAN STATE UNIVERSITY sis, algebra, geometry/topology, and dif­ East Lansing, Ml48824 ferential equations. Applicants must have proMSc Program in strong research credentials as well as Industrial Mathematics strong accomplishment or promise in teaching. Letter of application, current Direct your students toward one of the vita, description of research, and at least professional M.Sc. programs. Industry three letters of reference evaluating re­ needs business-savvy mathematicians. See search should be sent to: http: //www.sciencemasters .com/. Louis Pigno 000019 Department of Mathematics Cardwell Hall138 Kansas State University SWEDEN Manhattan, KS 66506 The department also requires that the can­ UPPSALA UNIVERSITY didate arrange for letters to be submitted Department of Mathematics evaluating teaching accomplishments and Uppsala, Sweden potentiaL Offers may begin by December 1, 2005, but applications for positions will One full professorship in mathematics. be reviewed until February 1, 2006, or until One full professorship in applied mathe­ positions are closed. AA/ EOE matics. See http: I /www . persona 1 avd. 000055 uu.se/ ledigaplatser/ for more infor­ mation. The deadline for application is SEPTEMER 30 2005. MASSACHUSETTS 000057

BOSTON UNIVERSITY MA Degree Program in Mathematical Finance SWITZERLAND

Exceptional candidates with expertise in UNIVERSITY OF GENEVA mathematical finance are invited to apply Department of Mathematics for a tenure-track Assistant Professor po­ sition at Boston University. The appoint­ The Department of Mathematics invites ment will be effective as early as January applications for a position in probability 1, 2006. All applicants should demonstrate and statistics at the full/associate profes­ outstanding potential as researchers and sor level beginning in or after October educators and extensive knowledge of the­ 2006. For more information and deadline oretical finance, stochastic analysis and see http: //www .unige.ch/ math / probability theory. Applicants should sub­ secretariat/pastes/. mit a cover letter and three copies of the 000052 following: (a) detailed vita; (b) detailed de­ scription of current and future research plans; (c) brief teaching statement; and (d) selected reprints and preprints. Complete applications must be mailed to: Mathematical Finance Search Com­ mittee MA degree program in Mathematical Finance Boston University 111 Cummington Street Boston, MA, 02215, USA Applicants should have at least four let­ ters of recommendation, one of which evaluates teaching, sent directly to the above address. Applications received by October 1, 2005, will be given full consid­ eration. Early application is advisable. Boston University is an Affirmative Ac­ tion/Equal Opportunity Employer. 000054

804 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Animated Tube Plot

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IMPORTANTINFORMATION 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 /www. 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.

Harold Rosenberg, University of Paris VII, Minimal and con­ Annandale-on­ stant mean curvature surfaces in homogeneous 3-manifolds. Alice Silverberg, University of California Irvine, Applying Hudson, New York number theory and algebraic geometry to cryptography. Bard C allege Christopher Sogge, Johns Hopkins University, Estimates for eigenfunctions of the Laplacian. October 8-9,2005 Benjamin Sudakov, Princeton University, Probabilistic Saturday - Sunday reasoning and Ramsey Theory.

Meeting #1 009 Special Sessions Eastern Section Algebraic and Geometric Combinatorics (Code: SS 12A), Associate secretary: Lesley M. Sibner Cristian P. Lenart, State University of New York at Announcement issue of Notices: August 2005 Albany, and Lauren L. Rose and Sheila Sundaram, Bard Program first available on AMS website: August 25, 2005 College. Program issue of electronic Notices: October 2005 Issue of Abstracts: Volume 26, Issue 4 Extremal and Probabilistic Combinatorics (Code: SS llA), Benjamin Sudakov, Princeton University. Deadlines Geometric Group Theory (Code: SS lA), Sean Cleary, The For organizers: Expired City College of New York, and Melanie I. Stein, Trinity For consideration of contributed papers in Special Sessions: College. Expired Geometric Transversal Theory(Code: SS 3A), Richard Pol­ For abstracts: August 16, 2005 lack, Courant Institute, New York University, and Jacob Eli Goodman, The City College of New York. The scientific information listed below may be dated. For the latest information, see www.ams.org/amsmtgs/ Global Theory of Minimal Surfaces (Code: SS 6A), David A. sectional . html. Hoffman, Mathematical Sciences Research Institute, and Harold Rosenberg, University of Paris VII. Invited Addresses History of Mathematics (Code: SS 2A), Patricia R. Allaire, Persi Diaconis, Stanford University, Erdos picture of 'most Queensborough Community College, CUNY, Robert E. things' (Erdos Memorial Lecture). Bradley, Adelphi University, and Jeff Suzuki, Bard College.

AUGUST 2005 NOTICES OF THE AMS 807 Meetings & Conferences

Homological Aspects of Commutative Algebra (Code: SS 4A), nonrefundable full deposits for their rooms, a discounted Alexandre Tchernev, University of Albany, SUNY, and rate ofUS$135.20i night is available through http: I lwww. Janet Vassilev, University of Arkansas. holiday-inn. com; note that the two-night minimum for Infinite Groups (Code: SS lOA), Anthony M. Gaglione, a Saturday night stay still applies. United States Naval Academy, Benjamin Fine, Fairfield Ramada Inn, Route 28, NYS Thruway Exit 19, Kingston, University, and Dennis Spellman, Philadelphia University. NY 12401; phone: 845-339-3900, fax: 845-338-8464. Full­ service hotel changing to Quality Inn by June 1, includes Invariants of Graphs and Matroids (Code: SS 8A), Gary indoor heated pool, restaurant and lounge on premises, Gordon and Lorenzo Traldi, Lafayette College. data ports in guest rooms; US$99Isingle or double. Dead­ Mathematical Methods for the Analysis ofImages and High­ line for reservations is September 7, 2005. Cancellation Dimensional Data (Code: SS 13A), Erik M. Bollt, Clarkson and early checkout policies vary; be sure to check when University, and Rick Chartrand, Los Alamos National you make your reservation. Laboratory. Super 8 Motel, 487 Washington Ave. (I-87 exit # 19), Measurable, Symbolic, and Tiling Dynamical Systems (Code: Kingston, NY 12401; phone and fax: 845-338-3078. Modest SS 9A), Natalie Preibe Frank, Vassar College, and Samuel]. hotel with restaurants within walking distance. US$751 Lightwood, Western Connecticut State University. single or double. Cancellation and early checkout policies Special Functions and Orthogonal Polynomials: Theory and vary; be sure to check when you make your reservation. Applications (Code: SS 7A), Diego Dominici, State Univer­ Food Service sity of New York at New Paltz. Information will be available at the meeting. Theory of Infinite-Dimensional Lie Algebras, Vertex Oper­ ator Algebras, and Related Topics (Code: SS SA), Antun Local Information Milas, SUNY at Albany, Alex J. Feingold, Binghamton The mathematics department's webpage is located at the University, and Yi-Zhi Huang, Rutgers University. university's homepage http: I lwww. bard. edul. Campus and area maps, as well as travel information, can be found Accommodations athttp:llwww.bard.edulcampuslmapsl. Participants should make their own arrangements directly with a hotel of their choice as early as possible. Special rates Other Activities have been negotiated with the hotels listed below. Rates Book Sales: Examine the newest titles from the AMS! Many quoted do not include sales tax of 10.25%. The AMS is not of the AMS books will be available at a special 50% discount responsible for rate changes or for the quality of the ac­ available only at the meeting. Complimentary coffee will commodations. When making a reservation, participants be served courtesy of AMS Membership Services. should state that they are with the American Mathematical AMS Editorial Activity: An acquisitions editor from Society (AMS) Meeting at Bard College group. Cancellation the AMS book program will be present to speak with and early checkout policies vary; be sure to check when you prospective authors. If you have a book project that you make your reservation. would like to discuss with the AMS, please stop by the book This is a holiday weekend in a very popular tourist exhibit. area. Participants should make reservations early. Please note there are no accommodations within walking Parking distance of Bard. There are some Bed and Breakfast Visitors can park in any of the campus lots at no charge. Inns closer than the hotels listed below, but not The closest parking is in the gravel lot across from Olin within walking distance. See the list published by the Hall as well as a large paved lot a short distance away. college at http: llwww.bard.edultoolslservicesl accommodationslindexlphp. Registration and Meeting Information The following hotels are in Kingston, NY, about 20 min­ The meeting is at Bard College, Annandale-on-Hudson, utes south of campus by car and about one hour south of New York. The talks will take place in Olin Hall, Olin Albany International Airport. Limited shuttle service be­ Language Center and Hegeman. The Invited Addresses tween these hotels and campus will be provided by Bard will be in Olin Auditorium. College for the meeting days: Holiday Inn, 503 Washington Ave. (New York State The registration desk, located in the Atrium, Olin Hall, Thruway, I-87, exit # 19), Kingston, NY 12401; phone: 845- will be open Saturday, October 8, 7:30 a.m.-4:00p.m. and 338-0400, fax: 845-340-1908. Full-service newly-decorated Sunday, October 9, 8:00 a.m.-noon. Fees are US$40 for AMS hotel with restaurant and lounge, indoor heated pool, fit­ or CMS members, US$60 for nonmembers, and US$5 for ness center, data ports in guest rooms; US$149Isingle or students, unemployed mathematicians, and emeritus mem­ double occupancy. N.B. If staying on Saturday night (1018), bers. Fees are payable on site by cash, check, or credit card. there is a two-night minimum, so you must also stay Friday or Sunday night as well. Deadline for reservations Social Event is September 7, 2005. Cancellation and early checkout The department of mathematics will host a reception on policies vary; be sure to check when you make your Saturday, October 8, from 6:00p.m. to 8:00 p.m. in Manor reservation. For those participants who wish to provide Cafe.

808 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Meetings & Conferences

Travel If you discover you do need a visa, the National Acad­ The official airline for the meetings is Delta Airlines. Take emies website (see above) provides these tips for suc­ advantage of Delta's new SimpliFares™ and enjoy the cessful visa applications: following benefits: '' Visa applicants are expected to provide evidence that • No Saturday-night stay required-more flexibility they are intending to return to their country of residence. provide proof of "binding" • Always affordable-realize up to 50% savings on Therefore, applicants should or sufficient ties to their home country or permanent everyday fares in the contiguous forty-eight states residence abroad. This may include documentation of • Lower change fees-reduced from $100 to $50 to the following: change travel plans • family ties in home country or country of legal • Just eight fares-less guessing and easier planning permanent residence, To make immediate reservations call Delta Air Lines at • property ownership, 800-221-1212. Be sure to reference US738367060 or visit • bank accounts, http: I /www. de 1 ta. com and enter Sky Bonus account • employment contract or statement from employer number US738367060 in your passenger information stating that the position will continue when the employee screen to be recognized as a participant of the Joint Math­ returns. ematics Meetings. Your benefits include: '' Visa applications are more likely to be successful if • No service fees done in a visitor's home country than in a third country. • 1,000 SkyMile bonus points '' Applicants should present their entire trip itinerary, • Skip the airport lines; check in online including travel to any countries other than the United Albany International Airport, 965 Old Albany Shaker States, at the time of their visa application. Rd., Latham, NY, is the closest airport serving most major '' Include a letter of invitation from the meeting orga­ airlines and is located about 60 miles from campus. Travel nizer or the U.S. host, specifying the subject, location and from the airport to the campus is available by taxi (ap­ dates of the activity, and how travel and local expenses will proximate fare is US$104.50 plus round-trip tolls) or Grey­ be covered. hound Bus service (http: I /www . greyhound. com or call ,., If travel plans will depend on early approval of the visa 800-231-2222 or 845-331-0744). The bus fare is around application, specify this at the time of the application. US$38 round trip and service is very limited. The bus sta­ ,., Provide proof of professional scientific and/ or tion in Kingston is across the street from the Super 8 and educational status (students should provide a university Holiday Inn. transcript). Some travelers may find it more convenient to fly into This list is not to be considered complete. Please visit Newark Liberty International Airport (EWR), about 120 the web sites above for the most up-to-date information. miles from Bard. Transfer is available from EWR to the New Weather York Port Authority at 8th and 42nd street in midtown New York City (Olympia Airport Express, 212-964-6233 or During October the average high and low temperatures are 908-354-3 330; fare is US$12) and on to Kingston via Trail­ 62 and 41, respectively (degrees Fahrenheit). ways bus service (http: I /www . trai lwaysny. com/) where the round-trip fare is approximately US$41. The bus sta­ tion in Kingston is across the street from the Holiday Inn Johnson City, and Super 8. Also see the Bard College website for links to other Tennessee airports and local transportation at http: I /www . bard. edu/admi ssi on/vi siting/ and http: I /www . bard. edu/ East Tennessee State University campus/maps/. October 15-16,2005 Car rentals are available at the Albany airport from Saturday - Sunday several companies. Enterprise seems to have the best rates starting at US$21/ day plus taxes/ fees. Meeting #1 010 Special Travel Information for International Partici­ Southeastern Section pants. Visa regulations are continually changing for Associate secretary: Matthew Miller travel to the United States. Visa applications may take Announcement issue of Notices: August 2005 from three to four months to process and require a Program first available on AMS website: September 1, 2005 personal interview, as well as specific personal informa­ Program issue of electronic Notices: October 2005 tion. International participants should view the important Issue of Abstracts: Volume 26, Issue 4 information about traveling to the U.S. found at http://www?.nationalacademies.org/ visas/ Deadlines Traveling_to_US.html and ht t p://travel .state. For organizers: Expired gov /visa/i ndex. html . If you need a preliminary con­ For consideration of contributed papers in Special Sessions: ference invitation in order to secure a visa, please send your Expired request to dl s@ams. org. For abstracts: August 23, 2005

AUGUST 2005 NOTICES OF THE AMS 809 Meetings & Conferences

The scientific information listed below may be dated. For ical Society (AMS) Meeting at ETSU group. Cancellation the latest information, see www. ams. org/amsmtgs/ and early checkout policies vary; be sure to check when section a 1 . html. you make your reservation. None of these hotels is within walking distance of Invited Addresses campus. Limited shuttle service between these hotels and Alberto Bressan, Pennsylvania State University, Optimal campus will be provided by Eastern Tennessee State Uni­ transportation metrics and nonlinear wave equations. versity for the meeting days: Super 8 Motel, 108 Wesley St., Johnson City, TN 37601; Assaf Naor, Microsoft Research, The b-Lipschi.tz theory of phone and fax: 423-282-8818. Modest hotel with refrigera­ metric spaces: A survey of recent progress and algorithmic tors in rooms; US$49.99/single, double, triple, or quadruple applications. occupancy. Several restaurants within walking distance. Prasad V. Tetali, Georgia Institute of Technology, Markov Property is about 3.1 miles from campus. Deadline for chain mixing: An update. reservations is September 16, 2005. Cancellation and Rekha R. Thomas, University of Washington, Groebner early checkout policies vary; be sure to check when you bases: From theory to applications and back. make your reservation. Howard johnson/Best Western Johnson City Hotel & Special Sessions Conference Center, 2406 N. Roan St., Johnson City, TN 37601; phone: 432-282-2161, fax: 423-282-2488. Full­ Approximation Theory(Code: SS SA), Robert Gardner, East service hotel includes pool and hot tub, restaurant and Tennessee State University, and Narendra Kumar Govil, lounge on premises, free high-speed Internet access (free Auburn University. wireless from lobby), exercise room, refrigerators/ Commutative Ring Theory (Code: SS 1A), David F. Ander­ microwaves in guest rooms; US$65/single or double son and David E. Dobbs, University of Tennessee at includes complimentary hot breakfast buffet. Guest rooms Knoxville. are accessible by exterior entrance or interior courtyard Discrete Models in Biology (Code: SS 7A), Debra Knisley, based upon availability; please specify when making your East Tennessee State University, and Michael A. Langston, reservation. Property is about 3.5 miles from campus. Department of Computer Science, University of Tennessee, Deadline for reservations is September 16, 2005. Cancel­ Knoxville. lation and early checkout policies vary; be sure to check Geometry and Algorithms in Metric Spaces (Code: SS 8A), when you make your reservation. W. J. Bo Brinkman, Computer Science & Systems Analysis Days Inn, 2312 Browns Mill Rd., Johnson City, TN 37604; Department, Miami University, and Beata Randrianan­ phone: 423-282-2211, fax: 423-282-6111. Modest hotel toanina, Miami University. with pool, refreigerators in rooms, and complimentary continental breakfast. US$46.99/single or double. Property Mathematical Applications in Survival Analysis and Bio­ is about 2.6 miles from campus. Cancellation and early statistics (Code: SS 6A), Don Hong, East Tennessee State checkout policies vary; be sure to check when you make University, and Tiejian Wu, Department of Public Health, your reservation. East Tennessee State University. See the webpage maintained by the local organizers Mathematical Aspects of Wave Propagation Phenomena athttp://www.etsu.edu/math/ams/AMS-Meeting.htm (Code: SS 2A), Boris P. Belinskiy, University of Tennessee for other hotel suggestions. at Chattanooga, and Anjan Biswas, Tennessee State University. Food Service Mathematical Education of Teachers (Code: SS 3A), Frederick There are several restaurants within walking distance; a Norwood and Michel Helfgott, East Tennessee State list will be available at the meeting. In addition the Culp University. Center hosts Quiznos, Chick-Fil-A, Burger King, and an all-you-can-eat buffet for US$6.50. Nonlinear PDE Evolutionary Systems and Their Control (Code: SS 9A), George Avalos, University of Nebraska­ Local Information and Maps Lincoln, and Irena M. Lasiecka, University of Virginia. The university's homepage is http: I /www. etsu. edu/. Nonlinear Wave Equations and Applications (Code: SS 4A), The Department of Mathematics is at http: I jwww. etsu. Alberto Bressan and Yuxi Zheng, Pennsylvania State edu/math/math. htm. Campus and area maps can be found University. athttp://www.etsu.edu/etsu/visitors.asp.

Accommodations Other Activities Participants should make their own arrangements directly Book Sales: Examine the newest titles from the AMS! Many with a hotel of their choice as early as possible. Special rates of the AMS books will be available at a special 50% discount have been negotiated with the hotels listed below. Rates available only at the meeting. Complimentary coffee will quoted do not include sales tax of 14.5%. The AMS is not be served courtesy of AMS Membership Services. responsible for rate changes or for the quality of the AMS Editorial Activity: An acquisitions editor from accommodations. When making a reservation, participants the AMS book program will be present to speak with should state that they are with the American Mathemat- prospective authors. If you have a book project that you

810 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Meetings & Conferences would like to discuss with the AMS, please stop by the book http: 1 jwww. avis. com. Meeting Avis Discount Number exhibit. Bl59266. Driving Directions. See the excellent map at http: I I Parking www.etsu.edu/etsu/files/MAPtoETSU.pdf. Free parking is available across the street from Rogers-Stout Special Travel Information for International Partici­ Hall. pants. Visa regulations are continually changing for travel to the United States. Visa applications may take from Registration and Meeting Information three to four months to process and require a personal in­ The meeting is at East Tennessee State University, John­ terview, as well as specific personal information. Interna­ son City, Tennessee. Sessions and Invited Addresses will tional participants should view the important information take place in Rogers-Stout Hall. about traveling to the U.S. found at http: I /www7. The registration desk will be in Rogers-Stout Hall and nationalacademies.org/visas/Traveling_to_US.html will be open Saturday, October 15, 7:30 a.m.-4:00p.m. and and http: 1/travel . state. gov /visa/index. html. If you Sunday, October 16, 8:00 a.m.-noon. Fees are US$40 for need a preliminary conference invitation in order to AMS or CMS members; US$60 for nonmembers; and US$5 secure a visa, please send your request to dl s@ams . o rg. for students, unemployed mathematicians, and emeritus If you discover you do need a visa, the National members. Fees are payable on site by cash, check, or credit Academies website (see above) provides these tips for card. successful visa applications: ,., Visa applicants are expected to provide evidence that Travel they are intending to return to their country of residence. The official airline for the meetings is Delta Airlines. Take Therefore, applicants should provide proof of "binding" advantage of Delta's new SimpliFaresT" and enjoy the or sufficient ties to their home country or permanent following benefits: residence abroad. This may include documentation of the • No Saturday-night stay required-more flexibility following: • Always affordable-realize up to 50% savings on • family ties in home country or country of legal everyday fares in the contiguous forty-eight states permanent residence, • Lower change fees- reduced from $100 to $50 to • property ownership, change travel plans • bank accounts, • Just eight fares-less guessing and easier planning • employment contract or statement from employer To make immediate reservations call Delta Air Lines at stating that the position will continue when the employee 800-221-1212. Be sure to reference US738367060 or visit returns. http: 1 jwww. delta. com and enter Sky Bonus account '' Visa applications are more likely to be successful if number US738367060 in your passenger information done in a visitor's home country than in a third country; screen to be recognized as a participant of the Joint Math­ ,., Applicants should present their entire trip itinerary, ematics Meetings. Your benefits include: including travel to any countries other than the United • No service fees States, at the time of their visa application. • 1,000 SkyMile bonus points ,., Include a letter of invitation from the meeting orga­ • Skip the airport lines; check in online Airline service is provided by Tri-Cities Regional Airport nizer or the U.S. host, specifying the subject, location and (TRI) in nearby Blountville, TN, about 20 miles from John­ dates of the activity, and how travel and local expenses will son City. Taxi fare to campus is about US$30; there is no be covered. shuttle service. '' If travel plans will depend on early approval of the visa There is also Greyhound Bus Line service at the John­ application, specify this at the time of the application. son City bus station. '' Provide proof of professional scientific and/or educational status (students should provide a university Car Rental transcript). Avis is the official car rental company for the sectional This list is not to be considered complete. Please visit meeting in Johnson City, Tennessee. All rates include un­ the websites above for the most up-to-date information. limited free mileage. Weekend daily rates are available Weather from noon Thursday-Monday at 11:59 P.M. Rates for this meeting are effective October 8, 2005-0ctober 23, 2005, During October the average high and low temperatures are and begin at US$26/day (weekend rate). Should a lower 69°F and 45°F, respectively. qualifying rate become available at the time of booking, Avis is pleased to offer a 5% discount off the lower qual­ ifying rate or the meeting rate, whichever is lowest. Rates do not include any state or local surcharges, tax, optional coverages, or gas refueling charges. Renters must meet Avis's age, driver, and credit requirements. Reservations can be made by calling 800-3 31 -1600 or online at

AUGUST 2005 NOTICES OF THE AMS 811 Meetings & Conferences

Dynamic Equations on Time Scales (Code: SS SA), Lynn H. Lincoln, Nebraska Erbe and Allan C. Peterson, University of Nebraska­ Lincoln. University of Nebraska in Lincoln Geometric Methods in Group Theory and Semigroup Theory October 21-2 3, 2005 (Code: SS 6A), Susan M. Hermiller and John C. Meakin, University of Nebraska-Lincoln, and Zoran Sunik, Texas Friday - Sunday A&M University. Meeting #lOll Geometry of Differential Equations (Code: SS llA), Jeanne Central Section Nielsen Clelland, University of Colorado, Irina A. Kogan, Associate secretary: Susan J. Friedlander North Carolina State University, and Zhijun Qiao, Univer­ Announcement issue of Notices: August 2005 sity of Texas-Pan American. Program first available on AMS website: September 8, 2005 Graph Theory(Code: SS SA), Andrew J. Radcliffe, University Program issue of electronic Notices: October 2005 of Nebraska-Lincoln, Zsuzsanna Szaniszlo, Valparaiso Issue of Abstracts: Volume 26, Issue 4 University, and Jonathan Cutler, University of Nebraska­ Lincoln. Deadlines K-theory and Algebraic Cycles (Code: SS 16A), Christian For organizers: Expired Haesemeyer, University of Illinois at Urbana-Champaign, For consideration of contributed papers in Special Sessions: and Gregory Grant Piepmeyer and Mark Edward Walker, Expired University of Nebraska-Lincoln. For abstracts: August 30, 2005 The scientific information listed below may be dated. For Large Cardinals in Set Theory (Code: SS 4A), Paul B. Larson, the latest information, see www. ams. org/amsmtgs/ Miami University, Justin Tatch Moore, Boise State University, sectional . html. and Ernest Schimmerling, Carnegie Mellon University. Mathematical Ecology (Code: SS 9A), David Logan, University Invited Addresses of Nebraska-Lincoln, and William Robert Wolesensky, Sir Michael Atiyah, University of Edinburgh, The nature College of St. Mary. of space. (AMS Einstein Public Lecture in Mathematics "in Mathematical Education of Teachers (Code: SS lSA), W. james celebration of the lOOth anniversary of Albert Einstein's Lewis, University of Nebraska-Lincoln, Cheryl Lynn Olsen, annus mirabilis"). Shippensburg University of Pennsylvania, and Ira J. Papick, Howard A. Masur, University of Illinois at Chicago, Billiards University of Missouri-Columbia. in polygons: Connections of geometry and complex analy­ Mathematical and Engineering Aspects of Coding Theory sis to dynamical systems. (Code: SS 3A), Lance Perez and Judy Walker, University Alejandro Uribe, University of Michigan, Title to be of Nebraska-Lincoln. announced. Nonlinear Analysis and Control of Partial Differential Judy Walker, University of Nebraska, Title to be announced. Equations (Code: SS 13A), George Avalos, Petronela Radu, Jack Xin, University of Texas, Title to be announced. Mohammad A. Rammaha, and Richard L. Rebarber, University of Nebraska-Lincoln. Special Sessions Randomness in Computation (Code: SS 7A), John M. Hitch­ Algebraic Geometry (Code: SS lA), Brian Harbourne, Uni­ cock, University of Wyoming, Aduri Pavan, Iowa State versity of Nebraska-Lincoln, and Bangere P. Purnaprajna, University, and Vinodchandran Variyam, University of University of Kansas. Nebraska-Lincoln. Analysis of Partial Differential and Integral Equations Recent Progress in Operator Algebras (Code: SS 2A), Allan P. (Code: SS 18A), Congming Li, University of Colorado. Donsig and David R. Pitts, University of Nebraska-Lincoln. Association Schemes and Related Topics (Code: SS 22A), Representation Theory ofNoetherian Rings (Code: SS 12A), Sung Yell Song, Iowa State University, and Paul M. Roger A. Wiegand and Sylvia Margaret Wiegand, Uni­ Terwilliger, University of Wisconsin. versity of Nebraska-Lincoln. Calculus of Variations (Code: SS 17A), Mikil Foss, University Scattering and Spectral Problems in Geometry(Code: SS 21A), of Nebraska-Lincoln, and Giovanni Leoni, Carnegie Mellon Peter A. Perry, University of Kentucky, and Alejandro Uribe, University. University of Michigan. Combinatorial Matrix Theory(Code: SS lOA), Leslie Hogben, Undergraduate Research (Code: SS 19A), Richard L. Iowa State University, and Bryan L. Shader, University of Rebarber and Gordon S. Woodward, University of Nebraska­ Wyoming. Lincoln. Commutative Algebra (Code: SS 14A), Lars Winther Universal Algebra and Order (Code: SS 20A), John William Christensen, Srikanth B. Iyengar, and Sean M. Sather­ Snow, Sam Houston State University, and Japheth L. M. Wagstaff, University of Nebraska-Lincoln. Wood, Chatham College.

812 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Meetings & Conferences

Accommodations Reception Participants should make their own arrangements directly The Department of Mathematics will a host a reception with a hotel of their choice as early as possible. Special rates immediately following the lecture in the Van Brunt Visitor have been negotiated with the hotels listed below. Rates Center. quoted do not include taxes. The AMS is not responsible for rate changes or for the quality of the accommoda­ Parking tions. When making a reservation, participants should The closest public parking to the meeting site is found at state that they are with the American Mathematical the Stadium Drive parking garage. From the Lincoln air­ Society (AMS) Sectional Meeting. Cancellation and early port take I-80 to the Downtown exit (401A) going south. checkout policies vary; be sure to check when you make Turn left on P Street; turn left onto 11th Street; turn left your reservation. onto Q Street; turn right onto 1Oth Street, staying on 1Oth Holiday Inn Downtown, 141 North 9th Street, Lincoln, until T Street. Entry to the parking garage will be to the NE 68508-1311; phone: 402-475-4011, fax: 402-475-4366; left. Cost at the time of this printing is US$0.45 per 1/2 US$71/single or double, about six blocks to the meeting hour for the first hour; US$0.60 per hour thereafter; site. Deadline for reservations is September 30, 2005. Be US$5.00 maximum per day. A map of the parking facili­ sure to check cancellation and early checkout policies. ties can be found at http: I /www. downtown lincoln. o rg/ Embassy Suites, 1040 P Street, Lincoln, NE; phone: 402- parking/pdfs/DowntownParkingMap.pdf. 474-1111; US$109/single or double, complimentary hot breakfast daily; about four blocks to the meeting site. Registration and Meeting Information Deadline for reservations is September 30, 2005. Be sure The meeting is on the city campus of the University of to check cancellation and early checkout policies. Nebraska-Lincoln, Nebraska. Sessions and Invited Town House Mini Suites Motel, 17 44 M Street, Lincoln, Addresses will take place in the Nebraska Union, Avery NE; phone: 800-279-1744; US$44 single or US$ 51 double, Hall, and surrounding buildings. The location of the about 1/2 mile to the meeting site. Deadline for reserva­ registration desk will be announced; it will be open tions is September 30, 2005. Be sure to check cancellation Friday, October 21, noon-5:00 p.m. and Saturday, and early checkout policies. October 22, 8:00 a.m.-4:30 p.m. Fees are US$40 for AMS or CMS members; US$60 for nonmembers; and Food Service US$5 for students, unemployed mathematicians, and There are many restaurants in the downtown area for emeritus members. Fees are payable on site by cash, lunch and dinner, as well as the student union. A list of check, or credit card. restaurants will be available at the registration desk. Travel and Campus Map local Information A campus map is found at http: I jwww. un l . edu/un l pub/ The mathematics department's webpage is located at tour/unlmaps/. The University of Nebraska-Lincoln http: I /www. math. un l . edu; the university's homepage is campus is four miles from the Lincoln Municipal Airport http: I /www. un l . edu. Other local information can be (LNK) (see http: I jwww. l i nco l nai rpo rt. com), which is found at the Lincoln Convention and Visitor's Bureau served by United and Northwest. It is also possible to website http: I /www. lincoln. o rg. fly into Omaha (OMA) (see www. epp l eyai rfi e l d. com), rent a car, and drive the 60-mile distance to Lincoln. Other Activities The official airline for the meetings is Delta Airlines. Take Book Sales: Examine the newest titles from the AMS! Many advantage of Delta's new SimpliFares™ and enjoy the of the AMS books will be available at a special discount following benefits: available only at the meeting. Complimentary coffee will • No Saturday-night stay required-more flexibility be served courtesy of AMS Membership Services. • Always affordable-realize up to 50% savings on everyday fares in the contiguous forty-eight states Special Presentation • Lower change fees-reduced from $100 to $50 to The American Mathematical Society is pleased to inaugu­ change travel plans rate a series of public lectures entitled The AMS Einstein • Just eight fares- less guessing and easier planning Public Lecture in Mathematics "in celebration of the 100th To make immediate reservations call Delta Air Lines at anniversary of Albert Einstein's annus mirabilis" to be 800-221-1212. Be sure to reference US738367060 or visit given annually at one of its eight sectional meetings. The http: I jwww. delta. com and enter Sky Bonus account Department of Mathematics at UNL is honored that the AMS number US738367060 in your passenger information has chosen the Lincoln meeting for its first public lecture screen to be recognized as a participant of the Joint Math­ and that Abel prizewinner Sir Michael Atiyah, University ematics Meetings. Your benefits include: of Edinburgh, will be the speaker. He will speak on "The • No service fees Nature of Space", Friday, October 21, in Kimball Hall at • 1,000 SkyMile bonus points 4:00p.m. • Skip the airport lines; check in online

AUGUST 2005 NOTICES OF THE AMS 813 Meetings & Conferences

Ground transportation from the airport: If you are ,., Visa applications are more likely to be successful if staying at the Holiday Inn or Embassy Suites, call the hotel done in a visitor's home country than in a third country. from the airport to request a shuttle. '' 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 Lincoln, Nebraska. All rates include unlimited nizer or the U.S. host, specifying the subject, location and free mileage. Special rates for this meeting are effective dates of the activity, and how travel and local expenses will October 14, 2005-0ctober 29, 2005, and begin at $27 / day be covered. for a subcompact car at the weekend rate (available from '' If travel plans will depend on early approval of the visa noon Thursday through Monday at 11:59 p.m.). Should a application, specify this at the time of the application. lower qualifying rate become available at the time of '' Provide proof of professional scientific and/or booking, Avis is pleased to offer a 5% discount off the educational status (students should provide a university lower qualifying rate or the Meeting rate, whichever is transcript). lowest. Rates do not include any state or local surcharges, This list is not to be considered complete. Please visit tax, optional coverages or gas refueling charges. Renters the websites above for the most up-to-date information. must meet Avis' age, driver, and credit requirements. Reminder: Machine-readable passports required by Reservations can be made by calling 800-331-1600 or on­ June 26, 2005. The Department of Homeland Security line at http: I /www . avis. com. Meeting Avis Discount reminds travelers from the 2 7 Visa Waiver Program (VWP) Number B159266. countries that as of June 26, 2005, they must have a Shuttle Services: Eppley Express, 800-888-9793, machine-readable passport to enter the United States http: I /www. eppl eyexpress. com; OMALiNK, 877-473- without a visa. Beginning June 26, 2005, transportation 5465, http: //www.omal ink.com. carriers will be fined US$3,300, per violation, for trans­ Driving Directions: If you are arriving in Lincoln via porting any VWP traveler to the United States without Interstate 80, take the Downtown Lincoln Exit (onto I-180). a machine-readable passport. Similarly, VWP travelers It is difficult to miss seeing the football stadium on the arriving in the United States on that date without a ma­ left as you enter downtown Lincoln from I-180. Stay on chine-readable passport should not anticipate being I-180 past the football stadium until it becomes 9th Street. granted one-time entry into the country. As an alternative Then turn left on P Street and left again on lOth Street. for persons with immediate travel plans who are unable Proceed north on lOth Street, keeping to the right-hand to obtain a machine-readable passport in time, the indi­ lane as you pass "Q" Street, and you will see the stadium vidual may apply for a U.S . visa at a U.S. consulate or (and the parking structure) on the right. embassy abroad. Special Travel Information for International Participants. Visa regulations are continually changing Weather for travel to the United States. Visa applications may Weather conditions in Lincoln during October are usually take from three to four months to process and require very pleasant, with lows of about 30°F and highs around a personal interview, as well as specific personal infor­ 50°F. mation. International participants should view the important information about traveling to the U.S. found at http: I jwww 7. national academies. o rg/vi sas/ Eugene, Oregon Traveling_to_US.html and http: //travel .state. gov /visa/index. html . If you need a preliminary University of Oregon conference invitation in order to secure a visa, please send your request to wsd@ams. org. November 12-1 3, 2005 If you discover you do need a visa, the National Saturday - Sunday Academies website (see above) provides these tips for successful visa applications: Meeting #1 012 ''Visa applicants are expected to provide evidence that Western Section they are intending to return to their country of residence. Associate secretary: Michel L. Lapidus Therefore, applicants should provide proof of "binding" Announcement issue of Notices: September 2005 or sufficient ties to their home country or permanent Program first available on AMS website: September 29, residence abroad. This may include documentation of the 2005 following: Program issue of electronic Notices: November 2005 • family ties in home country or country of legal Issue of Abstracts: Volume 26, Issue 4 permanent residence, • property ownership, Deadlines • bank accounts, For organizers: Expired • employment contract or statement from employer For consideration of contributed papers in Special Sessions: stating that the position will continue when the employee July 26, 2005 returns. For abstracts: September 20, 2005

814 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Meetings & Conferences

The scientific information listed below may be dated. For the latest information, see www. ams. o rg/ amsmtgs/ Taichung, Taiwan sectional . html. Tung-Hai University Invited Addresses December 14-18, 2005 Matthew Foreman, University of California Irvine, Title to be announced. Wednesday - Sunday Mark Haiman, University of California Berkeley, Title to be Meeting #1 013 announced. First ]oint International Meeting between the AMS and the Wilhelm Schlag, California Institute of Technology, Title Taiwanese Mathematical Society. to be announced. Associate secretary: John L. Bryant Hart H. Smith, University of Washington, Title to be Announcement issue of Notices: June 2005 announced. Program first available on AMS website: Not applicable Program issue of electronic Notices: Not applicable Special Sessions Issue of Abstracts: Not applicable Algebraic Combinatorics and Geometry (Code: SS 7A), Deadlines Sara C. Billey, University of Washington, and Mark Haiman, For organizers: Expired University of California Berkeley. For consideration of contributed papers in Special Sessions: Algebraic Geometry Motivated by Physics (Code: SS 9A), To be announced Alexander Polishchuk and Arkady Vaintrob, University For abstracts: To be announced of Oregon. Algebraic Topology of Moduli Spaces (Code: SS SA), The scientific information listed below may be dated. For Boris I. Botvinnik, University of Oregon, Uwe Kaiser, Boise the latest information, see www.ams.org/amsmtgs/ State University, and Dev Sinha, University of Oregon. i nternmtgs. html. Applications of Algebraic Topology(Code: SS 12A), Daniel Invited Addresses Dugger and Hal Sadofsky, University of Oregon. Harmonic Analysis and PDEs (Code: SS 13A), Wilhelm Ching-Shui Cheng, Institute of Statistical Science, Acade­ Schlag, California Institute of Technology, and Hart F. mia Sinica, Title to be announced. Smith, University of Washington. Lawrence Ein, University of Illinois at Chicago, Title to be K-Theory in M- Theory (Code: SS 6A), Gregory D. Landweber, announced. University of Oregon, and Charles F. Doran, University of Chang-Shou Lin, National Chung Cheng University, Title Washington. to be announced. New Directions in Spectral Theory and Geometric Analysis Richard M. Schoen, Stanford University, Title to be (Code: SS llA), Leon Friedlander, University of Arizona, announced. and Patrcik McDonald, New College of Florida. jing Yu, National Tsing Hua University, Title to be Noncom mutative Algebra and Noncommutative Birational announced. Geometry (Code: SS 3A), Arkady Dmitrievich Berenstein, Jiu-Kang Yu, Purdue University, Title to be announced. University of Oregon, and Vladimir Retakh, Rutgers Uni­ versity. Special Sessions Partial Differential Equations with Applications (Code: SS Affine Algebraic Geometry, Ming-Chang Kang, National 4A), Alexander Panchenko, Washington State University, Taiwan University, and Kwai-Man Fan, National Chung R. E. Showalter, Oregon State University, and Hong-Ming Cheng University. Yin, Washington State University. Algebraic Geometry, Jung-Kai Chen, National Taiwan Uni­ Regular Algebras and Noncommutative Projective Geom­ versity, Chin-Lung Wang, National Central University, and etry (Code: SS 2A), Brad Shelton, University of Oregon, Robert Lazarsfeld, University of Michigan. Michaela Vancliff, University of Texas at Arlington, and Differential Geometry, Dong-Ho Tsai, National Tsing Hua James J. Zhang, University of Washington. University, and Bennett Chow, University of California Representations of Groups and Algebras (Code: SS SA), San Diego. Jonathan W. Brundan, Alexander S. Kleshchev, and Viktor Discrete Mathematics (Graph Coloring), Gerard J. Chang, Ostrik, University of Oregon. National Taiwan University, Douglas B. West, University Resolutions (Code: SS lA), Christopher Alan Francisco, Uni­ of Illinois at Urbana-Champaign, and Xuding Zhu, versity of Missouri, and Irena Peeva, Cornell University. National Sun Yat-sen University. Wavelets, Frames, and Related Expansions (Code: SS lOA), Dynamics and Differential Equations, Song-Sun Lin, Marcin Bownik, University of Oregon, and Darrin M. National Chiao Tung University, and Shui-Nee Chow, Speegle, St. Louis University. Georgia Institute of Technology.

AUGUST 2005 NOTICES OF THE AMS 815 Meetings & Conferences

Lie Algebra and Representation Theory, Shun-Jen Cheng, The scientific information listed below may be dated. For National Taiwan University, and Brian J. Parshall and the latest information, see www. ams. org/amsmtgs/ Weiqiang Wang, University of Virginia. sectional . html. Number Theory (Arithmetic Geometry over Local and Global joint Invited Address Fields), Liang-Chung Hsia, National Central University, and William A. Cherry, University of North Texas. Svetlana Y. Jitomirskaya, University of California Irvine, Title to be announced (AMS-MAA Invited Address). Operator Theory and Control, Fang-Eo Yeh, Tung-Hai Uni­ versity, and Nicholas]. Young, University of Newcastle. AMS Invited Addresses Optimization and Applications, Soon-Yi Wu, National Cheng Herbert Edelsbrunner, Duke University, Title to be Kung University, and Shu-Cherng Fang, Industrial Engi­ announced. neering and Operations Research, North Carolina State University. David Eisenbud, Mathematical Sciences Research Institute, Title to be announced (AMS Retiring Presidential Address). Partial Differential Equations and Geometric Analysis, Charles L. Fefferman, Princeton University, Chiun-Chuan Chen and Yng-Ing Lee, National Taiwan Uni­ Title to be announced. versity, Sun-Yung Alice Chang, Princeton University, and Robert]. Sibner, Graduate College, City University of New Mikhail Kapranov, Yale University, Title to be announced. York. Hendrik W. Lenstra Jr., Universiteit Leiden, Title to be Probability, Tai-Ho Wang, National Chung Cheng Univer­ announced (AMS Colloquium Lectures). sity, Ching-Tang Wu, National Kaohsiung University, and Dusa McDuff, SUNY at Stony Brook, Title to be announced. George Yin, Wayne State University. Michael Savageau, University of California Davis, Title to Scientific Computing, Wei-Cheng Wang, National Tsing-Hua be announced (Josiah Willard Gibbs Lecture). University, and Thomas Y. Hou, California Institute of Technology. AMS Special Sessions Some sessions are cosponsored with other organiza­ Statiscal Modeling and Applications, Ming-Yen Cheng, tions. These are noted within the parenthesis at the end National Taiwan University, and Jianqing Fan, Department of each listing, where applicable. of Operations Research and Financial Engineering, Princeton University. Algebraic Groups, Symmetric Spaces, and Invariant Theory (Code: SS 15A), Aloysius G. Helminck, North Carolina State University, and Dan Gagliardi, St. Lawrence University San Antonio, Texas (AMS). Algebraic Statistics: Theory and Practice (Code: SS 4A), Henry B. Gonzalez Convention Center Seth M. Sullivant, University of California Berkeley, and Elizabeth S. Allman, University of Southern Maine (AMS). january 1 2-1 5, 2006 Algebraic and Enumerative Combinatorics (Code: SS 12A), Thursday - Sunday Catherine H. Yan, Texas A&M University, Marcelo Aguiar, Texas A&M University, Joseph P. Kung, University of North Meeting #1 014 Texas, and Laura F. Matusevich, University of Pennsylva­ ]oint Mathematics Meetings, including the 112th Annual nia (AMS). Meeting of the AMS, 89th Annual Meeting of the Mathe­ Analysis and Implementation of Finite Element Methods matical Association of America, annual meetings of the (Code: SS 19A), Atife Caglar, University of Wisconsin, Association for Women in Mathematics (A WM) and the Green Bay (AMS-SIAM). National Association of Mathematicians (NAM), the winter Ancient and Nonwestern Mathematics (Code: SS 14A), meeting of the Association for Symbolic Logic (ASL), with Duncan]. Melville, St. Lawrence University (AMS-MAA). sessions contributed by the Society for Industrial and Applied Mathematics (SIAM). Arithmetic Geometry and Modular Forms (Code: SS 16A), Associate secretary: Matthew Miller Matthew A. Papanikolas, Texas A&M University and Ahmad M. El-Guindy, Texas A&M University (AMS). Announcement issue of Notices: October 2005 Program first available onAMS website: November 1, 2005 Boundary Value Problems for Ordinary Differential Equations Program issue of electronic Notices: January 2006 (Code: SS 22A), John R. Graef, University of Tennessee at Issue of Abstracts: Volume 27, Issue 1 Chattanooga, and Johnny L. Henderson, Baylor University ( AMS-SIAM). Deadlines Commutative Rings and Monoids (Code: SS 25A), Scott T. For organizers: Expired Chapman, Trinity University, and James B. Coykendall, For consideration of contributed papers in Special Sessions: North Dakota State University (AMS). August 3, 2005 Contemporary Dynamical Systems (Code: SS 21A), Dmitry For abstracts: September 28, 2005 Zenkov, University of Michigan, Youngna Choi, Montclair

816 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Meetings & Conferences

State University, Anthony M. Bloch, University of Michi­ New Developments in Symplectic Topology (Code: SS 34A), gan, Todd L. Fisher, University of Maryland, Melvin Leok, Dusa McDuff, SUNY at Stony Brook, Aleksey Zinger, SUNY University of Michigan, David S. Richeson, Dickenson at Stony Brook and Stanford University, Ely Kerman, Uni­ College, and James S. Wiseman, Swarthmore College (AMS­ versity of Illinois Urbana-Champaign, and Margaret F. SIAM). Symington, Georgia Institute of Technology and Mercy Continued Fractions (Code: SS 6A), Nancy Wyshinsky, College (AMS). Trinity College, and James G. McLaughlin, Trinity College Nonautonomous Discrete Dynamics (Code: SS 36A), (AMS). Saber N. Elaydi, Trinity University, and Jim M. Cushing, Current Events (Code: SS lOA), David Eisenbud, Mathe­ University of Arizona (AMS). matical Sciences Research Institute (AMS). Nonlinear Dynamical Systems (Code: SS llA), Zhijun Qiao, Division Algebras, Galois Theory, Cohomology and Geom­ University of Texas Pan American, Andras Balogh, Uni­ etry (Code: SS lA), Kelly L. McKinnie, University of Texas versity of Texas Pan American, Guihua Fei, University of at Austin, and David J. Saltman, University of Texas at Minnesota Duluth, and Zhaosheng Feng, University of Austin (AMS). Texas Pan American (AMS-SIAM). Dynamic Equations With Applications (Code: SS 23A), Allan Quantum Invariants of Knots and 3-Manifolds (Code: SS C. Peterson, University of Nebraska, and Martin J. Bohner, 18A), Patrick M. Gilmer, Louisiana State University, and University of Missouri Rolla (AMS). Charles D. Frohman, University of Iowa (AMS). Extension of Functions (Code: SS SA), Alvario Arias, Recent Advances in Mathematical Biology and Epidemiol­ University of Denver, Charles L. Fefferman, Princeton ogy (Code: SS 29A), Sophia Jang, University of Louisiana University, Edward W. Odell, University of Texas Austin, at Lafayette, Linda Allen, Texas Tech University, and and Thomas Slumprecht, Texas A&M University (AMS). Lih-lng Roeger, Texas Tech University (AMS-MAA-SIAM). Field Extensions and Algorithms (Code: SS 33A), Peter Recent Trends in Convex and Discrete Geometry (Code: SS Stevenhagen, University of Leiden, and H. W. Lenstra, 17A), Valeriu Sol tan, George Mason University, Tibor University of Leiden (AMS). Bisztriczky, University of Calgary, and Paul Goodey, Uni­ versity of Oklahoma (AMS). Frames and Operator Theory in Analysis and Signal Processing (Code: SS 20A), Peter R. Massopust, Tuboscope Research in Mathematics by Undergraduates (Code: SS 28A), Vetco Pipeline Services, David R. Larson, Texas A&M Darren Narayan, Rochester Institute of Technology, Carl University, Manos I. Papadakis, University of Houston, V. Lutzer, Rochester Institute of Technology, Michael J. Zuhair Nashed, University of Central Florida, Ahmed I. Fisher, California State University Fresno, Bernard Brooks, Zayed, DePaul University, and Minh Chuong Nguyen, Rochester Institute of Technology, and Tamas I. Wiandt, Institute of Mathematics, Hanoi Vietnam (AMS-SIAM). Rochester Institute of Technology (AMS-MAA-SIAM). History of Mathematics (Code: SS 26A), Joseph W. Dauben, Stochastic, Large Scale and Hybrid Systems with Applica­ Herbert H. Lehman College (CUNY), Patti Hunter, Westmont tions (Code: SS 7A), Aghalaya S. Vatsala, University of College, and Karen H. Parshall, University of Virginia Louisiana at Lafayette, and Gangaram S. Ladde, University (AMS-MAA). of Texas Arlington (AMS-SIAM). Interdisciplinary Research Involving Analysis and Logic (Code: Symbolic-numeric Computation and Applications (Code: SS 3 SA), Su Gao, University of North Texas, Jose N. Iovino, SS 30A), Agnes Szanto, North Carolina State University, Jan University of Texas San Antonio, and Itay Ben-Yacov, Uni­ Verschelde, University of Illinois Chicago, and Zhong­ versity of Wisconsin Madison (AMS-ASL). gang Zeng, Northeastern Illinois University (AMS-SIAM). Invariant Theory (Code: SS 31A), Mara D. Neusel, Texas Syzygies in Commutative Algebra and Geometry (Code: SS Tech University (AMS). 32A), Irena Peeva, Cornell University, Sorin E. Popescu, SUNY at Stony Brook, and Gregory G. Smith, Queen's Mahler Measure and Heights (Code: SS 13A), Michael J. University (AMS). Mossinghoff, Davidson College, and Jeffrey D. Vaaler, University of Texas at Austin (AMS). Theory and Application of Stochastic Differential Equa­ tions (Code: SS 24A), Armando Arciniega, University of Many Lives of Lattice Theory, the Theory of Ordered Sets, Texas at San Antonio, and Edward J. Allen, Texas Tech and Universal Algebra (Code: SS 9A), Japheth L. M. Wood, University (AMS-SIAM). Chatham College, John W. Snow, Sam Houston State Uni­ versity, Jonathon D. Farley, Harvard University, Stefan E. Time Reversal Methods: Analysis and Applications (Code: Schmidt, Phoenix Math Systems Modeling, Inc., and SS 3A), Peter A McCoy, U.S. Naval Academy, and Reza Anthony A Harkin, Harvard University (AMS). Malek-Madani, U.S. Naval Academy (AMS-SIAM). Mathematics Education Reform (Code: SS SA), Bonnie S. Topological Spaces Associated with C(X) (Code: SS 27 A), Saunders, University of Illinois at Chicago, William H. Chawne M. Kimber, Lafayette College, and Warren Wm. Barker, Bowdoin College, Dale R. Oliver, Humboldt State McGovern, Bowling Green State University (AMS). University, and Kenneth Millet, University of California Value Distribution in Classical and p-adic Functions Theory Santa Barbara (AMS-MAA-MER). (Code: SS 2A), Alain Escassut, University Blaise Pascal,

AUGUST 2005 NOTICES OF THE AMS 817 Meetings & Conferences

Chung-Chun Yang, Hong Kong University of Science and Michael Larsen, University of Indiana, Title to be Technology, and Ilpo Laine, University of Joensuu (AMS). announced. Christopher M. Skinner, University of Michigan, Title to Miami, Florida be announced. Special Sessions Florida International University Combinatorial Algebraic Geometry (Code: SS 2A), Juan C. April1-2, 2006 Migliore, University of Notre Dame, and Uwe R. Nagel, Saturday - Sunday University of Kentucky. Commutative Algebra (Code: SS 1A), Alberto Corso, Meeting #1 015 University of Kentucky, Claudia Polini, University of Notre Southeastern Section Dame, and Bernd Ulrich, Purdue University. Associate secretary: Matthew Miller Developments and Applications in Differential Geometry Announcement issue of Notices: December 2005 (Code: SS 4A), Jianguo Cao, Xiaobo Liu, and Brian Smyth, Program first available on AMS website: February 16, 2006 University of Notre Dame. Program issue of electronic Notices: April 2006 Issue of Abstracts: Volume 27, Issue 2 Ergodic Theory (Code: SS 3A), Nikos Frantzikinakis, Pennsylvania State University, Bryna R. Kra, Northwestern Deadlines University, and Mate Wierdl, University of Memphis. For organizers: September 1, 2005 For consideration of contributed papers in Special Sessions: December 13, 2005 Durham, For abstracts: February 7, 2006 New Hampshire Notre Dame, Indiana University of New Hampshire University of Notre Dame April22-23, 2006 Saturday - Sunday April8-9, 2006 Saturday - Sunday Meeting #1 01 7 Eastern Section Meeting #1 016 Associate secretary: Lesley M. Sibner Central Section Announcement issue of Notices: January 2006 Associate secretary: Susan]. Friedlander Program first available on AMS website: March 9, 2006 Announcement issue of Notices: December 2005 Program issue of electronic Notices: April 2006 Program first available on AMS website: February 2 3, 2006 Issue of Abstracts: Volume 27, Issue 2 Program issue of electronic Notices: April 2006 Issue of Abstracts: Volume 27, Issue 2 Deadlines Deadlines For organizers: September 22, 2005 For consideration of contributed papers in Special Sessions: For organizers: September 9, 2005 January 3, 2006 For consideration of contributed papers in Special Sessions: For abstracts: February 28, 2006 December 20, 2005 For abstracts: February 14, 2006 The scientific information listed below may be dated. For The scientific information listed below may be dated. For the latest information, see www. ams. org/amsmtgs/ sectional . htm l. the latest information, see www. ams. org/amsmtgs/ sectional . htm l. Invited Addresses Invited Addresses Ailana M. Fraser, University of British Columbia, Title to Douglas N. Arnold, Institute for Mathematics and Appli­ be announced. cations, University of Minnesota, Title to be announced. Dmitri Nikshych, University of New Hampshire, Title to Bela Bollobas, Cambridge University and University of be announced. Memphis, Inhomogeneous random graphs (Erdos Memor­ Florian Pop, University of Pennsylvania, Title to be ial Lecture). announced. Steven C. Hofmann, University of Missouri, Title to be Konstantina Trivisa, University of Maryland, College Park, announced. Title to be announced.

818 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Meetings & Conferences

Special Sessions History and Philosophy of Mathematics (Code: SS 1A), Shawnee L. McMurran, California State University, San Regular Operators, and Applications (Code: Banach Lattices, Bernardino, and james j. Tattersall, Providence College. SS 3A), A. K. Kitover, Community College of Philadelphia, M. Orhon, University of New Hampshire, and A. W. Wickstead, Queen's University of Belfast. Salt Lake City, Utah Banach Spaces of Analytic Functions (Code: SS 2A), Rita A. Hibschweiler, University of New Hampshire, and University of Utah Thomas H. MacGregor, SUNY Albany and Bowdoin College. 8, 2006 Discrete and Convex Geometry (Code: SS 1A), Daniel A. October 7- Klain, University of Massachusetts (Lowell), Barry R. Saturday - Sunday Monson, University of New Brunswick, and Egon Schulte, Meeting #1 019 Northeastern University. Western Section Associate secretary: Michel L. Lapidus Announcement issue of Notices: July 2006 San Francisco, Program first available on AMS website: August 24, 2006 Program issue of electronic Notices: October 2006 California Issue of Abstracts: Volume 27, Issue 3

San Francisco State University Deadlines April29-30, 2006 For organizers: March 7, 2006 For consideration of contributed papers in Special Sessions: Saturday - Sunday June 20, 2006 Meeting #1 018 For abstracts: August 15, 2006 Section Western The scientific information listed below may be dated. For secretary: Michel L. Lapidus Associate the latest information, see www. ams. org/amsmtgs/ issue of Notices: January 2006 Announcement secti anal. html. Program first available on AMS website: March 16, 2006 Program issue of electronic Notices: April 2006 Invited Addresses Issue of Abstracts: Volume 27, Issue 2 William Arveson, University of California Berkeley, Title Deadlines to be announced. For organizers: September 30, 2005 Alexei Borodin, California Institute of Technology, Title For consideration of contributed papers in Special Sessions: to be announced. January 10, 2006 Izabella joanna Laba, University of British Columbia, Title For abstracts: March 7, 2006 to be announced. The scientific information listed below may be dated. For Darren Long, University of California Santa Barbara, Title see www. ams. org/amsmtgs/ the latest information, to be announced. sectional . html. Special Sessions Invited Addresses Harmonic Analysis: Trends and Perspectives (Code: SS 1A), of California Los Angeles, Title Lincoln Chayes, University Alex Iosevich, University of Missouri, and Michael T. to be announced. Lacey, Georgia Institute of Technology. C. Robin Graham, University of Washington, Title to be announced. Vadim Kaloshin, California Institute of Technology, Title Cincinnati, Ohio to be announced. University of Cincinnati Benoit B. Mandelbrot, Yale University, From pure mathe­ matics to roughness in art. (Einstein Public Lecture in October 21 - 22, 2006 Mathematics). Saturday - Sunday Yuval Peres, University of California Berkeley, Title to be announced. Meeting #1 020 Central Section Special Sessions Associate secretary: Susan ]. Friedlander Grabner Basis (Code: SS 2A), Bernd Sturmfels and Alexan­ Announcement issue of Notices: July 2006 der Yong, University of California Berkeley. Program first available on AMS website: September 7, 2006

AUGUST 2005 N OTICES OF THE AMS 819 Meetings & Conferences

Program issue of electronic Notices: October 2006 Issue of Abstracts: Volume 27, Issue 3 Fayetteville, Deadlines For organizers: March 21, 2006 Arkansas For consideration of contributed papers in Special Sessions: University of Arkansas July 5, 2006 For abstracts: August 29, 2006 November 3-4, 2006 Friday - Saturday The scientific information listed below may be dated. For the latest information, see www. ams. org/amsmtgs/ Meeting #l 022 sectional.html. Southeastern Section Associate secretary: Matthew Miller Invited Addresses Announcement issue of Notices: September 2006 Suncica Canic, University of Houston, Title to be Program first available on AMS website: September 21, announced. 2006 Bryna R. Kra, Northwestern University, Title to be Program issue of electronic Notices: November 2006 announced. Issue of Abstracts: Volume 27, Issue 4 Ezra N. Miller, University of Minnesota, Title to be Deadlines announced. For organizers: April 3, 2006 Jon G. Wolfson, Michigan State University, Title to be For consideration of contributed papers in Special Sessions: announced. July 18, 2006 For abstracts: September 12, 2006 Storrs, Connecticut University of Connecticut New Orleans, October 28-29, 2006 Louisiana Saturday - Sunday New Orleans Marriott Meeting #1 021 and Sheraton New Orleans Hotel Eastern Section Associate secretary: Lesley M. Sibner January 4-7,2007 Announcement issue of Notices: July 2006 Thursday - Sunday Program first available on AMS website: September 14, 2006 Meeting #l 023 Program issue of electronic Notices: October 2006 ]oint Mathematics Meetings, including the 113th Annual Issue of Abstracts: Volume 27, Issue 4 Meeting of the AMS, 90th Annual Meeting of the Mathe­ Deadlines matical Association ofAmerica (MAA), annual meetings of For organizers: March 28, 2006 the Association for Women in Mathematics (A TVM) and the For consideration of contributed papers in Special Sessions: National Association of Mathematicians (NAM), and the July 11, 2006 winter meeting of the Association for Symbolic Logic (ASL), For abstracts: September 6, 2006 with sessions contributed by the Society for Industrial and Applied Mathematics (SIAM). Associate secretary: Susan ]. Friedlander Announcement issue of Notices: October 2006 Program first available on AMS website: November 1, 2006 Program issue of electronic Notices: January 2007 Issue of Abstracts: Volume 28, Issue 1

Deadlines For organizers: April1, 2006 For consideration of contributed papers in Special Sessions: To be announced For abstracts: To be announced

820 NOTICES OF THE AMS VOLUME 52, NUMBER 7 Meetings & Conferences

For consideration of contributed papers in Special Sessions: Davidson, To be announced North Carolina For abstracts: To be announced Davidson Colege San Diego, California March 3-4,2007 San Diego Convention Center Saturday - Sunday Southeastern Section January 6- 9, 2008 Associate secretary: Matthew Miller Sunday - Wednesday Announcement issue of Notices: To be announced ]oint Mathematics Meetings, including the 114th Annual Program first available on AMS website: To be announced Meeting of the AMS, 91st Annual Meeting of the Mathe­ Program issue of electronic Notices: To be announced matical Association ofAmerica (MAA), annual meetings of Issue of Abstracts: To be announced the Association for Women in Mathematics (A WM) and the National Association of Mathematicians (NAM), and the Deadlines winter meeting of the Association for Symbolic Logic (ASL). For organizers: August 3, 2006 Associate secretary: Michel L. Lapidus For consideration of contributed papers in Special Sessions: Announcement issue of Notices: October 2007 To be announced Program first available on AMS website: November 1, 2007 For abstracts: To be announced Program issue of electronic Notices: January 2008 Issue of Abstracts: Volume 29, Issue 1 Deadlines Oxford, Ohio For organizers: April1, 2007 Miami University For consideration of contributed papers in Special Sessions: To be announced March 16-l 7, 2007 For abstracts: To be announced Friday - Saturday Central Section Associate secretary: Susan]. Friedlander Bloomington, Indiana Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Indiana University Program issue of electronic Notices: To be announced April4- 6, 2008 Issue of Abstracts: To be announced Friday - Sunday Deadlines Southeastern Section For organizers: To be announced Associate secretary: Susan]. Friedlander For consideration of contributed papers in Special Sessions: Announcement issue of Notices: To be announced To be announced Program first available on AMS website: To be announced For abstracts: To be announced Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced Deadlines Tucson, Arizona For organizers: September 4, 2007 University of Arizona For consideration of contributed papers in Special Sessions: To be announced April2l-22, 2007 For abstracts: To be announced Saturday - Sunday Southeastern Section Associate secretary: Michel L. Lapidus Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Program issue of electronic Notices: To be announced Issue of Abstracts: To be announced

Deadlines For organizers: September 21, 2006

AUGUST 2005 NOTICES OF THE AMS 821 Meetings & Conferences Washington, New Orleans, District of Columbia Louisiana Marriott Wardman Park Hotel New Orleans Marriott and Sheraton New and Omni Shoreham Hotel Orleans Hotel January 7-l 0, 2009 January 5-8,2011 Wednesday - Saturday Wednesday - Saturday ]oint Mathematics Meetings, including the 117th Annual ]oint Mathematics Meetings, including the llSth Annual Meeting of the AMS, 94th Annual Meeting of the Mathe­ Meeting of the AMS, 92nd Annual Meeting of the Mathe­ matical Association ofAmerica, annual meetings of the As­ matical Association of America (MAA), annual meetings of sociation for Women in Mathematics (A WM) and the National the 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). winter meeting of the Association for Symbolic Logic (ASL). Associate secretary: Susan ]. Friedlander Associate secretary: Lesley M. Sibner Announcement issue of Notices: October 2010 Announcement issue of Notices: October 2008 Program first available on AMS website: November 1, 2010 Program first available on AMS website: November 1, 2008 Program issue of electronic Notices: January 2011 Program issue of electronic Notices: January 2009 Issue of Abstracts: Volume 32, Issue 1 Issue of Abstracts: Volume 30, Issue 1 Deadlines Deadlines For organizers: April 2, 2011 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 San Francisco, California Moscone Center West and the San Francisco Marriott January 6-9, 201 0 Wednesday - Saturday ]oint Mathematics Meetings, including the 116th Annual Meeting of the AMS, 93rd Annual Meeting of the Mathe­ matical Association ofAmerica (MAA), annual meetings of the Association for Women in Mathematics (A WM) and the National Association of Mathematicians (NAM), and the winter meeting of the Association for Symbolic Logic (ASL). Associate secretary: Matthew Miller Announcement issue of Notices: October 2009 Program first available on AMS website: November 1, 2009 Program issue of electronic Notices: January 2010 Issue of Abstracts: Volume 31, Issue 1

Deadlines For organizers: April1, 2009 For consideration of contributed papers in Special Sessions: To be announced For abstracts: To be announced

822 NOTICES OF THE AMS VOLUME 52, NUMBER 7 l.OO ClAy RESEA The Clay Mathe .RCH FEllOWS ANN AMS members may Manolescu and n:tlcs Institute (CMI) has UNCED Venkartesh of th aryam Mirzakhani of H appomted four Research F . . subscribe to receive Fellows' researche foMatwssachusetts Institutea ;~d University, and And~llowVs . Ciprian r o years. echnology. The lnsn as . asy and twice-a-month email MAI.HEMA TICAL S I ute Will fully support The Na tiona~~~s__I;J.. ..f.CTED notifications of news, associates in . emy of Engineerin ( -IQl'lAf announcements about professor ~f cludmg these individual; . NAE) has elected 76 new ~~~i~~o;~~~i,{~~~n~r!~~~~~~s~~a:i~~~~:~~hrn~~:~~= l ~fc~e~~~:~~e~~ -~~~;;~~~:~~n programs, publications, gmeenng and computati o:;:~ programs, and profes~~· lmda R. Petzold Clence, University of C 1.: · mechanical and , and events, as well as a horn1a, Santa alerts about deadlines for fellowship and grant applications, calls for proposals, and meeting registrations. AMS members can sign RANT APPLICATIONS . T I Grants for travel to take up for the service at CThHINA~1~~~;~~ing a ppli cation~next rouenrd2~fo~h~:thr~:;a rtm ents in the U.S. adnd e 05 demic year or summ · h from Ch1na, an www.ams.org/enews. ~=~~J~~;y t: ~~~~~fun~~avis it to t~ e;~ ifus~~u~i~~s~~oath~~~~~~~~i~~ b~ra promin~~~eu .S. math departments .in China may ~~~~d by a gift from Ky and Yu-Fen Fan. The we mathematician. ThiS program 's/ __ due MARCH 15, 2004. includes details and the applica lon THE YEAR PROGRAM . ENTRIES FOR U.S. PROFESSORS OF rt of Education (CASE) and The Carnegie The Council for Advancement and Suppo the U S Professors of the Year Programt for the Advancement of Te~~~ nfr;~~~s~~rtificat~ ~f recognition, and are3 h~na~~e~r~f:sso rs winners recelldve a~~~~~~g~on DC. State winners are also nam~d~~n;uon~ty College District) luncheon he. '" 0 1 th) and Judy Kasab1an (EI Cammo . · Joseph Gallian u u

The deadlines for consideration of contributed papers in Special Sessions at the first AMS fall Section Meetings are as follows: Southeastern Section meeting at Vanderbilt University, Nashville, TN, October 16-17: JUNE 29,2004. See http://www.arns.org/arnsmtgs/210 8 _ deadlines.html. Western Section meeting at the University of New Mexico, Albuquerque, October 16-17: JUNE 29, 2004. See http://www.ams.org/arnsmtgs/2112 _ deadlines.html.

Headlines & Deadlines is a twice-a-month email news service available to AMS members. www.am s.org To unsubscribe from this mailing list visit http://www.ams.org/enews. 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: 1 api dus@math. ucr. edu; telephone: 951- e-mail: [email protected]; telephone: 718-260-3505. 827-5910. Southeastern Section: Matthew Miller, Department of Math­ Central Section: Susan J. 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: mi 11 er@math. sc. edu; telephone: 803-777-3690. 249), Chicago, IL 60607-7045; e-mail: susan@math. nwu. edu; tele­ phone: 312-996-3041.

The Meetings and Conferences section of the Notices March 16-17 Oxford, Ohio p.821 gives information on all AMS meetings and conferences April21-22 Tuscan, Arizona p. 821 approved by press time for this issue. Please refer to the page numbers cited in the table of contents on this page for more 2008 detailed information on each event. Invited Speakers and January 6-9 San Diego, California p.821 Special Sessions are listed as soon as they are approved by Annual Meeting the cognizant program committee; the codes listed are needed April4-6 Bloomington, Indiana p.821 for electronic abstract submission. For some meetings the list may be incomplete. Information in this issue may be dated. 2009 Up-to-date meeting and conference information can be January 7-10 Washington, DC p.822 'found at www. ams. org/meeti ngs/. Annual Meeting 2010 Meetings: January 6-9 San Franciso, California p.822 Annual Meeting 2005 2011 October 8-9 Annandale-on-Hudson, January 5-8 New Orleans, Louisiana p. 822 New York p.807 Annual Meeting October 15-16 Johnson City, Tennessee p.809 Important Information regarding AMS Meetings October 21-23 Lincoln, Nebraska p. 811 Potential organizers, speakers, and hosts should refer to November 12-13 Eugene, Oregon p.814 page 100 in the January 2005 issue of the Notices for general December 14-18 Taiwan p.815 information regarding participation in AMS meetings and conferences. 2006 Abstracts January 12-15 San Antonio, Texas p.816 Speakers should submit abstracts on the easy-to-use interactive Annual Meeting Web form. No knowledge of L:ITJ:X is necessary to submit an April1-2 Miami, Florida p.818 electronic form, although those who use L:ITJ:X may submit April8-9 Notre Dame, Indiana p.818 abstracts with such coding, and all math displays and simi­ April 22-23 Durham, New Hampshire p.818 larily coded material (such as accent marks in text) must be typeset in L:ITJ:X. Visit http://www.ams.org/cgi-bin/ April29-30 San Francisco, California p.819 abstracts/abstract.pl. October 7-8 Salt Lake City, Utah p.819 Questions about abstracts and requests for paper forms October 21-22 Cincinnati, Ohio p.819 may be sent to abs-i nfo@ams. org. October 28-29 Storrs, Connecticut p.820 Paper abstract forms must be sent to Meetings & Confer­ November 3-4 Fayetteville, Arkansas p.820 ences Department, AMS, P.O. Box 6887, Providence, RI 02940. There is a $20 processing fee for each paper abstract. There 2007 is no charge for electronic abstracts. Note that all abstract dead­ January 4-7 New Orleans, Louisiana p.820 lines are strictly enforced. Annual Meeting Close attention should be paid to specified deadlines in this issue. Unfortunately, late abstracts cannot be accommodated. March 3-4 Davidson, North Carolina p.821

Conferences: (see http: I /www. ams. org/meeti ngs/ for the most up-to-date information on these conferences.) June 5-July 21, 2005: Joint Summer Research Conferences in the Mathematical Sciences, Snowbird, Utah (see November 2004 Notices, page 1294). July 25-August 12, 2005: Summer Research Institute on Algebraic Geometry, Seattle, Washington (see November 2004 Notices, page 1293).

824 NOTICES OF THE AMS VOLUME 52, NUMBER 7 MATHEMATICAL MOMENTS

The Mathematical Moments program is a series of illustrated "snapshots" designed to promote appreciation and understanding of the role mathematics plays in science, nature, technology, and human culture.

Download these and other Mathematical Moments pdf files at www.ams.org/mathmoments.

• Recognizing Speech Unlocking the Cell • Compressing Data • Being a Better Sport • Targeting Tumors The processes that cells perform are as wondrous as their individual mechanisms are mysterious. Molecular biologists • Defeating Disease and mathematicians are using models to begin to understand operations such as cellular division, movement, and communi­ • Getting Results on cation (both within the cell and between cells). The analysis of cells requires many diverse branches of mathematics since the Web descriptions of cellular activity involve a combination of • Designing Aircraft continuous models based on differential equations and discrete models using subjects such as graph theory. • Eye-dentifying Yourself • Enhancing Your Image • Simulating Galaxies • Revealing Nature's Secrets • Securing Internet Communication • Making Movies Come Alive j • Listening to Music j • Making Votes Count C The Mathematical Moments program promotes AM L..J) appreciation and understanding of rhe role mathematics • Forecasting Weather AMEJ.Jr.AN MAnrEMAT rc AL. soa ETT ploys in science, nature, technology. and human culture. www.ams.or /mathmoments

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