AMERICAN MATHEMATICAL SOCIETY Available Exclusively front the Anterican Mathentatical Society

The AMS is the exclusive publisher of classic titles formerly available from Chelsea Publishing, a respected imprint within the mathematical community. Here are som e recent titles in this important AMS book series.

FOR CLASSROOM USE The Theory of Probability Fourth Edition B. V. Gnedenko

This classic book is the first introduction to probability and statistics written with an emphasis on the analytic approach to problem-solving. Written in a clear and concise style, this volume can serve as a textbook for undergraduate and graduate courses in probability. AMS Chelsea Publishing; 1962; 529 pages; Hardcover; ISBN 0-8218-3746-X; List $55; All AMS members $50; Order code CHEU 132.H

Solvable Models in Quantum Mechanics Second Edition S. Albeverio, University of Bonn, Germany, F. Gesztesy, University of Missouri, Columbia, MO, R. Heegh-Krohn, and H. Holden (with an appendix by Pavel Exner), Norwegian University of Science & Technology, Trondheim, Norway

"There is a wealth of very pretty examples of Schrodinger operators here which could be presented ... in an elementary quantum mechanics course." -MathSciNet

The first edition of this book generated considerable interest for those learning advanced mathematical topics in quantum mechanics. This second edition includes a new appendix containing a summary of the progress made in the field since 1988. AMS Chelsea Publishing; 2005; 488 pages; Hardcover; ISBN 0-8218-3624-2; List $69;AII AMS members $62; O rder code CHEU3SO.H

FOR CLASSROOM USE Functional Integration and Quantum Physics Second Edition Barry Simon, California Institute ofTechnology, Pasadena, CA

Written with great care and containing many highly illuminating examples, the main theme of this classic text­ book is the "path integral technique" and its applications to constructive methods of quantum physics. It is highly recommended to those interested in applications of functional integration to quantum physics. It also will make an ideal textbook for a course in functional integration. ., AMS Chelsea Publishing; 2005; 306 pages; Hardcover; ISBN 0-8218-3582-3; List $39;AII AMS members $35; Order code CHEU35 I.H

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For many more publications of interest, 1111 visit the AMS Bookstore (i).~AMs AMS BOOKSTORE www.ams.org/bookstore ~;~~AN MATHEMATICAL SOCIETY 12/04 N CAMBRIDGE NEW FROM CAMBRIDGE UNIVERSITY PRESS

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Introduction to Plane Geometric Mechanics Harmonic Analysis, Algebraic Curves on Riemannian Manifolds Signal Processing, ERNST KUNZ, University of Regensburg, Germany Applications to Partial and Complexity RICHARD G. BELSHOFF, Southwest Missouri State Differential Equations Festschrift in Honor of the 60th Birthday University, Springfield, MO {Translator) OVIDIU CALIN, Eastern Michigan University, East Lansing, of Carlos A. Berenstein This work treats an introduction to commutative ring Ml and DER-CHEN CHANG, Georgetown University, Washington, DC IRENE SABADINI, Politecnico di Milano, Italy; and theory and algebraic plane curves , requiring of the DANIELE C. STRUPPA and DAVID F. WALNUT, both, student only a basic knowledge of algebra, with all of the This work presents a purely geometric treatment George Mason University, Fairfax, VA (Eds.) algebraic facts co ll ected into several appendices that of problems in physics involving quantum harmonic Carlos A. Berenstein has had a profound influence on can be easily referred to, as needed. Kunz's proven osci llators, quartic oscillators, minimal surfaces, and scholars and practitioners alike amid a distinguished conception of teaching topics in commutative algebra Schri:idinger's, Einstein's and Newton's equations. mathematical career spanning nearly four decades. This together with their applications to algebraic geometry The text is enriched with good examples and exercises volume, which celebrates his sixtieth birthday, reflects makes this book significantly different from others on at the end of every chapter and will be suitable for his research plane algebraic curves. The exposition focuses on the students, pure and applied mathematicians, and interests and contains original and survey articles covering topics in harmonic purely algebraic aspects of plane curve theory, leaving theoretical physicists. and complex analysis, as we ll as signal processing. the topological and analytical viewpoints in the back­ 2005/ 278 PP./HARDCOVER/ ISBN 0-8 176-43 54 -0/$ 79.95 ground, with only casual references to these subjects APPLIED AND NUMERICAL HARMONIC ANALYSIS Contributors include: J. Baras, CA. Berenstein, L. and suggestions for further reading. Includes examples, Ehrenpreis, G. Kaiser, C. Kiselman, S.G. Krantz, exercises, figures, and suggestions for further study. Introduction to Vertex Krishnaprasad, B.Q. Li, I. Sabadini, B. Shiffman, D. C. 2005/APPROX. 300 PP. , 40 ILLUS./HARDCOVER Struppa, A. Taylor, D. F. Walnut ISBN 0-8176-4381 -8/$69.95 (TENT.) Operator Algebras and 2005/A PPROX. 176 PP./HARDCOVER ISBN 0-8176-4358-3/$89.95 (TENT.) Their Representations PROGRESS IN MATHEMATICS Also by Ernst Kunz JAMES LEPOWSKY, Rutgers University, Piscataway, NJ and Introduction to HAISHENG LI , Rutgers University, Camden, NJ, and Harbin Normal University, China Harmonic Analysis Commutative Algebra This book introduces the reader to the fundamental and Applications and Algebraic Geometry theory of vertex operator algebras and its basic tech­ In Honor of John J. Benedetto niques 'lln excellent introduction to the subject .... The presen­ and examples. Beginning with a detailed presen­ CHRISTOPHER HEll, Georgia Institute of Technology, tation is very clear and the theory is accompanied by tation of the theoretical foundations and proceeding to Atlanta, GA (Ed.) a range of applications, the text includes a number of numerous interesting exercises ... This is a highly This volume, in honor of John J. Benedetto on the recommended text for students and lecturers. " new, original results and also highlights and brings fresh perspective to important works of many researchers. occasion of his 65th birthday, features invited articles -MATHEMATICA covering a wide range of topics in areas where he has 2004/3 18 PP./HARDCOVER/ ISBN 1985/ 256 PP./HARDCOVER/ ISBN 0-8176-3065-1 /$59.95 0-817 6-3408 -8/$ 89.9 5 PROGRESS IN MATHEMATICS, VOL 227 made fundamental and lasting contributions, such as harmonic analysis, number theory, weighted norm Frobenius Splitting inequalities, wavelet theory, time-frequency analysis, The Universe of and sampling theory. Although the scope of the book is Methods in Geometry and General Relativity broad, chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. Representation Theory JEAN EISENSTAEDT, Observatoire de Paris, France and MICHEL BRION, Universitcf Grenoble- CNRS, St.-Martin A.J. KOX, Universiteit van Amsterdam, The Netherlands (Eds.) Contributors: A. Aldroubi, L. Baggett, G. Benke, C.A. d'Heres, France and SHRAWAN KUMAR, University of North This vo lume from th e Einstein Series is based largely on Cabrelli, P.G. Casazza, 0. Christensen, W. Czaja, C. Davis, Carolina, Chapel Hill papers presented at the Sixth International Conference H. G. Feichtinger, M. Fickus, J.-P. Gabardo, K. Groechenig, The theory of Frobenius splittings has made a signifi­ on the History of General Relativity. These contributions K. Guo, E. Hayashi, C. Heil, H.P. Heinig, J. Hogan, P.E.T. cant impact in the study of the geometry of flag varieties from notable experts offer both new and historical Jorgensen, K. Kornelson, J. Kovacevic, D. Labate, J.D. and representation theory. This work systematically insights on gravitation, general relativity, cosmology, Lakey, D.R. Larson, M.T. Leon, S. Li, W.-Q. Lim, A. Linder, develops the theory of Frobenius splittings and covers unified field theory, and the history of science. U.M. Molter, E. Schu lz, T. Sorre ls, D. Speegle, K.F. Taylor, all its major developments. The concise, efficient J.C. Tremain, D.F. Walnut, Y. Wang, G. We iss, E. Wilson Contributors include: K. Brading, G. Gale, H.F.M. exposition unfolds from basic introductory material on 2005/ APPROX. 320 PP./HARDCOVER Goenner, J. Goldberg, S. Katzir, D. Kennefick, H. Kragh, Frobenius splittings- definitions, properties, and ISBN 0-8176-3778-8/$89.95 (TENT.) C. Lehner, U. Majer, J. Mattingly, E.T. Newman, J.D. examples- to cutting-edge research. Many examples, APPLIED AND NUMERICAL HARMONIC ANALYSIS Norton, J. Renn, R. Rynasiewicz, J.M. Sanchez-Ron, T. exercises, and open problems suggested throughout. Sauer, C. Smeenk, J. Stachel, M. Wazeck, D. Wunsch 2005/ 246 PP./HARDCOVER/ISBN 0-8176 -4 191-2/$ 69.95 2005/A PPROX. 510 PP./HARDCOVER PROGRESS IN MATHEMATICS, VOL 231 ISBN 0-8176-4380-X/$99.95 (TENT.) EINSTEIN STUDIES, VOL 11

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200 Quiver Representations (0:1:0) Harm Derksen and ]erzy Weyman A quiver is a directed graph, and a representation of a quiver is a collection of finite dimensional vector spaces, one for each graph vertex, and linear transformations, one for each directed edge. Representations of a given quiver form a category, which, as the authors discuss, can be surprisingly rigid and rich.

208 Racial Equity Requires Teaching Elementary School Teachers More Mathematics Patricia Clark Kenschaft The author argues that societal imperatives, particularly in minority edu­ cation, necessitate improving the mathematical competence of elementary school teachers, and she shares her own experiences in so doing. Communications Commentary

214 WHATIS ... aBrane? 197 Opinion Gregory W Moore 1 98 Letters to the Editor 216 Presidential Reflections: Interview 221 ... asmallideaofwhatitisido with David Eisenbud all day ... Introductions to Allyn jackson Mathematics- Book Reviews 219 AMS Website Connects Math and the Reviewed by Giinter M. Ziegler Public Allyn jackson 225 InterviewwithMichaelAtiyahand Isadore Singer Martin Raussen and Christian Skau 234 Teachers, Exams, Standards: AMS Committee on Education Examines Issues Allyn jackson 2 36 2 004 Annual Survey of the . Matl)ematical Sciences (First Report) Ellen E. Kirkman, ]ames W Maxwell, and Colleen Rose Notices Departments Mathematics People ...... 252 Banuelos Awarded Blackwell-Tapia Prize, Clay Research Award EDITOR: Andy Magid Winners Announced, Hirzebr uch Awarded Cantor Medal, Izumi ASSOCIATE EDITORS: Awarded Operator Algebra Pr ize, NRC-Ford Foundation Susanne C. 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If the United States is to continue to lead the way in the Gambling with U.S. creation of new technologies and jobs, we can't afford to put federal research on hold. Today, federal research in­ Sdence vestment is less than 1% of GDP-less than half the rate of the 1960s. In other nations, the rate is much higher. The election and its polarizing debates are over, but basic In a competitive global market, where corporate time research still plays a central role in sustaining U.S. lead­ horizons are measured in months rather than years, com­ ership in science and in creating high-wage jobs. The for­ panies simply cannot provide substantial support for long­ mula is as certain as it gets in economics: research in­ vestments spark innovation, which fosters productivity and term, high-risk research. This is why the government plays job growth, which drive the economy. Yet budget pressures such a dominant, irreplaceable role in basic research. and the lack of a national science and technology strategy The current budget deficit is clearly a major concern. are driving down federal investments in research. This is But cutting investments that eventually generate the growth a dangerous gamble at a time when the stakes could not and revenue sought by policymakers is not the way to solve be higher. deficit problems. Cutting basic research is like cutting U.S. leadership in science and technology used to be a your child's education fund during tough times: it will foregone conclusion. No longer. The European Union, compound the problem over the long haul. China, Japan, India, Russia, and other nations are rapidly In 1950, Popular Mechanics predicted that "computers building scientific capabilities that rival ours-as evidenced in the future may weigh no more than 1.5 tons." Today, by more U.S. companies moving science and engineering PDAs have more computing power than NASA mission con­ jobs and facilities offshore and by fewer international stu­ trol had during the Apollo program. We simply have seen dents applying for U.S. graduate programs in science and too many amazing technological advances not to antici­ engineering. pate the many that lie ahead. Is our technological leadership slipping? If so, how will Steps lost in scientific leadership are difficult to re­ that affect our ability to generate future breakthroughs gain. So we must ask: Will our nation make the research and high-wage jobs? These questions are not being asked investments needed to stay a competitive step ahead in often enough in Washington, D. C. Instead, the president's the global economy? Or will we hold back and take our budget request cuts basic research at the Departments of chances? Let's not roll the dice. Energy and of Defense, and the House of Representatives recently slashed National Science Foundation research. -Charles P. Casey, president Because these agencies dominate federal investments in nonmedical research, our elected leaders are running a very American Chemical Society risky national experiment at a pivotal time in U.S. history. Like a thoroughbred in a race without a finish line, sci­ -Helen R. Quinn, president ence runs nonstop for the American people. Our military American Physical Society supremacy, industrial strength, and quality of life depend heavily on it. However, if we leave critical areas unex­ -Robert D. Wells, past president plored, we will fall back in science and create a void other Federation of American Societies nations are certain to fill. To keep pace, we must make for Experimental Biology sustained and smart investments in basic research. The trend toward flat research budgets is troubling be­ -David Eisenbud, president cause basic research supported by NSF and other agencies American Mathematical Society ensures a steady stream of scientific discoveries that can transform entire industries and even create new ones. While the nation's sluggish job growth is gaining much attention, too little attention is being paid to America's long­ standing reliance on innovative new industries to create high-wage jobs. No one knows which next big innovation will produce a wave of new jobs, although biotechnology, nanotechnology, and renewable energy are strong con­ tenders. But we do know that major job-producing inno­ vations stem from strong basic research investments. The American public believes in job growth through in­ novation. In fact, in a recent poll, more than 70% of Amer­ icans said the nation spends too little on basic research.

FEBRUARY 2005 NOTICES OF THE AMS 197 Letters to the Editor

About the Cover The Canonical Decomposition Ph.D.'s and the K-12 Classroom ing Ph.D.'s to enable them to teach in Configuration At the end of Andy Magid's Letter their schools. It is called training, and This month's cover accompanies the from the Editor, p. 1184 of the No­ its purpose is to render the Ph.D. in­ article by Harm Derksen and Jerzy vember 2004 Notices, he mentions the distinguishable, from the standpoint Weyman in this issue and amounts to issue of how mathematicians can con­ of quality control, from his/ her col­ an elaboration of figures in that arti­ tribute to K-12 education and invites league who doesn't know how to cle and also in On the canonical de­ personal experiences from readers of bisect a line segment. The only composition ofquiver representations the Notices. First, I'd like to ask a ques­ remaining distinctions between them (Camp. Math. 133) by the same two tion: when there are so many unem­ have to do with salary and perhaps authors. It illustrates how the canon­ ployed math Ph.D.'s and at a time status. So, my second question is: ical decomposition of dimension vec­ to not actively re­ when public schools are crying that why, in addition tors works in different geometrical cruiting math Ph.D.'s, do schools not they don't have enough teachers, why regions of two-dimensional projec­ take advantage of their special capa­ is it that these schools aren't making tive space. The interior of the ellipse bilities when they do get them? I, for more of an effort to recruit math (the Tits cone) represents imaginary one, would like to see experimental Ph.D.'s? I don't really want that ques­ roots. The nodes represent individual programs in high schools in which tion answered: I want to see the re­ roots-yellow for ordinary real roots, they do hire math Ph.D.'s and let them cruitment. It is obvious why most red for Schur roots, blue for certain educate in their own way, instead of s . The math Ph.D.'s would not want to teach important imaginary root reconstructing them in the image of darker outer triangles, whose vertices in public schools. The conditions of what u sed to be their weakest stu­ are Schur roots, are what Derksen and such employment tend to select the dents. What b etter preparation can Weyman call compartments: inside kind of person who does want to teach the students get for college than to ex­ one of these, the canonical decom­ there. I had a class nearly full of them perience the kind of teacher they are position involves exactly the trian­ at Ohio State Univer­ a few years ago likely to have there? Instead, many gle's vertices. In the lighter inner tri­ sity. This was after the state legisla­ angles the canonical decomposition is colleges are reversing the process and ture had enacted a reform that, among increasingly giving students the same mixed real and imaginary. In the in­ other things, required that future high terior region the canonical decompo­ kind of teachers they had in high school teachers display c ompetence sition is just a single imaginary root. school, both in educational philoso­ own subjects and The algorithm for generating the pic­ as majors in their phy and in ability. ture was explained to me by Derksen only take education courses in grad­ -Allan Adler and is based on the principal theorem uate school. Formerly, apparently, of Exceptional sequences of represen­ they could graduate by taking courses (Received October 20, 2004) tations of quivers (Can. Math. Soc. in how to teach mathematics without Conf. Proc. 14) by William Crawley­ actually knowing any. Boevey. This algorithm suitably mod­ It was in everybody's interest to The Two-Body Problem ified seems also to be the most effi­ defeat this reform: (1) The nature of I am writing in response to the p air cient way to generate Schur roots. Not the working conditions in public of articles "Has the Women-in­ all of the patterns seen in this diagram schools guaranteed that the same cal­ Mathematics Problem Been Solved?" and similar ones for other quivers iber of people as before would want by Allyn Jackson and "Women in One seem to be perfectly understood. to teach in them and be able to survive Academia: Are We Asking the Right interesting problem suggested is that there; (2) In particular, they were not Questions?" by Carolyn Gordon and of describing the statistical distribu­ capable of p roving themselves as Barbara Lee Keyfitz that appeared in tion of real roots. For quivers with math majors; (3) The department hyperbolic links the distribution the August 2004 Notices. Both articles nevertheless had to graduate expected seems to be a kind of Cantor dust addressed many important issues for numbers of them or else be yelled at spread around the Tits cone. women and for the mathematical com­ - Bill Casselman, Graphics Editor by the same people who had told them munity at large. I would like to focus ([email protected]) to raise their standards. So, reform attention on another issue tbat has was cynically defeated by an unofficial a profound impact on the career deci­ policy of social promotion for math sions of women entering academia majors, even though that policy that was not m entioned in eith er tended to pollute the very waters from article- the "two-body problem" faced which the university drew its students. b y dual-career couples seeking I had, for example, future high school employment. teachers who did not know how to I do not know of any source of bisect a line segment with straight­ h ard data describing how the two­ edge and compass but were somehow body problem affects women in math­ expected to learn non-Euclidean geom­ ematics. However, the experience of etry at the level of math majors. the physics community suggests what There are some public school sys­ such data might look like. In 1998, a tems that have policies for rehabilit- Web-based survey of physicists was

198 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Letters to the Editor undertaken by Laurie McNeil and Marc Hiding Homework from Google Editor's Note: Queen's was misiden­ Sher (http: I jwww. physics. wm. Bob Proctor's letter (December 2004) tified in the article about Grothendieck edu/-sher/survey. html). In their raises some excellent issues related to that appeared in the November 2004 article online they write, "For the pro­ the posting of homework solutions Notices. It is Queen's University, fession as a whole, it is important to on the Web. He seems unaware of a Kingston, Ontario, Canada. recognize that the dual-career prob­ relevant detail. The root directory of The "What Is?" Column lem represents a significant barrier to every website has a file, robots.txt, the enhancement of the representa­ which tells search engines about con­ I am a Ph.D. student in mathematics tion of women in physics." See also tent that should not be made avail­ at Brandeis, and I find the "What Is .. .?" "The dual-career-couple problem," able. To exclude your solutions from columns of Notices very useful. Their McNeil and Sher, Physics Today, July being covered by search engines, sim­ concise, elementary exposition of ideas is appealing. I hope that Notices 1999, 32-37. ply tell your systems administrator to continues to broach the plethora of The problem is complex, and there add the following lines to robots.txt: mathematical concepts with this rel­ may be no simple solution. However, Disallow: [name of the directory which atively new column. we do not make headway by ignoring contains the solutions]. it. The AMS could play a valuable role I implemented this solution after I - jim Tseng in beginning a discussion of the two­ discovered that Alexa had picked up Brandeis University body problem in the mathematical some of my homework solutions. [email protected] community. A first step would be to - Michael Renardy (Received November 15, 2004) gather data so that we can frame the Virginia Tech issues with a clear picture of the scope of the problem. The 1990 American (Received November 10, 2004) Religion in the Notices Physical Society Membership Survey It is my understanding that the Notices found that "Eighty percent of mar­ went the "no politics" route lately. Grothendieck at Queen's ried female physicists are married to Shouldn't then that be the case with other scientists, compared to only I was a graduate student at Queen's religion as well? If an article deals 16% of married male physicists." "APS University in Kingston in the 1970s. with some religious aspects of the life survey demonstrates changing com­ I attended Grothendieck's lectures of a mathematician, I would see no position of membership," American both in mathematics and Survival. problems with it since that is part of Physical Society Bulletin, Vol. 36, One of the members of Survival, Mr. a person's total picture. However, if an No. 8, 1991, pgs. 2051-2053). What Gordon Edwards, was so inspired by obituary writer injects a sentence such are the data in mathematics? Grothendieck that he devoted his con­ as "God gave her an easy death", as Other steps could also be taken. siderable talents to the antinuclear done on page 1321 of the December movement in Canada. Even then, The AMS has done a wonderful service 2004 issue of the Notices, I find it of­ though, Grothendieck expressed re­ to the community in helping to make fensive, just as many readers of the gret that the attitudes he abhorred in the employment process friendlier Notices would feel if I elaborated on mathematics were creeping into the my views on religion in this letter. toward the applicant. For instance, Survival movement. We graduate stu­ the AMS publicizes the names of dents followed him around for obvi­ - PaulNevai institutions that have agreed to let Ohio State University ous reasons. He lived in a modest [email protected] recipients of postdoctoral positions room in Kingston. Before the rental wait until a specified date in February had to be formalized, the landlady (Received November 16, 2004) before they must accept or reject made him aware of the rules of the positions. Could the AMS also help house in rather condescending tones. to publicize which institutions have In these walks through Kingston, he spousal hiring policies? Ultimately, talked a lot about mathematics. I also each couple must make their own per­ went to Buffalo, New York, to attend sonal decisions about how to balance a series of mathematics lectures he their careers and their personal lives. gave. One afternoon in Buffalo, he The mathematical community can outlined various mathematical prob­ help by making information relevant lems he wanted to solve. At one point to these decisions more easily acces­ he said, "if only I knew more about dif­ sible in an effort to make the process ferential equations". He went on to of navigating the job market more lament the gaps in his mathematical transparent for dual-career couples. knowledge. -jessica Sidman -Frank Okoh Mount Holyoke College Wayne State University (Received October 27, 2004) (Received November 11, 2004) fEBRUARY 2005 NOTICES OF THE AMS 199 Quiver Representations Harm Derksen and ]erzy Weyman

Introduction Example 1. A representation of the quiver A quiver is just a directed graph.1 Formally, a a quiver is a pair Q = (Qo, Qd where Q 0 is a finite set of vertices and Ql is a finite set of arrows be­ 0 ------~ 0 tween them. If a E Q 1 is an arrow, then ta and ha 1 2 denote its tail and its head, respectively. Let us fix a quiver Q and a base field K . At­ is a collection of two finite-dimensional vector tach a finite dimensional vector space to each spaces V1, Vz together with a linear map vertex of Q and a linear map to each arrow (with Va: V1 ~ Vz . the appropiate domain and codomain). Then this is called a representation of Q . Formally, a repre­ Example 2. A representation of the loop quiver sentation V of Q is a collection a Wx I X E Qo} of finite-dimensional K-vector spaces together with 0 a collection 1 {Va: Vra ~ Vha I a E Qd is a vector space V1 together with an endomor­ of K -linear maps. If Vis a representation of Q , then phism Va: V1 ~ V1. its dimension vector dv is the function Q0 ~ ~ defined by dv(x) = dimK(Vx) for all x E Q0 • Here Example 3. A representation of the star quiver ~ = {0, 1, 2, ... } denotes the set of nonnegative integers. The set of all possible dimension vectors 1 is ~Qo . Here are a few typical examples of quiver 0 representations. 5 all a 2 0 ~~ 0 Harm Derksen is associate professor of mathematics at the University of Michigan. H is e mail address is [email protected]. ]erzy Weyman is professor of mathematics at Northeast­ ('~ 0 0 ern University. His email address is j . weyman@neu. edu. 4 3 The authors are partially supported by NSF Grants DMS 0349019 and 0300064, respectively. is a collection of six vector spaces V1 , V2 , ..• , V6 to­ gether with five linear maps Vai : V; ~ V , 1 The underlying motivations of quiver theory are quite 6 different from those in the traditional graph theory. To i = 1, 2, ... , 5. If all maps are injective, then we can emphasize this distinction, it is common in our context to view such a representation as a subspace use the word "quivers" instead of "graphs". configuration.

200 NOTICES OF THE AMS VOLUME 52, NUMBER 2 If V and W are two representations of Q, then blocks. Two representations, Va : V1 ~ V1 and a morphism

commutes for every arrow a E Q1. That is, Waisomorphism. Indecomposable Representations If V arid W are two representations of the same Example 4. Consider Example 1. For a linear map quiver Q, we define their direct sum V Ell W by Va : V1 ~ V2 we can always choose bases in V1 and in V2 in which Va is given by the block matrix (V Ell W)x : = Vx Ell Wx Ir 0) for all x E Q0 , and ( 0 0 ' (V Ell W)a := (~a ~a): Vra Ell Wra ~ Vha Ell Wha where r is the rank of A and Ir is the r x r: iden­ tity matrix. Two representations Va : V1 ~ V2 and for all a E Q 1. Wa: W1 ~ W2 are isomorphic if and only if We say that Vis a trivial representation if Vx = 0 dim vl = dim WI' dim v2 = dim w2' and Va and Wa have the same rank. for all x E Q0 . If V is isomorphic to a direct sum WEll Z, where W and Z are nontrivial representa­ tions, then V is called decomposable. Otherwise Example 5. Consider Example 2. Assume that the V is called indecomposable. Every representation base field K is algebraically closed. IfVa : V1 ~ V1 has a unique decomposition into indecomposable is an endomorphism of the finite-dimensional representations (up to isomorphism and permu­ K-vector space V1, then for some choice of basis tation of components). The classification problem in V1, the matrix ofVa has the form reduces to classifying the indecomposable repre­ sentations. 0 jnz,l\z 0 Example 6. Let us go back to Examples 1 and 4. 0 ) (1) . ' There are 3 indecomposable representations A,B, C, namely 0 jn~,Ar A: K ~ 0, B: 0 ~ K, C: K .!. K. where jn,A denotes then x n jordan block Any representation Vis isomorphic to 1 V =Ad1-r Ell Bdrr Ell cr A 1 0 where d1 = dim V1, d2 = dim V2 and r = rank Va. [' 0 A Example 7. Consider again Examples 2 and 5. Inde­ ~l composable representations correspond to the The matrix (1) is the well-known jordan normal jordan blocks. The jordan normal form shows how form of Va. It is unique up to permutation of the a representation decomposes into indecomposables.

FEBRUARY 2005 NOTICES OF THE AMS 201 Although there are infinitely manyindecomposable rected graph is a union of Dynkin graphs of type representations, they can still be parametrized by a A, D, orE, shown below: discrete parametern and a continuous parameter A..

Example 8. In Example 3, one can identify a An o----o---o···· ···o----o---o 2-dimensional family of pairwise nonisomorphic indecomposable representations, namely,

K

K

where Va 1 , ••• , Va 5 are given by the matrices The Dynkin graphs play an important role in the classification of simple Lie algebras, of finite crys­ tallographic root systems and Coxeter groups, and other objects of "finite type". For quivers of tame type, a similar description exists, namely: respectively, with ,\, J.1 E K. Theorem 10 ([5], [14]). A quiver Q which is not of Furthermore, there exist other families of inde­ finite type is of tame type if and only if the un­ composables for this particular star quiver, where derlying directed graph is a union ofDynkin graphs the number of parameters of the family is arbitrarily and extended Dynkin graphs of type or large. In this example, describing explicitly the set A, D, E, of indecomposable representations is essentially an shown below: impossible task.

Theorems of Gabriel and Kac We have observed different behavior of indecom­ posables for various quivers. If a quiver has only finitely many indecomposable representations, it is called a quiver of finite type. If there are infinitely many indecomposables, but they appear in fami­ lies of dimension at most 1, then the quiver is called of tame type. 2 If the representation theory of the quiver is at least as complicated as the rep­ resentation theory of the double loop quiver, then the quiver is called of wild type. These definitions given here are imprecise but hopefully convey the right intuition. The precise definitions of tame and wild type are omitted. It is known that every quiver is either of finite type, tame, or wild. We will later see that such a trichotomy is true in a more gen­ Gabriel proved a stronger statement for quivers eral setting. of finite type: Forgetting the orientations of the arrows yields Theorem 11 [Gabriel's Theorem, part 2]. The in­ the underlying undirected graph of a quiver. The decomposable representations are in one-to-one following amazing theorem is due to Gabriel (see [8], correspondence with the positive roots of the [13]). corresponding root system. For a Dynkin quiver Theorem 9 [Gabriel's Theorem, part 1]. A quiver Q, the dimension vectors of indecomposable is of finite type if and only if the underlying undi- representations do not depend on the orientation of the arrows in Q. Amazingly, this result is just the tip of an ice­ 2 In some papers, the definition of tame type includes finite berg. Define the Euler form (or Ringel form) of a type.

202 NOTICES OF THE AMS VOLUME 52, NUMBER 2 quiver Q to be the asymmetric bilinear form on 7l_Qo on the orientation of arrows in Q. The dimension given by vectors of indecomposable representations corre­ spond to positive roots of the corresponding root (01, {3) = 2: 01(x){3(x)- 2: 01(ta){3(ha). system. xEQo In the theory of Kac-Moody algebras one dis­ The Euler form is represented in the coordinate tinguishes between real roots and imaginary roots. basis of 7l_Qo by the matrix E = (bi,j) where the In Theorem 13, real roots correspond to dimension vectors for which there is exactly one indecom­ bi,j = 6i,j - #{ a E Q1 I ta = i, ha = j}, posable representation, while imaginary roots cor­ where bi,j is the Kronecker delta symbol. One also respond to dimension vectors for which there are defines a symmetric bilinear form families of indecomposable representations. If a positive root 01 is real, then q(01) = 1. If it is imag­ inary, then q(01) .:s; 0. a b Example 14. The real roots for the wild quiver 0 --=--- 0 --- 0 2 3

(01, {3) := (01, {3) + ({3, 01), 0 -----~ 0 1 2 called the Cartan form of the quiver Q. The Cartan form does not depend on the orientation of the arrows in Q. are (1, 0), (3, 1), (8, 3), (21, 8), .. . Example 12. For the quiver (0, 1), (1, 3), (3, 8), (8, 21), .. .

the Euler matrix is (pairs of consecutive odd Fibonacci numbers). The imaginary roots are all (p, q) E ~ 2 with -1 1 E = 3-.JS p 3+-15 (~ 0 --2- < q < --2-.

and the Cartan matrix is The connections with the theory of Lie algebras and algebraic groups can be developed much fur­ -1 ther. Ringel showed how to construct the upper tri­ c = ( ~1 2 angular part of the enveloping algebra of a simple -1 Lie algebra from the representations of the corre­ sponding Dynkin quiver Q, using the Hall algebra The Tits form q of Q is defined by associated to Q ([15]). The connections between q(OI) = (01, 01) = ~(01, 01). quiver representations and canonical bases of quan­ tum groups is an active area of current research. The number of continuous parameters for 01-dimensional (01 * 0) representations is known to Canonical Decompositions be at least 1- q(01). The Tits form plays an inte­ gral role in Gabriel's theorem. For a quiver of finite Kac's theorem describes the dimension vectors in type and a nonzero dimension vector 01, there are which indecomposable representations appear. only finitely many representations up to isomor­ However, this theorem does not tell us how to con­ phism, so q(01) 2: 1. From this one can prove that struct indecomposable representations. One might the Cartan form is positive definite and that the think that a "generic" representation of dimension underlying undirected graph is a union of Dynkin 01 is indecomposable if 01 is a root. This is not the diagrams. One can also show that a dimension case. Because the classification of (indecompos­ vector 01 is a positive root if and only if q(01) = 1. able) representations is no longer feasible, we About the same time at which Gabriel proved his will set ourselves more modest goals. We will ask theorem, Kac and Moody came up with a general­ ourselves the following questions: ization of root systems and corresponding Lie If we fix a dimension vector 01 and we choose all algebras for Cartan matrices of arbitrary quivers. the linear maps at random, when will such a rep­ Kac proved in 1980 the following result (see [9]). resentation be indecomposable? When will such a representation be rigid? (This means: for which rep­ Theorem 1 3 [Kac's Theorem]. For an arbitrary resentations does every small enough perturbation quiver Q, the set of dimension vectors of inde­ of the linear maps result in an isomorphic repre­ composable representations ofQ does not depend sentation?)

FEBRUARY 2005 NOTICES OF THE AMS 203 We say that a general representation of dimen­ injective, Vb is surjective, Vc is an isomorphism, sion ()( is indecomposable if there is a nontrivial and Vb Va = 0. The dimension vector (1, 2, 1) is a polynomial equation in the entries of the matrices real root (up to isomorphism there is only one such that every decomposable representation of indecomposable representation). For a general dimension ()( satisfies the polynomial equation. representation of dimension ( 1, 2, 1), however, the Even for the loop quiver from Example 2 we see composition Vb Va will be nonzero, and an inde­ that in dimension vector (n) a representation can composable summand be indecomposable only if all its eigenvalues are the same. One might ask a different question: how does a general representation decompose? Kac showed that if Vis a "sufficiently general" repre­ sentation with dimension vector ()(, then the di­ mension vectors of the direct summands will not depend on V. This general decomposition of the will split off. Thus (1, 2, 1) is not a Schur root. dimension vector of ()( into the dimension vectors of indecomposable summands is called the canon­ The canonical decomposition is homogeneous ical decomposition of()(. This notion depends on the in the following way. If orientation of arrows in Q. We write ()( = ()(1 El1 • • • El1 ()(r

()( = ()(1 El1 • • • El1 ()(r is the canonical decomposition for some dimension vector, then if a general representation of dimension vector ()( has r indecomposable summands of dimension (2) n()( = [n()(d EB ••• El1 [n()(,], vectors ()( 1, ... , ()(,. If a general representation of where [n()(] denotes n()( if (()(, ()() < 0 and ()(

This representation is indecomposable if Va is 1 3

204 NOTICES OF THE AMS VOLUME 52, NUMBER 2 [0:1 :0] [0:1 :0]

[1 :0:0] [1 :0:1] [0:0:1] [1 :0:0] [1 :0:1] [0:0:1]

Figure 1. Figure 2.

[0:1 :0] [0:1 :0]

[1 :0:0] [1 :0:1] [0:0:1] [1 :0:0] [1 :0:1] [0:0:1]

Figure 3. Figure 4.

For this particular quiver, the imaginary positive enormous progress in the area of finite­ roots are exactly all dimension vectors 01 for which dimensional algebras. Because of space limitations q(01) ::::; 0. The quadric q(01) = 0 is plotted in we will not be able to do justice to this subject. We Figure 1. This quadric and its interior correspond will just give a glimpse of this area and its con­ to the imaginary roots. nection to quivers. The imaginary Schur roots are the dimension vec­ A path in a quiver Q is a sequence a 1a 2 • • ·a, tors inside the nonconvex fractal-like polygon of arrows in Q1 with ta; = ha;+1 for shown in Figure 2. Since the polygon is properly i = 1, 2, ... , r- 1. We also define a trivial path ex contained inside the quadric in Figure 1, we see that with tex = hex = x for each vertex x E Q0 • The path there exist imaginary roots that are not imaginary algebra of K Q is the vector space spanned by all Schur roots. paths in Q. The algebra structure of KQ is given 1n figure 3 we plotted some real roots for this by the concatenation of paths. There is a natural bijection between representations quiver. The dimension vectors 01 for which a gen­ of the quiver Q eral representation is rigid are those that lie out­ and (left)-KQ -modules. side the fractal-like polygon in the Figure 4. A real Example 1 7. Consider the quiver root 01 is a real Schur root if and only if 01 is a rigid dimension vector. We see that some of the real a b c roots in Figure 3 lie inside the polygon in Figure 4. o--~--o--~--o--~--0 This shows that some real roots are not real Schur 1 2 3 4 roots. For every i, j with 1 ::::; i ::::; j ::::; 4 there is a unique Representation Theory of Finite­ path from ito j. Identify this path from ito j with Dimensional Algebras the matrix E1.; having a 1 in row j and column i and There is a close connection between quivers and 0 everywhere else. Using this identification, we see the representation theory of finite-dimensional that the path algebra for this quiver is isomorphic algebras. In the last few decades there has been an to the set of 4 x 4 lower triangular matrices.

FEBRUARY 2005 NOTICES OF THE AMS 205 If A is a finite-dimensional algebra over the com­ References plex numbers Oxford Ser. (2) erties of the Auslander-Reiten transform imply 45(1994),no. 180,515-530. that if IX is a real root/ imaginary root/ real Schur [13] H. KRAFT and CH. RIEDTMANN, Geometry of represen­ root/imaginary Schur root/ rigid dimension vec­ tations of quivers, Representations of Algebras tor, then so is T(IX). (Durham, 1985), 109-145, London Math. Soc. Lecture The Auslander-Reiten transform is visible in the Note Ser. 116, Cambridge Univ. Press, Cambridge, figures of the previous section. In that case, the map 1986. [14] L.A. NAZAROV A, Representations Tis given by of quivers of infinite type (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 37 5 (1973), 752-791. 3 -3)-2 . [15] C. M. RINGEL, Hall algebras and quantum groups, (~ 2 -1 Invent. Math. 101 (1990), no. 3, 583-591. [16] A. ScHOFIELD, General representations of quivers, Proc. Note that for example T(O, 1, 1) = (2, 1, 1) and London Math. Soc. (3) 65 (1992) 46-64. T(1, 0, 1) = (0, 1, 0). Using the homological proper­ [17] __ , Birational classification of moduli spaces of ties of the Auslander-Reiten transform, we have vector bundles over IP' 2, Indag. Math. (N.S.) 12 (2001), discovered the map T that leaves the quadric in no. 3, 433-448. Figure 1, the infinite polygon in Figure 2, the real roots3 (Figure 3), and the infinite polygon in Fig­ ure 4 invariant.

3 The set of positive real roots is not completely invariant under T. If R is the set of positive real roots, then each of T(R) \ R and R \ T(R) consists of only three vectors.

206 NOTICES OF THE AMS VOLUME 52, NUMBER 2 New Releases

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E de Gruyter Berlin · New York Prices are subject to change. Racial Equity Requires Teaching Elementary School Teachers More Mathematics Patricia Clark Kenschaft

strongly believe that the most crucial step for mathematically by our system. They need to be promoting racial equality in this country is to taught. I have found them eager and quick to educate all elementary teachers mathemati­ learn-and appallingly ignorant of the most basic I cally. This conviction began after a survey I did mathematics. in the mid-1980s of black mathematicians in "Teach us math! Teach us math! Teach us math!" New Jersey. Seventy-five black people with at least chanted dozens of elementary school teachers dur­ one degree in mathematics responded to a variety ing one after-school workshop. There was an of questions, including, "What can be done to bring amazed silence while we all absorbed what had just more blacks into mathematics?" happened. Then one of them said, "If you taught The second most common answer to this ques­ us math the way you did just now, we could teach tion was, "Publicize role models." I might have it to the children." They all nodded emphatically. been planting that answer because I was clearly col­ This incident followed my statement that those of lecting role models. However, the most common an­ us who thrive mathematically have had some good swer (by far) I definitely did not plant; it came as mathematical experience early, typically at home. a total surprise to me. It was, "Teach mathematics Someone had asked for an example out of my own better to all American children. The way it is now, childhood, and I had explained how my father had if children don't learn mathematics at home, they described the meaning of rr to me several months don't learn it at all, so any ethnic group that is un­ before I started kindergarten. Their response was derrepresented in mathematics will remain so until the chanting, "Teach us math!" children are taught mathematics better in ele­ One study of nine hundred Texas school districts mentary school." revealed that the large disparities in achievement That answer caused me to seek opportunities to between black and white students were almost en­ work in elementary schools. Much of what follows tirely accounted for by socioeconomic status and will be evidence corroborating the statement that was so frequent among the black mathematicians differences in the measurable qualifications of 1 of New Jersey-and the great need to teach math­ their teachers. It is no secret that minority students ematics to elementary school teachers. Like most across the country have less mathematically edu­ Americans, I found it difficult to believe how poorly cated teachers than whites. However, even in inte­ prepared mathematically they are. They are well grated districts, the lack of home preparation of chosen. They are kind, diligent, and smart, quali­ ties that nobody can teach. They have been failed 1 Doing What Matters Most: Investing in Quality Teaching, National Commission on Teaching and America's Future, Patricia Clark Kenschaft is professor of mathematics at November 199 7, page 8, quoting Ronald Ferguson in "Pay­ Montclair State University. Her email address is ing for Public Education: New Evidence on How and Why kenschaft@pegasus. montclair. edu and her postal ad­ Money Matters, "Harvard Journal of Legislation 28 (Sum­ dress is 56 Gordonhurst Avenue, Montclair, N] 07043. mer 1991), pp. 465-98.

208 NOTICES OF THE AMS VOLUME 52, NUMBER 2 minority students means that they are more de­ one was not unusual. Perhaps it was above aver­ pendent on their teachers for their mathematical age in the enthusiasm of the teachers and their loy­ knowledge. It has been my observation that the rea­ alty to the school. son that scores are higher in white districts is that Its principal invited me to consider that school some parents teach their children mathematics at "my school". He and the teachers really wanted to home, and these children teach many of the oth­ help the students. Its students had a median ers. It has appeared to me that the teachers are no achievement in mathematics of about the 25th per­ better prepared in the high-scoring districts. centile on the "Iowas", one of the lowest levels in The teachers are eager and able to learn. I vividly Newark. I am now convinced that its rank was due remember one summer class when I taught why the to the fact that the principal did not pressure the multiplication algorithm works for two-digit num­ teachers to cheat in any way on standardized tests. bers using base ten blocks. I have no difficulty When I told him this years later, his eyes widened. doing this with third graders, but this particular He was president of the principals' union. "What? class was all elementary school teachers. At the end You are saying ... " I nodded. Since then I have read of the half hour, one third-grade teacher raised numerous reports of systemic cheating on stan­ her hand. "Why wasn't I told this secret before?" dardized tests and other forms of deception by she demanded. It was one of those rare speechless school administrators, most notably the recent ar­ moments for Pat Kenschaft. In the quiet that en­ ticles in The New York Times about Houston, while sued, the teacher stood up. Secretary of Education Roderick Paige was super­ "Did you know this secret before?" she asked the intendent. person nearest her. She shook her head. "Did you The following year Montclair State facilitated know this secret before?" the inquirer persisted, my going once a week after school to that school walking around the class. "Did you know this se­ to talk mathematics with whomever showed up. At cret before?" she kept asking. Everyone shook her least one teacher always did show up, and some­ or his head. She whirled around and looked at me times six or seven. It's not an effective way to make with fury in her eyes. "Why wasn't I taught this be­ change, but we did get acquainted. fore? I've been teaching third grade for thirty years. A year later I won one of the first K-3 grants from If I had been taught this thirty years ago, I could Exxon Education Foundation. This enabled me to have been such a better teacher!!!" spend twelve days on campus in the summer with Indeed she could have been. The understanding five teachers from that school and to visit the of the area of a rectangle and its relationship to mul­ school two mornings a week during the following tiplication underlies an understanding not only of school year. I spent those mornings teaching math the multiplication algorithm but also of the com­ to one to three first-grade classes, one to three mutative law of multiplication, the distributive law, third-grade classes, and one fifth-grade class. and the many more complicated area formulas. During my first class teaching elementary school Yet in my first visit in 1986 to a K-6 elementary children, a fifth grader raised his hand and asked, school, I discovered that not a single teacher knew "What is that word you keep using instead of take how to find the area of a rectangle. away?" Enter "minus"- for fifth graders! In those innocent days, I thought that the teach­ The best first-grade teacher told me she never ers might be interested in the geometric interpre­ bothered to teach subtraction during the first half tation of (x + y)2. I drew a square with (x + y) on a of the year because the children couldn't learn side and showed the squares of size x2 and y 2 . everything at once. I started visiting the school in Then I pointed to one of the remaining rectangles. October, and it seemed to me natural to teach ad­ "What is the area of a rectangle that is x high and dition and subtraction together. She told me she y wide?" I asked. would not reinforce my teaching of subtraction There was no response, so I asked the question between my weekly visits, and I said that was no again. "What is the area of a rectangle that is x by problem. y?" One of the games I played with the children was The teachers were very friendly people, and they holding five unifix blocks in front of me, putting know how frustrating it can be when no student them behind my back, and bringing forward three. answers a question. "x plus y?" said two in the front "How many are behind my back?" I asked. The simultaneouslY, children could answer correctly. Then I told them "What?!!!" I said, horrified. that one way of writing this was "5 - 3 = 2". Then all fifty of them shouted together, "x plus "Oh, no!" said the teacher. y." Apparently my nonverbal reaction had not been "Why not?" I asked. a sufficient clue that the original answer was wrong. "Because subtraction means "take away" and How can children in such a school attain a profound you took away two blocks. So it should be written understanding of fundamental mathematics? I am '5-2= 3."' I explained that subtraction could mean now convinced, after visiting many schools, that this "take away", but it could also mean "missing

FEBRUARY 2005 NOTICES OF THE AMS 209 addend". It seemed to me that since the children school, I would feel the flying glass sting my legs. could see three blocks, "5 - 3 = 2" was preferable, But the next hour was one of the most intellectu­ but "5-2= 3" is not wrong. The next week we ex­ ally exciting of my life. I just answered one ques­ plored the "difference" meaning of subtraction tion after another and made sure that every child and the "motion" meaning. (I walk five steps toward was following. An hour! With eight-year-olds! To­ the window and three steps away. How many steps tally focused. am I from where I began?) At the end, the teacher, who had been on the She was startled when half the children passed edge of her seat the entire time, asked, "What do the subtraction part of the November standardized you call this kind of mathematics, Dr. Kenschaft?" test-without any reinforcement from her. She had Suddenly I began to meta-think-no longer focused never had a child pass it before. The crucial role on the here and now. of mathematical knowledge on the part of the "This is the beginning lesson in calculus that I teacher was becoming obvious to me. do with my college students!" I had considered the The following year I led a team that won an limit of 60/x as x goes to zero. The children had Eisenhower grant and began working in an urban­ never heard of division before, but they learned it suburban coalition, going to both all-black schools in that hour-all of them. I used six Cuisenaire and all-white schools. My first time in a fifth grade ten-rods and asked first how many sixties there are in one of New Jersey's most affluent districts (white, in sixty, then how many thirties, then how many of course), I asked where one-third was on the tens, and then how many ones. Then I told them number line. After a moment of quiet, the teacher about tenths. Then I asked how many tenths there called out, "Near three, isn't it?" The children, how­ are in sixty, telling them I didn't want anyone to ever, soon figured out the correct answer; they shout out. Slowly hands were raised-and they had came from homes where such things were dis­ the right answer. I had everyone whose hand had cussed. Flitting back and forth from the richest to been raised explain the reason for the answer to the poorest districts in the state convinced me that the entire class, and then I asked how many hun­ the mathematical knowledge of the teachers was dredths there were in sixty. Of course, I had to ex­ pathetic in both. It appears that the higher scores plain what a hundredth was first. This time almost in the affluent districts are not due to superior half the class raised their hands fairly quickly. The teaching in school but to the supplementary in­ concept of infinity and how it might arise had been formal "home schooling" of children. constructed in their minds, and they were excited. Tests encourage systemic cheating, but there is Later that spring the Iowa scores were revealed no way to deceive an educated observer about stu­ for the three third grade-classes with whom I had dent and teacher enthusiasm. In the spring of my been working intermittently for three years. Two first year in the Newark school, Exxon sent Pat classes had median scores at the 60th percentile, Hess to observe what was happening. The princi­ a great increase from the 25th percentile only three pal said, "We haven't had enough standardized years earlier. The third class had a median at the tests yet to be sure of a measurable difference, but 70th percentile, with only one child below the 50th I can assure you I hear far more conversation about and that child in the 40s. This dramatic increase mathematics than I ever did before. I hear the chil­ in Iowa scores was accomplished by the same teach­ dren talking about math in the hallway. When I walk ers and a mathematician with no elementary school into the teachers' lunchroom, I hear them talking background whatsoever. I did have high school about math!" certification; I had one year of high school teach­ The Eisenhower grant paid me to visit each ing experience and the background of having raised school only once a month. During the spring of the two children of my own, but no official profes­ third year that I had been visiting the original sional preparation except a doctorate in mathe­ school, one of the third-grade teachers said at the matics with a specialty in functional analysis. The beginning of the class, "Could we put aside the les­ teachers and I shared a concern for the students. son you and I planned and just have you answer They were good teachers, and I had access to the the questions of the children that I can't answer?" national materials of the late 1980s. We talked Think about what that question indicates about her with each other. I certainly was not teaching "to" eagerness to learn and about our relationship-and the Iowas. I was trying to share my understanding then what it indicates about the need for third-grade of fundamental mathematics-and it seems that teachers to learn more mathematics. that was what was needed for the children to do The children were all African American. The well on the highly computational old-fashioned school is in one of the worst neighborhoods of our standardized tests. country's poorest city. There were no greens grow­ A couple of years later I was in another city in ing within a block of the school except an occasional another all-black class that was much more umuly. dandelion that would poke up between the sidewalk The teacher continually complained to me aloud cracks. When the wind blew as I approached the about the children's misbehavior. They too were

210 NOTICES OF THE AMS VOLUME 52, NUMBER 2 tlllnking out of bounds. I watched her try to squelch young exploring mathematical minds such as I en­ the children's impudent mathematical questions, joyed so much in the poorest city in our country. and then hesitantly asked if I could try to answer I wonder if she realized when she was eight that them. I told her it would take some time, and she the average height of the children in her class al­ agreed. I went through the same explanation of the together was between the average height of the boys limit of 60/x as x goes to zero, not sure if this class and the average height of the girls. Was that un­ could pay attention well enough. But they did. The derstanding taught out of her by teachers who in­ teacher was amazed not just that they all seemed sist upon memorization because they themselves to understand division lickety-split, but that they don't understand? Will she, kindly, well-meaning paid attention to this obviously very difficult topic. person that she is, do the same to classes of inno­ How much are our social problems due to our cent children over her lifetime? not challenging children enough? Life can be bor­ My own interest in elementary school mathe­ ing if you just tread water intellectually. How much matics education grew out of my equity concerns. do humans need intellectual challenge? How much Ever since my great-great-grandfather came north would providing an excellent mathematics educa­ from a slave-holding family to fight on the North­ tion for our elementary school teachers help mit­ ern side of the Civil War, my family has been ac­ igate our drug and crime problems? tive in race relations. The men have encouraged the A couple of years ago I discovered that the prob­ women to be "real people," and the women have lems are even more basic than I had realized ear­ tried to live up to the advantages we were given. lier; teachers' understanding of addition is murky. My survey of black mathematicians in New Jer­ Montclair State certifies teachers without provid­ sey, like my earlier survey of black women with doc­ ing a special course in either mathematics or math­ torates in mathematics,3 was done by networking. ematics education for them, so they are scattered I started with some former Montclair State stu­ in our general education courses. I had one pleas­ dents, and each time I reached another black math­ ant, diligent young woman in such a class who in­ ematician, I asked for names of others. With only tends to be an elementary school teacher. On the two (nonconsecutive) semesters of released time, last day of her formal mathematics education she while teaching three classes during those semes­ responded to my offer to answer questions before ters, I located one hundred fifty black mathemati­ the exam by saying there was something wrong with cians in New Jersey. My subjects were surprised exercise 11 on page 69 of the text (my book Math­ there were so many by the time I told them I had ematics for Human SurvivaZZ). "In 1999 U.S. cars achieved an average of 28.11 located thirty, but at the rate I was going when I mpg, but light trucks were rated a mere 20.3 mpg. ran out of time, I suspect there were three hundred. Their mileage was 23.8 mpg altogether. What pro­ In my limited time I was able to get responses from portion of American vehicles were light trucks in only seventy-five- twenty-six written responses to 1999?" my mailed inquiry, and forty-nine successful fol­ "What's wrong?" I asked. low-up phone calls. I will be glad to send a packet '"Altogether' means add, so the mileage alto­ of my writing about blacks in mathematics and/or gether must be 48.41 miles per gallon." I tried to women in mathematics to anyone who requests explain but to no avail. Some of the other students them by emailing me at kenschaft@pegasus. gave fine explanations. She is a cooperative person montclair. edu. An outside indicator that others and realized she was outvoted, but it was clear appreciate my concern with minorities' participa­ she did not understand. tion in mathematics is indicated by the fact that in One of the other students noticed my frustra­ 2003 I was chosen to lead the Task Force on Eq­ tion and anger-not at her, but at a system that will uity and Diversity Integration of the National Coun­ send people so poorly prepared into the elemen­ cil of Teachers of Mathematics, an organization of tary school classroom. "You know, Dr. Kenschaft. about 100,000 members. Key words. We've all been taught that 'altogether' I support improving pedagogy and helping mi­ means add." The rest of the class nodded as I norities feel better about themselves. Indeed, my sighed. avid collecting of role models has been a major fac­ "And 'left' always means subtract," said another tor in providing young African Americans a math­ with a wry smile. ematical heritage. I strongly approve of programs The student who will be an elementary school that involve families. However, none of these ac­ teacher earned a legitimate "B" in that course. With­ tivities will begin to close the racial mathematics out a course about the fundamentals of elementary achievement gap until American elementary school mathematics, she is woefully unprepared to face 3 P. C. Kenschaft, "Black Women in Mathematics in the 2 P. C. Kenschaft, Mathematics for Human Survival, Whit­ United States," American Mathematical Monthly, 88:8, tier Publications, Island Park, NY, 2002. October 1981, 592-604.

FEBRUARY 2005 NOTICES OF THE AMS 211 teachers know mathematics much better than they they need to know and how do they use it? There do now. already are some adequate programs available, but What can mathematicians do about this situa­ further insight and improvement is needed. Hyman tion? There are many possibilities, but they seem Bass of the University of Michigan has been work­ to fall into three categories: ing with math educator Deborah Ball, also of Michi­ 1. Structural Change: The mathematical com­ gan, to investigate these questions. munities need to collaborate with anyone else who Roger Howe of Yale University has been work­ will join the effort to lobby strenuously for the need ing with current math educators to help them clar­ for radically improved teacher knowledge. The . ify their own mathematical knowledge and extend major argument is that while once only a few peo­ that of their students. Jerome Dancis of the Uni­ ple (white men?) needed to know mathematics, versity of Maryland at College Park has been mon­ now a large segment (a majority) of the population itoring state tests and finding appalling errors in need to know significant mathematics for career, questions that reflect either lack of mathematical citizenship, and personal reasons, and it is ex­ knowledge or careless proofreading among those ceedingly wasteful to have a primary-level teach­ who compose high-stake tests. ing corps with such limited knowledge; remedial 3. Remedial Work: Until the current cohort of mathematics learning later is more difficult and, elementary school teachers retire, the mathemat­ therefore, expensive. That the current situation is ical competence of today's children will require also unfair to minorities may have less political that their teachers receive continual remedial pro­ clout but should also be emphasized. This change grams. Hung-Hsi Wu of the University of Califor­ of understanding on the part of decision-makers nia, Berkeley, has written about his leadership at and the public will not be easy, especially since Berkeley in summer programs jointly sponsored many harbor deep math anxiety due to their own with a math educator. Paul Sally of the University poor education and are threatened by the thought of Chicago has done extensive work with both that others might learn it easily-and/or are re­ teachers and high school students evenings and luctant to "inflict" on innocent children the "bur­ weekends. He reports working fifty hours a week den" of learning mathematics well. as a mathematician and another fifty as a mathe­ The AMS can play a leadership role, but it will matics educator. Most of us don't have that level need collaboration from all member organizations of energy and/or commitment, but some of us will be needed for teacher remediation until the system of the Joint Policy Board for Mathematics. The In­ is healed. stitute of Electrical and Electronic Engineers (IEEE) The above is far from an exhaustive list of ei­ has expressed similar concerns, and there are ther people or activities; it merely indicates exam­ doubtless other technical societies that could be re­ ples of good beginnings. Significant efforts at re­ cruited. The mathematical education of elementary mediation for teachers have taken place throughout school teachers is basic to the health of all these the country. However, remediation is far from disciplines, as well as the economic and political enough. All aspiring elementary school teachers health of our country. must be taught appropriate mathematics before 2. Individual Actions: Those who teach in in­ they begin teaching children. stitutions that certify eiementary school teachers Children who have been mathematically abused can work to make sure adequate specific courses are much less able to benefit from mathematically are provided for them and volunteer to do a con­ competent teachers when they finally reach them. scientious job when teaching such courses. Such One lesson our current elementary school teach­ teaching requires patience, and a determination to ers convey powerfully is that math is too difficult direct one's anger at the system, not the victims of to understand. Because knowledge of mathemat­ it. Teaching a "profound understanding of funda­ ics correlates strongly with economic and political mental mathematics"4 is very different from teach­ achievement, the mathematical education of all el­ ing traditional collegiate mathematics, but for the ementary school teachers is the paramount equity next few decades, some mathematically knowl­ issue. As Will Rogers said long ago, "You can't edgeable people must do it if all university math­ teach what you don't know any more than you can ematicians are to be able to teach university-level come back from where you ain't been." mathematics some day. What mathematics is appropriate to teach as­ piring elementary school teachers? What math do

4 This phrase was coined by Liping Ma in her important book, Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States, Lawrence Erlbaum, Mahwah, N], 1999.

212 NOTICES OF THE AMS VOLUME 52, NUMBER 2 AMERICAN MATHEMATICAL SOCIETY

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

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

The Prize Selection Committee requests nominations for the initial award, which will be presented at the Joint Mathematics Meetings in San Antonio, Texas, in January 2006. Letters of nomination may be submitted by one or more individuals. Nomination of the writer's own institution is per­ mitted. The letter should describe the specific program(s) for which the department is being nominated as well as the achievements that make the program( s) an outstanding success, and may include any ancillary documents which support the success of the program(s). The letter should not exceed two pages, with supporting documentation not to exceed an additional three pages.

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

Deadline for nominations is April l, 2005. W H A T s aBrane? Gregory W. Moore

The term "brane" has come to mean many things I-form of electromagnetism. Heuristically, these to many people. Broadly speaking, it refers to a may be thought of as differential form-valued fields physical object appearing in field theories of grav­ on spacetime, although a proper description turns ity and strings. It can refer to widely diverse notions, out to require notions of K-theory and differential from soli tonic solutions of (super)gravity and (su­ cohomology theories. Charged branes are sources per)string theories, to local boundary conditions in for these generalized gauge potentials. two-dimensional conformal field theory, to objects Let us translate some of these physical in certain categories associated with sheaves on notions into mathematics. The action principle algebraic varieties. governing a point particle of mass m and The essential physical intuition underlying the electric chargee, moving through a spacetime Jvl, notion of a "brane" may be captured by a few sim­ with metric g and Maxwell connection A, is ple examples. A p-brane is simply any object of Sparticle = hv mds+ hv e1> *(A), where ds is the p-dimensional spatial extent. Thus a 0-brane is a induced line element on the worldline. When point particle, whereas a string is a I-brane. The added to the standard action for g and A, namely, etymological root of "brane" is "membrane", the Sbulk = 16; cN f.Jvtvol(g):R - f.Jvt ~F 1\ *F (where case p = 2. The surface of the earth's ocean may GN is Newton's constant, :R is the scalar curvature be viewed as a 2 -brane wrapping the earth and of g, and F = dA is the Maxwell fieldstrength), propagating in the (3 +I)-dimensional spacetime the action Sparticle represents a source term in of our solar system. The history of a p-brane may the Einstein-Maxwell equations of motion. Thus be described mathematically by a map 1> : W ~ Jvl, the brane may be studied as a solution in field where W is some reference (p + I)-dimensional theories of gravity with localized energy and manifold, while Jvl represents a "spacetime" charge density. The generalization of the brane through which the brane propagates. Jvl is also re­ action to p-branes is of the form ferred to as the "target space", while 1J(W) is re­ ferred to as the "worldvolume". Sometimes a brane (I) Sbrane = f-w Tvol(1> * (g)) + f-w E1> * (C) can have thickness, provided this is small on the where Cis a differential form gauge potential, and scale of the spatial extent in p-dimensions. Thus, E is the "charge" (which may itself be represented a rope is effectively a I-brane and the earth's ocean by a differential form). The generalization of Sbulk is effectively a 2 -brane. is the action principle of a (super)gravity or Branes play an important role in theories of (super)string theory on Jvl. The typical supergrav­ gravity, so a key physical attribute is the tension ity brane solution is a soliton-its stability is guar­ T, the energy per unit volume of the brane. The ten­ anteed by topological considerations, which are sion of a 0-brane is its mass. Branes can have other often intimately connected with supersymmetry. attributes, such as "charge". The supergravity and A central point is that a brane has dynamics: it superstring theories in which branes play promi­ can wiggle and bend. The oscillations are sections nent roles are generalizations of Einstein-Maxwell of the normal bundle to 1J(W) c Jvl and hence are gauge theories. In addition to the gravitational described by a (p +I)-dimensional scalar field the­ field, string theories typically include a collection ory on the brane. For the earth's ocean, the scalar of gauge potentials generalizing the connection field would represent the height of the waves. Mathematically, these degrees of freedom arise be­ Gregory W. Moore is professor of physics at Rutgers cause the soliton solutions come in families. University. His email address is gmoore@physi cs. Physicists consider Wand Jvl of different sig­ rutgers.edu. natures. They add various structures to both the

214 NOTICES OF THE AMS VOLUME 52, NUMBER 2 target space and worldvolume, endowing them the brane's dynamics. The normal bundle scalars with gauge bundles and tensor fields, and gener­ become N x N hermitian matrices. The connection alizing them to supermanifolds. In some cases they on a line bundle becomes a nonabelian gauge field, propose to discuss the quantum behavior of branes i.e, a connection on a rank N vector bundle over by integrating e-1 I liSbrane over the space of all maps W. This fundamental phenomenon has ultimately ¢; they even boldly contemplate summing over led to many startling new insights into gauge the­ topologies of 1¥. One instance in which these ory. Just one example of such an insight is the dreams can be realized, with some degree of rigor, AdS/CFT correspondence, a vast generalization of is the case in which the 1-branes are the funda­ the famous relation between three-dimensional string theory. mental strings in a supersymmetric Chern-Simons gauge theory and two-dimensional One distinguished class of branes are the "D­ (rational) CFT. The replacement of the normal bun­ branes" of string theory. For these one can introduce N N to connections a fundamentally different viewpoint on the ques­ dle scalars by x matrices leads tion: "What is a brane?" String theory describes a between D-branes and noncommutative geome­ profound relation between a quantum conformal try. Using these insights in the framework of branes field theory (CFT) on a two-dimensional worldsheet within branes leads to new perspectives on hy­ Wand a corresponding quantum field theory on the perkahler quotient constructions and the ADHM target space Jvl. The spacetime field theory includes construction of instantons. gravity. In this context, D-branes correspond to CFTs We began by describing a brane as an object on Riemann surfaces W with boundary. For exam­ propagating through a spacetime. This puts the ple, suppose W = [0, rr] x R so that 1> describes the spacetime on a primary, and the brane on a sec­ propagation of an open string through spacetime. We ondary footing. However, a common theme in the now select a submanifold S c Jvl and impose the study of D-branes has been the idea that in fact, boundary condition that ¢ : oW - S. For certain the (string) field theory on the brane is the primary submanifolds, the associated two-dimensional field concept, whereas the spacetime itself is a sec­ theory will be conformal. (Typical examples of such ondary, derived, concept. This notion has been submanifolds include holomorphic subvarieties of given some degree of precision in the so-called complex manifolds and special Lagrangian subvari­ Matrix theory formulation of M-theory. A rough eties of symplectic manifolds.) The "D" in D-brane analogy of what physicists expect may be described refers to the fact that some of the coordinate direc­ in the context of purely topological branes, where tions in thus carry Dirichlet boundary conditions. 1> the field theory on a brane is described in terms One may recover the notion of branes as solitons in of a noncommutative Frobenius algebra, and the supergravity via a semiclassical approximation to string field theory. "spacetime" in which it propagates is derived from Now, purely in the context of CFT, a D-brane may the Hochschild cohomology of that algebra. These be defined to be a local boundary condition preserv­ ideas might ultimately lead to a profound revision ing conformal invariance. Conformal field theories of the way we regard spacetime. on Riemann surfaces with boundary can be described The recognition of the importance of branes in axiomatically as a functor from a geometric category string theory has been a central development, one to an algebraic category. Simple considerations of that is still undergoing vigorous evolution. We have gluing show that the boundary conditions should be focused above on D-branes, but there are other regarded as objects in an additive category. It is via important, but less well-understood, branes. For this route that D-branes are identified with objects example, a deeper understanding of the "solitonic in certain categories. Moreover, some CFTs carry a 5-branes" will lead to constructions of quantum CFTs special type of supersymmetry, known as N = 2, and string theories in six-dimensional spacetimes. which allows a "twisting" or association with a related Further development of the theory is likely to have topological field theory. If the target space is a a wide variety of important mathematical applica­ Calabi-Yaumanifold, then some of the branes in the tions. CFT can be interpreted as objects in the derived cat­ egory of coherent sheaves on the target. This in turn References has beautiful applications in the theory of mirror [1) Virtually all relevant research and reviews on this symmetry. material can be found on thee-print archive, http: I I One more crucial point is that the dynamics on www. arxi v. or g. An example of a recent review is the D-brane worldvolume is a gauge theory. In C. V. Johnson, D-brane primer, http: I l www. arxi v. addition to the scalar field describing fluctuations orgl absl hep-thl 0007170. of the brane in the normal directions, there is a line [2) Mirror Symmetry, K. Hori et al., AMSI Clay Mathemat­ bundle with connection on 1¥. When N "elementary" ics Institute, 2003. branes are placed on top of each other, new non­ [3) Topology, Geometry and Quantum Field Theory, abelian degrees of freedom are needed to describe U. Tillmann, ed. Cambridge Univ. Press, 2004. f EBRUARY 2005 N OTICES OF THE AMS 215 Presidential Reflections: Interview with David Eisenbud

There is also the Committee on Committees, Every other year, when a new AMS president takes office, the which helps the president do this, because there Notices publishes interviews with the incoming and outgoing are something like 300 appointments a year that president. What follows is an edited version of an interview have to be made. My first act as president-really with David Eisenbud, whose two-year term as president ends as president-elect-was to gather together people on January 31, 2005. The interview was conducted in fall2004 by Notices senior writer and deputy editor Allyn Jackson. who I thought would be very well connected and Eisenbud is director of the Mathematical Sciences Research also who would reach into many different popu­ Institute (MSRI) in Berkeley and professor of mathematics at lations of mathematicians. One of my ambitions was the University of California, Berkeley. to provide a diverse new group of committee mem­ An interview withAMS president-elect James Arthur will bers-young people and people from the minority appear in the March 2005 issue of the Notices. community. I also tried hard to make sure that women are well represented on committees and slates for elections. And I am proud of what we did Notices: The president of the AMS has two types in that respect. That's actually the largest part of of duties. One type consists of the things that he or the president's job, in terms of just sheer time and she has to do, by virtue of the office. engagement. Eisenbud: Which is almost nothing, right? The Another thing I enjoyed is running council meet­ unique duty that's in the Bylaws is to give theRe­ ings. For a long time I've felt that, if I had to be on tiring Presidential Address, which I haven't done a committee, I would prefer to be its chair. I try hard yet! to bring out what people have to say and help Notices: That's true-and still you have been them to express it. That kind of facilitator position very busy! The first type of duty is what the presi­ is one that I think I have become good at and that dent is traditionally expected to do. The second type I like. consists of things you do because you are interested Notices: What meetings did you chair? in particular issues. Eisenbud: The main ones are the meetings of Eisenbud: Yes. Certainly the largest part of the the Executive Committee and the meetings of the job that has to be done by the president is ap­ Council. pointments to committees, and that has turned One area that's been of special interest to me out to be rather fun. [AMS secretary] Bob Daverman is scientific meetings. Of course, MSRI runs lots and I get together, mostly on the phone. He has a of conferences, and I am also engaged in the long list of appointments that have to be made, and Banff conference center. So I have a broad view of we talk about how to recruit people who would be the conference scene and strong opinions about interested in the topics the committees are ad­ how conferences should be done. I have thought dressing. It's gossip with a purpose. about the AMS conferences, and there are two

216 NOTICES OF THE AMS VOLUME 52, NUMBER 2 things that I have done that I think are interesting Eisenbud: Here a few estab­ and that maybe will have lasting impact. One is the lished leaders come, and they Special Sessions on "Current Events in Math", held may give survey talks, but the at the Annual Meetings, which I organized with vast majority of the participants the help of an excellent committee. The idea came are very young people, just start­ from a suggestion by Mike Artin. I thought the ing out in mathematics. The two first session, in 2003, went well; the second, in conferences were run differ­ 2004, was even better. We have a wonderful lineup ently, and both worked well. In for 2005 in Atlanta. one of them, the young people Notices: Can you describe the format of those presented their own research. sessions? In the other, the senior people Eisenbud: The easiest way to describe it might decided on five big topics, and be to say that it's like the Bourbaki Seminar, but the young people ran seminars broader and more accessible: broader in the sense around those topics with young that there is more applied math mixed in, because people as speakers and with a I feel that that sweep of math is part of what's ex­ senior mentor in each one. citing in our field, and more accessible in the sense My model for such young that the talks aim to be comprehensible to more people's conferences was a mathematicians. Each talk is split into two halves; series of conferences called David Eisenbud the first part is supposed to be super-elementary Geometrie Algebrique en and the second also quite accessible. Different Liberte (GAEL) started, I believe, by Andre speakers have handled this in different ways, and Hirschowitz, that take place in Luminy, France. some of the speakers did an incredible job of mak­ They are organized by and for young people, and ing topics I considered sketchy for such presenta­ the name refers to the fact that they are free of the tions quite interesting and accessible. In 2003 two control of their elders in this. The GAEL conferences out of the four speakers produced writeups, and have been sponsored by EAGER, the European in 2004 four out of four. [AMS staff member] Raquel Algebraic Geometry network. EAGER has just lost Storti produced a wonderful little booklet of them. its funding from the European Community; I hope They will appear in improved form in the Bulletin GAEL is not jeopardized. of the AMS, too. Notices: Bringing in a lot of young people and Notices: After you stop being president will you having them make decisions about what's on the continue organizing this Special Session? program sounds like a good idea. Eisenbud: The session doesn't yet have a long­ Eisenbud: Yes, it's a heady mix, it's exciting for term structure. My original idea was that after them, and it has worked very well. Also, it is a new itself known to the first two years I would pass it to another chair way in which the AMS could make and committee, but this hasn't happened yet. I cer­ young folks. back to the AMS itself, some of the other tainly do want to give it a life beyond my tenure. Coming I've found exciting in this job have been the By the way, I haven't been doing this alone, by things Washington communications, such as the Congres­ any means. It would not have been nearly as good sional Luncheons that the AMS runs every year. Sam without the committee that has worked on it. That Rankin [director of the AMS Washington Office] committee was loosely based on MSRI's Scientific organizes these. I think they have the potential to Advisory Committee. have a big effect on Congressional staffers. We have The other conference innovation I've worked on had very good people speak on interesting things Research Conferences has to do with the Summer connected to mathematics research. It's been fun to [SRCs], which are up for renewal now. Two years connive with Sam in planning these events. in a row we've experimented with a special con­ I've also been interested in the structure of the ference for young people, in which the presenters AMS. For example I have begun a discussion-it would are mostly pre- and Uust) postdoctoral mathe­ be several years before the discussion could possi­ maticians. I think it's a niche that's not being filled bly lead to any action, since this would require a by anyone else and one that I would like to see the change in bylaws!- about the structure of the pres­ AMS step into in one way or another. I am hopeful idential elections. Typically we have a committee that such young people's conferences will play a that works hard to find two really good candidates. large role in the grant application that the AMS and One of them wins the election, and the other is usu­ SIAM (Society for Industrial and Applied Mathe­ ally rather put out by this- understandably enough. matics) are about to make [for the SRCs], and I They are both very good people, and either could hope that application is granted. have done the job well. We often lose someone who Notices: Usually one would want to have estab­ is all primed for service and who could do a good lished leaders at a conference, but what you're job. So my proposal is to make the one who polls describing is different.

FEBRUARY 2005 NOTICES OF THE AMS 217 fewer votes vice-president that year. In the current joining unions as much as they used to, either. But system we elect a vice-president each year. Why not it really is true that the AMS does a lot of things have the vice-president-elect be the failed presiden­ for the community that are just not in the agenda tial candidate every second year? The failed presi­ of individual mathematicians, so it's very impor­ dential candidate usually polls about as many votes tant for the community that the AMS remains as any vice-presidential candidate. I would like to strong. The AMS is also one of the biggest pub­ see that change. There are complexities and ramifi­ lishers of advanced mathematics books now-it cations-it's going to be discussed, and I'm sure all may well be the biggest, after the shakedown of these difficulties will be aired. But I think something commercial publishers. It's a very important orga­ like that would be a good idea. nization for the world mathematical community Notices: Do you think contested elections are a and for the American mathematical community in good thing for the AMS? We have not had them for particular. very long. Notices: Why aren't young people joining in Eisenbud: Ten years, a little more. Well, it's greater numbers? mixed. There are people who simply won't serve Eisenbud: Across our society, professional iden­ under those circumstances, and there are people tity and professional membership have become who are quite turned off by losing. On the other less important. It's a trend visible in practically hand, I think it's good for the membership to feel every membership organization. Within our par­ that they have some choice, and that it's not just ticular community, I don't know if there are special the old fogies on a committee who are making the forces. The AMS has been studying this problem and decision. It gives freshness to the procedure. I trying to understand better what members want and think it's a mixed blessing, but I don't propose to how the Society can be of use to members, and I get rid of it. think there will be several initiatives appearing Notices: Maybe your proposal is a good com­ soon. The Membership Department is working hard promise. to make AMS membership per se more valuable. A Eisenbud: It would make the system a little problem, in a way, is that the AMS is so community­ gentler. spirited: the idea of making some benefit not avail­ When I was asked whether I would stand for able to the people who are not members is painful. election myself, I had quite mixed feelings- partly For example, very few societies make the mem­ because of what we just talked about but, even bership list available to everybody without being more, I wondered: how am I going to fit this into members. Very few societies make the most-read my life? I had a sabbatical coming up, I had all journal, which is our Notices, available to every­ kinds of plans about what research I wanted to do. body without being members. Making those things I keep up some research while I am director at freely available may not be in the self-interest of the MSRI, but it's a struggle. I had mixed feelings about Society, but at least in the short run it is good for the AMS job because of that, and I think many peo­ the greater mathematical community. It is good in ple who are asked to consider the job of president the long run too unless it damages the Society, have similar worries. I would like to record my feel­ whose well-being is good for the mathematical ing that, knowing what I know now, I would kick community in many ways. A new balance may have myself if I hadn't said yes to that nomination. It's to be struck between these needs. been quite an interesting experience. I have met peo­ Notices: Any thoughts on the future role of the ple I would not have met otherwise, and have AMS? learned about an organization that I think is just Eisenbud: The future looks bright to me; there marvelous. It functions by and large extremely well. is a huge amount going on. I think the AMS core So I am very pleased to have done this job. Not that staff- John Ewing and Bob Daverman in particu­ I'm sorry my term is ending! It's been quite intense, lar-are wonderful, and it has been a great pleasure and I have plenty else to do. I have a wonderful to work with both of them, and I admire them a lot. successor in Jim Arthur, who has thrown himself I really enjoyed working with each of them in dif­ into learning about the job, and I think he'll do ferent ways and learned a lot from them. And with extremely well. Sam Rankin too, concerning advocacy for mathe­ Notices: One thing the AMS has been consider­ matics in Washington. All the mathematics orga­ ing a lot lately is membership and how to renew the nizations are in there pitching, and the AMS is one stream of members. Young people who are enter­ of the leaders. I think the Society is in good hands ing the field don't automatically become members, and will continue to be. There is a huge pool of as they used to. talented and committed people the Society draws Eisenbud: When I was a graduate student I re­ on. That impressed me a lot, how seriously people member [Irving] Kaplansky, who was one of my take their role in the AMS and how willing they are teachers, said to a group of us: "Of course you to spend time on committees and such, making sure should join the AMS. It's the union!" People aren't the AMS functions well.

218 NoTICEs oF THE AMS VOLUME 52, NUMBER 2 AMS Website Connects Math and the Public

Math in the Media is an online magazine posted aimed at the general public. The reviews appeared monthly on the AMS website. Its main aim is to in­ in a variety of newspapers, magazines, and jour­ form and entertain both mathematicians and in­ nals, and links to the reviews are provided where terested members of the general public, by high­ possible. One also finds here references to reviews lighting coverage of mathematics in the mainstream of about ten movies and plays that feature math­ media. Another offering on the AMS website is the ematicians as main characters- a sign of the new­ monthly Feature Column, which provides exposi­ found appeal of mathematics as a theme in pop­ tions about mathematical topics accessible to the ular culture. general public. This fall, the AMS inaugurated a that con­ snazzy new design for both Math in the Media and Another offering of the AMS website the Feature Column that makes them even more nects math and the general public is the Feature fun and easier to use. Column, which each month presents a lively and Each month, the main page of Math in the Media accessible introduction to a mathematical topic. For carries "Tony's Take", a survey of the previous the past three years, Joseph Malkevitch of York Col­ month's news relating to mathematics, written by lege of the City University of New York has writ­ Tony Phillips of the State University of New York ten columns on such topics as marriage theorems, at Stony Brook. His brief synopses of stories ap­ voting, bin packing problems, prime numbers, and pearing in print and on radio and television are mathematics and art. A patient and knowledgeable witty and eloquent. As one sees in his recent sum­ guide, Malkevitch strikes a good balance between mary of a story in Nature about how cells develop providing needed details and shielding the reader in the eyes of fruit flies, Phillips has a knack for from complications. These essays can be prof­ distilling the mathematical substance in stories itably read by members of the general public, as He has a broad view of about all kinds of things. well as by mathematicians interested in broaden­ mathematics as a subject in its own right and in ing their horizons or finding topics to awaken its relations to art, literature, society, and science. As a way of keeping up on how the media are cov­ their students' interest. ering mathematics, Phillips's column is a must­ The Feature Column archives contain a total of read. more than 80 columns written since 1997, when The "Math Digest" section takes a more com­ this section of the AMS website was started by prehensive approach to following math coverage Steven Weintraub of Lehigh University. Tony in the media. Pooling the efforts of AMS staff and Phillips wrote the columns for three years, and AMS-AAAS Mass Media Fellows, the "Math Digest" Bill Casselman of the University of British Colum­ section provides bibliographic references and short bia also wrote a few. Starting in February 2005, Cas­ summaries of media stories about mathematics. selman, Malkevitch, Phillips, and David Austin of Among the outlets systematically covered are Sci­ Grand Valley State University will collaborate on ence, Nature, New Scientist, the New York Times, editing the column, with pieces written by one of the Chronicle of Higher Education, and American them or by other authors. Scientist. The "Math Digest" contributors also stay On the Math in the Media page one also finds on the lookout for math stories in other print out­ links to AMS news, the "Headlines and Deadlines" lets and on radio and TV. With archives reaching email news service, and "This Mathematical Month," back to 1995, this may be the most comprehensive resource for media coverage of mathematics avail­ which contains vignettes about mathematics or­ able on the web. ganized according to the month. Overseen by the The "Reviews" pages contain pointers to re­ AMS Public Awareness Office, these web offerings views of books, plays, movies, and television shows are excellent resources for the mathematical com­ that are related to mathematics. There are refer­ munity and the general public. Check them out. ences for reviews of nearly 200 books, most of them · - Allyn jackson

FEBRUARY 2005 NOTICES OF THE AMS 219 Feature Column http:/ /www.ams.org/featurecolumn

l-Th ill Malf1'" Featu- e Col.om n Euler's Polyhedral Formula A theorem which would make both my liat of 10 favorite theorem• &nd my liat of Theee wab eeaaya •re designed tor thoae who 10 moat influential theor•m• ... hlveal..:f)' dilcova..t thl )l)'& of ITIIthlrrl:ti:e u wellu for rrathiiTIIti:e eaptCe. Mathlrrati::1 il a 1 . ..tmd.:tita fat gJOWill3 ill'd a¥Otvirg eubjllct. Tta domin at lt'l corrirg 10 tlw en:l of thlcalln::ilrye~r ard • b t otp.:>pll&lll pfOdu::irg !ida. Whit waye that l'l'llltarrati::a il beill3 appliki B growirt~ .... thlta lllglllt box-offi:e bbcld:u.111811? Whll w... It'll to bait nova. of tha b)' a.r- ard b:Jun::ta . (Elar'fllllil irclu:JeCA.T ac.,., yar?WI'Da•tt•to batd-«1 rrenan:::i tOwotatd-«

De.: l rl'lk8 .,... to COI1IIIU:It liAI ~ 10 rrathlrr81i::1? Whit about a lilt of tt. 10 o-a-.c ITIIt._.Cil.n~? to g,...t wonwn rrattwrlll::ilr.? Tt. 10 ITDit inllwntillthlo,.rTI? Thlt o nihillt thm18IT'I? • O.C:..Hr:Euler8 Pct,.hedra.l Form.Jia • No.,...Hr:Mattanwfi::al Ma~ai Onttwor-.twrdcorwtru=tirt~lint ltperhlpeeitt)'. • OCID ..r. Votirg G&miB II HeM c.. or. rrat. a lilt of tht 10 Q..-.t a.,...... : VoiirgGanllB I COfTlD... of cU.i::.ll rnai::? M~ I talva • Jat,a·..a:-MachinaSchedulirg Tctw.iklvekyoutiO in::k..DeUahtlrorHan::tel? Yet, • .Ia•: Sin Pa:liiJrgard MachinBScheduli!'l;l • M.y: Sin P.: kirg ftomarat. J:*~p.:IWe corwtr...:tirg lil11 of thil • a,nfNBfworta kin:l ,..._o,.thinltab.lutawi::tllvarillty of vall• • ..rclli:- Oi&g::nliJil : Part II ildM -~ . Whit ITII ... a COfTlD_. g...t? • Fa•r.ry : OiiQon~.B : Part I StDUti &COfTlD- of ... o-t pile• be put • •••ry:Cul:&l on a eton *' of g.- whMiaral'ar COfTlDiaf wt'D perhlp. cofTlD-=I rothirg that 10• 10 thl V_~ _t.tafuU41Ch_,fia t.ghla a1 thl tnt pe~~on. )'M co~ too tirml • nwy pile• • • Yet)' hgh llwe& of inlpiratbn. il orra.:rl T~ t.rg tht f"-t of ny Ut two colurml .. 10b .-or of thl F.. ute Colulm, ~ - wl inll9"" WI wrill • AMS t'DR9paga two cotunn abol,j a tt.D..m whi::h woutj .,... • Your web account • About thaAMS m::atinfkantllllt'-::1...,... Thil both ny lilt of 1Dfl..worlilthiO..n11 .m nr lilt of10 • Joinl haAMS Math and the Media http://www .ams.org/mathmedia

Tony Phillips' Take on Math In Math Digest Media a~ •• ,.,..,IMol•rtioMaliiMt ....tlletMtioel• tllepopea.,,....

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Recent Math Digest Su mmo.,ies: IT and the Riemann Hypothesis Posted hfNe 2 December 2004 :

"What is th e Riemann Hypothesis and why "Wh at Makes an Equat ion Beautiful," Now Shou ld I Care?" is th e provccat ive title of a York Times . 24 Octob er 2004 piece by Rob in Bloor posted at IT-Director .com on October 5, 2004 . Th e site "provides IT In a colu mn in Physics World magazi ne, decision makers with aonestop sourceof all ph ilosopher an d historian Rob ert P. Craase current IT news. information, analysis and as ked readers whic h eq uat ions th ey ad vice." (IT = In formation Tec hnology) . Na turally, considered to beth a gr eatest . He got 120 Di gest report on there is no attempt at a correct statamerH at th e r es pon ses proposing 50 differen t equations. math ematics and art. Ri emann Hypoth esis ("Without bothering tostate This artic led iscussas Crea.sa's experimen t 1 th e details, it is a proposed formu la that and also provid as readers with J. nice lh-' l.lh'd l.tnk..•.; calculates th e nu mber of primes lass than a context to apprecial e the power of lllo,:...a given nu mber") but t he reason why IT decision math ematical equat ions . The top vote-g etter s Fe ture Column makers mig ht be concerned is t he "worrying were Maxwell's eq uat ions for RecentNowa predictions that if the Rieman n Hypothesis is electromagnetism and Euler 's equ ation, e i1t Newafromthe D.C. confirmed mathematically, th en mo.st of th e + 1 = 0. A list of 1&oth er winners is giv en in a Office en cryption sch emes we use in c ommerceand sid abar. Most of t he eq uations relate to ' Thia Mathematical Month government will sudd enly be vu In erable ... • physics, but the Pyth agorean th aoremand the Riemann zeta f u net ion made it onto t he ForJoumaliats togeth er with news of its possibleconfirmat ion by Lo uis de Br ang es and perhaps by others. Th a list. Pre» A•lease.a risk for IT is • if the mathematics surrounding th e AMS in the Newa solution reveals quicker ways to factorize -- llJiyn Jackson numb ers. k tually even th en it wi ll only matter if ~ S,•,n\hlht• it raveals much quicker ways to fac torize More . . Ill! I \\IS numbers ." Because public -key cryptoQraphy • is

220 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Book Review

• • • a small idea of what it is ldo all day ... Introductions to Mathematics

Giinter M. Ziegler

What Is Mathematics? An Elementary Approach 4. What are the most important problems in math­ to Ideas and Methods ematics? And why don't all mathematicians Richard Courant and Herbert Robbins work on these? 5. Second edition, revised by Ian Stewart What does it mean to a mathematician that something is proved? And what does it mean if Oxford University Press, 1996 he believes a proof? Paperback, 592 pages, $21.50 6. How and why is mathematics relevant for "the ISBN 0-19-510519-2 real world"? The Heart of Mathematics: An Invitation to 7. Why is mathematics so unreasonably effective Effective Thinking in some applications? Edward B. Burger and Michael Starbird 8. Why is mathematics so hard to understand? Key College Publishing (Springer-Verlag), 2000 And why is most of it so hard to explain? Hardcover, 646 pages, $69.95 All these are valid questions. There are classical an­ ISBN 0-555953-407-9 swers: G. H. Hardy's A Mathematician's Apology Mathematics: A Very Short Introduction probably contains the most famous and the most Timothy Cowers controversial ones. But none of them are eternal Oxford University Press, 2002 or universally valid. As mathematics and the na­ ture of mathematics develop and change, we have Paperback, 144 pages, $9.95 to come up with new explanations again and again. ISBN0-19-285361-9 One may also try to come up with answers that are 1089 and All That. A journey into Mathematics not even intended to be universally valid, with per­ David Acheson sonal views of the world of mathematics. I believe Oxford University Press, 2002 that these are equally useful and important. So, Hardcover, 178 pages, £9.95 what is mathematics to you? ISBN 0-19-851623-1 Suggested Answers One reason why you should look for, and provide, What Is Mathematics? your own answers to such questions is that you Here are some questions for you: won't like many of the answers that you'll get from 1. What is mathematics? others. 2. What are you doing when you are "doing math­ For example: Why is it that these days we start ematics"? with applications whenever we try to present math­ 3. Mathematical research-how does that hap­ ematics to the public? Perhaps this is the easiest pen? Can it be planned? Can it be cast into "pro­ and the most effective way, or the most convinc­ jects"? ing? The one that even politicians might under­ stand? My own experience certainly supports this Gunter M. Ziegler is professor of mathematics at Technische impression. I can't explain the high-dimensional Universitiit Berlin. His email address is zi egl er@math. geometry I do to nonmathematician friends at night tu-berlin.de. at a bar, but I can tell them about mathematicians' fEBRUARY 2005 NOTICES OF THE AMS 221 Robbins

I Was ist emotik?

Springer

work on bus schedules and on hyperthermia can­ Courant was perhaps one of the most influen­ cer therapy (to mention two Berlin examples), and tial "applied mathematicians" of the twentieth they'll be suitably impressed. However, although ap­ century. But there's no "applied math" in his book! plications answers may be interesting and easy However, there is a lot of mathematics, just very and effective, they shouldn't be the only ones! little about mathematics. Courant and Robbins' Another example: What kind of pictures of answer to his title question is to develop and "what mathematics is like" do your kids bring home explain mathematics, a wealth of very classical from school? Do these pictures have anything to and fundamental topics: numbers and number do with what we believe they should be? Aren't their theory, geometry, topology, calculus. The last views of mathematics very lopsided and incomplete, sentence of the introduction reads at best? Do they represent what mathematics "really is about"? Do kids experience the power of For scholars and laymen alike it is not mathematics, the virtues of precision and ab­ philosophy but active experience in straction, mathematical creativity and mathemat­ mathematics itself that alone can an­ ical ideas? Do they learn about this in a way that swer the question: What is mathematics? we think is fair, colorful, multifaceted, exciting, and inviting? Do they get to see mathematics as New Answers we would view it? How do we view it? What is mathematics? Is it changing? Of course it Mathematics According to Courant is, and so we have to ask for, and attempt to give, new answers to the old question. What Is Mathematics? is the title of a classic book The Heart of Mathematics: An Invitation to by Richard Courant and Herbert Robbins from Effective Thinking is the title of one such answer, 1941, published by Oxford University Press, with successful translations into German, Italian, and a book by Edward B. Burger (Williams College) and Russian. Apparently Courant was quite hesitant Michael Starbird (University of Texas at Austin). It about the title and thought that Mathematical is a large volume (650 pages in the first edition), Discussions of Basic Elementary Problems for the with ample four-color illustrations throughout, General Public might be more accurate, but also and a bit of arrogance in the title. What a contrast "a little bit boring." to Courant's book, in style, but also in contents. This Constance Reid tells the story that at a dinner is a textbook for a "math appreciation" under­ in Princeton Courant talked to Thomas Mann, who graduate class; but also fun reading and Viewing told him about one of his books, a little novel for anyone else. The choice of topics is guided by whose German title was Lotte in Weimar. Mann what is or should be interesting to an audience of thought that the same title might work in English, non-science majors. So some classical topics appear; whereas his publisher Alfred Knopf (or rather after a lot of introductory drumming the book Knopf's \Vife) had suggested The Beloved Returns, starts with the pigeon-hole principle and Fibonacci saying that Lotte in Weimar would sell 10,000 or numbers. But this is not part of a systematic de­ perhaps 20,000 copies, but The Beloved Returns velopment. There are rope tricks, games, aperiodic might sell 100,000-with the corresponding au­ tilings, fractals, lots of "modern mathematics", all thors' royalties. So Thomas Mann went for The of this embedded into lots of motivational talk, "fun Beloved Returns, and Richard Courant went for and games", "rrundscapes", "creating new ideas", What Is Mathematics? Courant sold more than "invitations to further thought", and "lessons for 100,000 copies. I don't know about Mann's book. life". It's well done, I think it is good to have, it is

222 NOTICES OF THE AMS VOLUME 52, NUMBER 2 fun, but it is not my style. At forty-one, I may be of mathematics", without having to do any difficult too old or too old-fashioned for this. math. He speaks clearly and concretely about the Personally, I prefer the small and modest attempts role of models and about abstractions, concluding to answer the old question. One recent such attempt "Once one has learned to think abstractly, it can is Mathematics: A Very Short Introduction by Tim be exhilarating, a bit like suddenly being able to ride Gowers (of 1998 Fields Medal fame). It appeared in a bicycle without having to worry about keeping an Oxford University Press series of "Very Short one's balance." He talks about limits and infinity Introductions" that treats an extensive list of topics and about dimension, and at this point even a frac­ concerning nearly everything under the sun, such tal curve comes up, including a picture! And he ex­ as religion, philosophy, and history, but also animal plains why most mathematicians don't worry about rights, cryptography, evolution, Heidegger, Hin­ foundational questions such as "whether numbers duism, and linguistics. There's even "Schizophre­ exist" or about "infinity". nia: A Very Short Introduction". Gowers' last chapter, "Some Frequently Asked Questions", treats mathematics as a human An Author Needs to Be Convinced endeavor. Here's his list of questions: Let's just imagine one of the friendly Oxford Uni­ 1. Is it true that mathematicians are past it by the versity Press mathematics editors knocking at time they are thirty? Professor Gowers's office door. She would introduce 2. Why are there so few women mathematicians? herself, and say "Well, you know, we have this lit­ 3. Do mathematics and music go together? tle book series ... it is really quite successful ... this, 4. Why do so many people positively dislike math- for example, is the little volume on atheism ... it ematics? has just appeared ... couldn't you, for example, 5. Do mathematicians use computers in their work? write one for us ... about mathematics .. .??" And 6. How is research in mathematics possible? Professor Gowers is quite thoughtful and a bit 7. Are famous mathematical problems ever solved skeptical, and he doesn't want to say no right away, by amateurs? because somehow he is intrigued by the challenge, 8. Why do mathematicians refer to some theorems so he just promises " ... to think about it ... " And and proofs as beautiful? then it comes as a considerable surprise (first to Of course I won't give you his answers here. You him, then to his editor) that he does get started on should look at his volume: He certainly does not the impossible task, takes on the challenge. And give "the only possible correct answers", but con­ he succeeds, with style. vincing, modest, and thoughtful ones. For example, on Question 4 he does (of course!) talk Mathematics According to Gowers about instruction at schools, and he thinks that The result is quite British, serious but not without there's need and room for improvement, but humor. The preface sets the stage: also he says "I do not advocate any revolutionary change-mathematics has suffered from too many Very little prior knowledge is needed of them already-but a small change in emphasis to read this book [. .. ] but I do presup­ could pay dividends. For example [... ]".On Ques­ pose some interest on the part of the tion 8, he thinks that "from an aesthetic point of reader rather than trying to drum it up view, a mathematician is more anonymous than an myself. For this reason I have done with­ artist. While we may greatly admire a mathemati­ out anecdotes, cartoons, exclamation cian who discovers a beautiful proof, the human marks, jokey chapter titles, or pictures story behind the discovery eventually fades away." of the Mandelbrot set. I have also Does it? I believe that it's our duty to also record avoided topics such as chaos theory and the human story, the story about what we all do, Godel's theorem, which have a hold on the stories about those who solve the big prob­ the public imagination out of proportion lems-and about those who put decades into the to their impact on current mathemati­ quest for such solutions. cal research, and which are in any case well treated in many other books. Mathematics According to Acheson And then he gets going: There's not much David Acheson's 1089 and All That. A journey into space-140 small pages. No space to explain large Mathematics is a little volume from the same pub­ amounts of mathematics. But Gowers gives a cap­ lisher as Gowers's book. It appeared in the same tivating, interesting, and quite personal1 intro­ year, in the same small format-but what a contrast duction into some mathematical questions, which it is otherwise! This contains all the "anecdotes, surprisingly fast get surprisingly close to the "heart cartoons, exclamation marks, jokey chapter titles" that Gowers wouldn't do. It's an amusing and 1 The title of this review quotes the last few words from entertaining roller-coaster ride into the world of the preface. mathematics, as seen by David Acheson. It is a

FEBRUARY 2005 NOTICES OF THE AMS 223 London Mathematical Society announces lively, funny, multifaceted view, with lots of pic­ Open Access Trial for 2004/2005 ... tures, drawings, cartoons: the ride starts with a As publishers of some of the most eminent journals in magic trick based on numbers (whose result is 1089) from I-SPY magazine that intrigued Acheson the international mathematics communit~ the LMS are as a boy. In the end, it leads up to an elementary adopting atrial open-access policy for 2004/2005, in which discussion of differential equations, in which he now, perhaps not quite seriously, sees answers to the most recent two issues of each journal will be freely the "mystery of life". But in any case differential available online as part of a one year experiment. Support equations provide useful models for the real world, and they do have applications. Probably 1089 and society publishing and visit the home pages of the following All That is not an important book in any sense, but three journals involved in this exciting online initiative!!! a fun piece to look into on a rainy afternoon. Bulletin of the London Mathematical Society Mathematics According to You! is a well-established journal with over thirty-five years' If you are a mathematician, and not one of the coverage extending across the whole range of pure very introverted kind, then I think you ought to give mathematics, together with some more applied areas your own answers. You needn't think about it as of analysis, theoretical computing and mathematical starting to write a book. Just get a little notebook, physics, publishing important short research articles, perhaps the size in which we wrote our diaries in the good old times when people like us would still authoritative survey articles and advanced expositions, write by hand. To begin, put down your own list reviewing all major developments in an important area of questions that you think need good answers; you over many years. might start with "What is mathematics?" www.journals.cambridge.org/jid_BLM Whatever you want to share with people, make Journal of the London Mathematical Society, it available. Some colleagues have a few pages of founded in 1926 and now in its 2nd Series, has a notes, views, or advice for students on their home pages. The most outspoken example I know is reputation for publishing some of the highest quality Doron Zeilberger's famous, wonderfully outrageous research on the whole spectrum of mathematics, "Opinions" page.2 Why are mathematician's pro­ with a wide scope ranging from number theory to fessional home pages so impersonal? I don't mean functional analysis, from finite simple groups to the that I want to see more baby photos- I'd want to mathematical foundations of quantum theory and from see more thoughts about what you are doing, what logic and topos theory to the topology of Lie groups the mathematics means to you, where the chal­ www.journals.cambridge.org/jid_JLM lenges are, and why this is interesting and impor­ tant to you and to all of us. Proceedings of the London Mathematical Society has been published since 1865. Papers from the Proceedings cover a wide range of mathematical topics that include real and complex analysis, differential equations and related areas, topology, geometry, logic, probability, statistics, algebra, number theory and combinatorial theory. www.journals.cambridge.org/jid_PLM

also available from Cambridge University Press and the London Mathematical Society... Compositio Mathematica is published by the LMS on behalf of the Foundation Compositio Mathematica. The journal publishes first-class research papers in the mainstream of pure mathematics, including such areas as algebra, number theory, topology, albebraic and analytic geometry, and geometric analysis. www.journals.cambridge.org/jid_COM

CAMBRIDGE 2 "Dr. Z's opinions," http: I jwww. rna th. rutgers. " UNIVERSITY PRESS edu/-zeilberg/OPINIONS.html.

224 NOTICES OF THE AMS VOLUME 52, NUMBER 2 InterviewwithMichael Atiyah and Isadore Singer Martin Raussen and Christian Skau

The interviewers were Martin Raussen, Aalborg University, Denmark; and Christian Skau, Norwegian University of Science and Technology, Trondheim, Norway. This interview took place in Oslo on May 24, 2004, during the Abel Prize celebrations. It originally appeared in the European Mathemati­ cal Society Newsletter, September 2004, pages 24-30.

The Index Theorem of zero. And certainly the Index Theorem is sim­ Raussen & Skau: First, we congratulate both of you ply a continuation of work that, I would like to say, for having been awarded the Abel Prize for 2004. began with Abel. So of course there are precursors. This prize has been given to you for "the discovery A theorem is never arrived at in the way that log­ and the proof of the Index Theorem connecting ical thought would lead you to believe or that pos­ geometry and analysis in a surprising way and terity thinks. It is usually much more accidental, your outstanding role in building new bridges be­ some chance discovery in answer to some kind of tween mathematics and theoretical physics". Both question. Eventually you can rationalize it and say of you have an impressive list of fine achievements that this is how it fits. Discoveries never happen in mathematics. Is the Index Theorem your most im­ as neatly as that. You can rewrite history and make portant result and the result you are most pleased it look much more logical, but actually it happens with in your entire careers? quite differently. Atiyah: First, I would like to say that I prefer to Singer: At the time we proved the Index Theo­ call it a theory, not a theorem. Actually, we have rem we saw how important it was in mathematics, worked on it for twenty-five years, and if I include but we had no inkling that it would have such an all the related topics, I have probably spent thirty effect on physics some years down the road. That years of my life working on the area. So it is rather came as a complete surprise to us. Perhaps it obvious that it is the best thing I have done. should not have been a surprise because it used a Singer: I, too, feel that the Index Theorem was lot of geometry and also quantum mechanics in a but the beginning of a high point that has lasted way, a la Dirac. to this very day. It's as if we climbed a mountain R & S: You worked out at least three different and found a plateau we've been on ever since. proofs with different strategies for the Index The­ R & S: We would like you to give us some com­ orem. Why did you keep on after the first proof? ments on the history of the discovery of the Index What different insights did the proofs give? Theorem. 1 Were there precursors, conjectures in Atiyah: I think it is said that Gauss had ten dif­ this direction already before you started? Were there ferent proofs for the law of quadratic reciprocity. only mathematical motivations or also physical Any good theorem should have several proofs, the ones? more the better. For two reasons: usually, differ­ Atiyah: Mathematics is always a continuum, ent proofs have different strengths and weak­ linked to its history, the past-nothing comes out nesses, and they generalize in different direc­ tions-they are not just repetitions of each other. Martin Raussen is associate professor of mathematics And that is certainly the case with the proofs that at Aalborg University, Denmark. His email address is we came up with. There are different reasons for [email protected]. the proofs, they have different histories and back­ Christian Skau is professor of mathematics at Norwegian grounds. Some of them are good for this applica­ University of Science and Technology, Trondheim, Norway. tion, some are good for that application. They all His email address is csk@math. ntnu. no. shed light on the area. If you cannot look at a 1 More details were given in the laureates' lectures. problem from different directions, it is probably

FEBRUARY 2005 NOTICES OF THE AMS 225 not very in­ ground. And of course there are also a lot of peo­ teresting; ple who did fundamental work in analysis and the the more study of differential equations: Hormander, Niren­ perspec­ berg .. .. In my lecture I will give a long list of names2; tives, the even that one will be partial. It is an example of in­ better! ternational collaboration; you do not work in iso­ Singer: lation, neither in terms of time nor in terms of There isn't space-especially in these days. Mathematicians just one are linked so much, people travel around much theorem; more. We two met at the Institute at Princeton. It there are was nice to go to the Arbeitstagung in Bonn every generaliza­ year, which Hirzebruch organized and where many tions of the of these other people came. I did not realize that theorem. at the time, but looking back, I am very surprised One is the how quickly these ideas moved. families R & S: Collaboration seems to play a bigger role Abel Prize winners Michael Atiyah (left) and index thea- in mathematics than earlier. There are a lot of con­ Isadore Singer. rem using ferences, we see more papers that are written by two, K-theory; three, or even more authors-is that a necessary another is the heat equation proof that makes the and commendable development or has it drawbacks formulas that are topological more geometric and as well? explicit. Each theorem and proof has merit and Atiyah: It is not like in physics or chemistry has different applications. where you have fifteen authors because they need an enormous big machine. It is not absolutely nec­ Collaboration essary or fundamental. But particularly if you are R & S: Both of you contributed to the Index Theo­ dealing with areas that have rather mixed and in­ rem with different expertise and visions-and other terdisciplinary backgrounds, with people who have people had a share as well, I suppose. Could you de­ different expertise, it is much easier and faster. It scribe this collaboration and the establishment of is also much more interesting for the participants. the result a little more closely? To be a mathematician on your own in your office Singer: Well, I came with a background in analy­ can be a little bit dull, so interaction is stimulat­ sis and differential geometry, and Sir Michael's ex­ ing, both psychologically and mathematically. It has pertise was in algebraic geometry and topology. For to be admitted that there are times when you go the purposes of the Index Theorem, our areas of solitary in your office, but not all the time! It can expertise fit together hand in glove. Moreover, in also be a social activity with lots of interaction. You a way, our personalities fit together, in that "any­ need a good mix of both; you can't be talking all thing goes": Make a suggestion-and whatever it the time. But talking some of the time is very stim­ was, we would just put it on the blackboard and ulating. Summing up, I think that it is a good de­ work with it; we would both enthusiastically explore velopment-! do not see any drawbacks. it; if it didn't work, it didn't work. But often enough, Singer: Certainly computers have made collab­ some idea that seemed far-fetched did work. We oration much easier. Many mathematicians col­ both had the freedom to continue without worry­ laborate by computer instantly; it's as if they were ing about where it came from or where it would talking to each other. I am unable to do that. A lead. It was exciting to work with Sir Michael all sobering counterexample to this whole trend is these years. And it is as true today as it was when Perelman's results on the Poincare conjecture: we first met in '55-that sense of excitement and He worked alone for ten to twelve years, I think, "anything goes" and "let's see what happens". before putting his preprints on the Net. Atiyah: No doubt: Singer had a strong expertise Atiyah: Fortunately, there are many different and background in analysis and differential geom­ kinds of mathematicians, they work on different etry. And he knew certainly more physics than I did; subjects, they have different approaches and dif­ it turned out to be very useful later on. My back­ ferent personalities-and that is a good thing. We ground was in algebraic geometry and topology, so do not want all mathematicians to be isomorphic, it all came together. But of course there are a lot of people who contributed in the background to the 2 buildup of the Index Theorem-going back to Abel, Among those: Newton, Gauss, Cauchy, Laplace, Abel, jacobi, Riemann, Weierstrass, Lie, Picard, Poincare, Castel­ Riemann, much more recently Serre, who got the nuovo, Enriques, Severi, Hilbert, Lefschetz, Hodge, Todd, Abel Prize last year, Hirzebruch, Grothendieck, and Leray, Cartan, Serre, Kodaira, Spencer, Dirac, Pontrjagin, Bott. There was lots of work from the algebraic Chern, Wei/, Borel, Hirzebruch, Bott, Eilenberg, Grothen­ geometry side and from topology that prepared the dieck, Hbrmander, Nirenberg.

226 NOTICES OF THE AMS VOLUME 52, NUMBER 2 we want variety: different mountains need differ­ Singer: The Index theorem was in fact instru­ ent kinds of techniques to climb. mental in breaking barriers between fields. When Singer: I support that. Flexibility is absolutely it first appeared, many old-timers in special fields essential in our society of mathematicians. were upset that new techniques were entering their R & S: Perelman's work on the Poincare conjec­ fields and achieving things they could not do in the ture seems to be another instance in which analy­ field by old methods. A younger generation im­ sis and geometry apparently get linked very much mediately felt freed from the barriers that we both together. It seems that geometry is profiting a lot view as artificial. from analytic perspectives. Is this linkage between Atiyah: Let me tell you a little story about Henry different disciplines a general trend-is it true that Whitehead, the topologist. I remember that he told important results rely on this interrelation between me that he enjoyed very much being a topologist: different disciplines? And a much more specific he had so many friends within topology, and it question: What do you know about the status of the was such a great community. "It would be a tragedy proof of the Poincare conjecture? if one day I would have a brilliant idea within func­ Singer: To date, everything is working out as tional analysis and would have to leave all my Perelman says. So I learn from Lott's seminar at the topology friends and to go out and work with a dif­ University of Michigan and Tian's seminar at Prince­ ferent group of people." He regarded it to be his ton. Although no one vouches for the final details, duty to do so, but he would be very reluctant. it appears that Perelman's proof will be validated. Somehow, we have been very fortunate. Things As to your first question: When any two subjects have moved in such a way that we got involved with use each other's techniques in a new way, fre­ functional analysts without losing our old friends; quently, something special happens. In geometry, we could bring them all with us. Alain Cannes was analysis is very important; for existence theorems, in functional analysis, and now we interact closely. · the more the better. It is not surprising that some So we have been fortunate to maintain our old new [at least to me] analysis implies something in­ links and move into new ones-it has been great teresting about the Poincare conjecture. fun. Atiyah: I prefer to go even further-! really do not believe in the division of mathematics into Mathematics and Physics specialities; already if you go back into the past, R & S: We would like to have your comments on the to Newton and Gauss .... Although there have been interplay between physics and mathematics. There times, particularly post-Hilbert, with the axiomatic is Galilei's famous dictum from the beginning of the approach to mathematics in the first half of the scientific revolution, which says that the laws of na­ twentieth century, when people began to special­ ture are written in the language of mathematics. ize, to divide up. The Bourbaki trend had its use Why is it that the objects of mathematical creation, for a particular time. But this is not part of the gen­ satisfying the criteria of beauty and simplicity, are eral attitude to mathematics: Abel would not have precisely the ones that time and time again are distinguished between algebra and analysis. And I found to be essential for a correct description of the think the same goes for geometry and analysis for external world? Examples abound; let me just men­ people like Newton. tion group theory and, yes, your Index Theorem! It is artificial to divide mathematics into separate Singer: There are several approaches in answer chunks and then to say that you bring them to­ to your questions; I will discuss two. First, some gether as though this is a surprise. On the contrary, parts of mathematics were created in order to they are all part of the puzzle of mathematics. describe the world around us. Calculus began by Sometimes you would develop some things for their explaining the motion of planets and other mov­ own sake for a while, e.g., if you develop group the­ ing objects. Calculus, differential equations, and ory by itself. But that is just a sort of temporary con­ integral equations are a natural part of physics venient division of labor. Fundamentally, mathe­ because they were developed for physics. Other matics should be used as a unity. I think the more parts of mathematics are also natural for physics. examples we have of people showing that you can I remember lecturing in Feynman's seminar, trying usefully apply analysis to geometry, the better. And to explain anomalies. His postdocs kept wanting not just analysis; I think that some physics came into to pick coordinates in order to compute; he stopped it as well: many of the ideas in geometry use them, saying: "The laws of physics are independent physical insight as well-take the example of of a coordinate system. Listen to what Singer has Riemann! This is all part of the broad mathemati­ to say, because he is describing the situation cal tradition, which sometimes is in danger of be­ without coordinates." Coordinate-free means ing overlooked by modern, younger people who geometry. It is natural that geometry appears in say "we have separate divisions". We do not want physics, whose laws are independent of a coordi­ to have any of that kind, really. nate system. fEBRUARY 2005 NOTICES OF THE AMS 227 Symmetries are useful in physics for much the R & S: Is it too strong to say that the mathemat­ same reason they're useful in mathematics. Beauty ical problems solved and the techniques that arose aside, symmetries simplify equations, in physics from physics have been the life blood of mathe­ and in mathematics. So physics and math have in matics in the past; or at least for the last twenty-five common geometry and group theory, creating a years? close connection between parts of both subjects. Atiyah: I think you could turn that into an even Second, there is a deeper reason, if your ques­ stronger statement. Almost all mathematics orig­ tion is interpreted as in the title of Eugene Wigner's inally arose from external reality, even numbers and essayThe Unreasonable Effectiveness of Mathe­ counting. At some point, mathematics then turned matics in the Natural Sciences. 3 Mathematics stud­ to ask internal questions, e.g., the theory of prime ies coherent systems which I will not try to define. numbers, which is not directly related to experience But it studies coherent systems, the connections but evolved out of it. There are parts of mathe­ between such systems, and the structure of such matics about which the human mind asks internal systems. We should not be too surprised that questions just out of curiosity. Originally it may be mathematics has coherent systems applicable to physical, but eventually it becomes something in­ physics. It remains to be seen whether there is an dependent. There are other parts that relate much already developed coherent system in mathemat­ closer to the outside world with much more inter­ ics that will describe the structure of string theory. action backward and forward. In that part of it, [At present, we do not even know what the sym­ physics has for a long time been the life blood of metry group of string field theory is.] Witten has mathematics and inspiration for mathematical said that 21st-century mathematics has to develop work. There are times when this goes out of fash­ new mathematics, perhaps in conjunction with ion or when parts of mathematics evolve purely physics intuition, to describe the structure of string internally. Lots of abstract mathematics does not theory. directly relate to the outside world. It is one of the Atiyah: I agree with Singer's description of math­ strengths of mathematics that it has these two and ematics having evolved out of the physical world; not a single life blood: one external and one inter­ nal, one arising as response to external events, the it therefore is not a big surprise that it has a feed­ other to internal reflection on what we are doing. back into it. More fundamentally: to understand the Singer: Your statement is too strong. I agree outside world as a human being is an attempt to with Michael that mathematics is blessed with both reduce complexity to simplicity. What is a theory? an external and internal source of inspiration. In A lot of things are happening in the outside world, the past several decades, high-energy theoretical and the aim of scientific inquiry is to reduce this physics has had a marked influence on mathe­ to as simple a number of principles as possible. matics. Many mathematicians have been shocked That is the way the human mind works, the way at this unexpected development: new ideas the human mind wants to see the answer. from outside mathematics so effective in mathe­ If we were computers, which could tabulate vast matics. We are delighted with these new inputs, but amounts of all sorts of information, we would the "shock" exaggerates their overall effect on never develop theory-we would say, just press the mathematics. button to get the answer. We want to reduce this complexity to a form that the human mind can Newer Developments understand, to a few simple principles. That's the R & S: Can we move to newer developments with nature of scientific inquiry, and mathematics is a impact from the Atiyah-Singer Index Theorem? That part of that. Mathematics is an evolution from the is, string theory and Edward Witten on the one human brain, which is responding to outside in­ hand, and on the other hand, noncommutative fluences, creating the machinery with which it then geometry represented by Alain Cannes. Could you attacks the outside world. It is our way of trying describe the approaches to mathematical physics to reduce complexity into simplicity, beauty, and epitomized by these two protagonists? elegance. It is really very fundamental; simplicity Atiyah: I tried once in a talk to describe the dif­ is in the nature of scientific inquiry-we do not look ferent approaches to progress in physics like dif­ for complicated things. ferent religions. You have prophets, you have fol­ I tend to think that science and mathematics are lowers-each prophet and his followers think that ways the human mind looks and experiences-you they have the sole possession of the truth. If you cannot divorce the human mind from it. Mathemat­ take the strict point of view that there are several ics is part of the human mind. The question whether different religions, and that the intersection of all there is a reality independent of the human mind these theories is empty, then they are all talking has no meaning-at least, we cannot answer it. nonsense. Or you can take the view of the mystic, who thinks that they are all talking of different as­ 3 Comm. Pure App. Math., 13(1), 1960. pects of reality, and so all of them are correct. I tend

228 NOTICES OF THE AMS VOLUME 52, NUMBER 2 to take the second point of view. The main "or­ thodox" view among physicists is certainly repre­ sented by a very large group of people working with string theory, such as Edward Witten. There are a small number of people who have different philoso­ phies; one of them is Alain Connes, and the other is Roger Pemose. Each of them has a very specific point of view; each of them has very interesting ideas. Within the last few years, there has been non­ trivial interaction between all of these. They may all represent different aspects of re­ ality and, eventually, when we understand it all, we may say "Ah, yes, they are all part of the truth". I think that that will happen. It is difficult to say which will be dominant when we finally under­ Abel Prize winners Isadore Singer and Michael Atiyah with stand the picture-we don't know. But I tend to be Queen Sonja and King Harald of Norway at the royal palace open-minded. The problem with a lot of physicists in Oslo, May 2004. is that they have a tendency to "follow the leader": as soon as a new idea comes up, ten people write Bang. I would encourage young physicists to un­ ten or more papers on it, and the effect is that every­ derstand noncommutative geometry more deeply thing can move very fast in a technical direction. than they presently do. Physicists use only parts But big progress may come from a different di­ of noncommutative geometry; the theory has much rection; you do need people who are exploring dif­ more to offer. I do not know whether it is going to ferent avenues. And it is very good that we have lead anywhere or not. But one of my projects is to people like Connes and Pemose with their own in­ try and redo some known results using noncom­ dependent line from different origins. I am in favor mutative geometry more fully. of diversity. I prefer not to close the door or to say R & S: If you should venture a guess, which math­ "they are just talking nonsense." ematical areas do you think are going to witness the Singer: String theory is in a very special situa­ most important developments in the coming years? tion at the present time. Physicists have found new Atiyah: One quick answer is that the most ex­ solutions on their landscape-so many that you citing developments are the ones that you cannot cannot expect to make predictions from string predict. If you can predict them, they are not so theory. Its original promise has not been fulfilled. exciting. So, by definition, your question has no Nevertheless, I am an enthusiastic supporter of answer. super string theory, not just because of what it Ideas from physics, e.g., quantum theory, have has done in mathematics, but also because as a had an enormous impact so far, in geometry, some coherent whole, it is a marvelous subject. Every few parts of algebra, and in topology. The impact on years new developments in the theory give addi­ number theory has still been quite small, but there tional insight. When that happens, you realize how are some examples. I would like to make a rash little one understood about string theory previ­ prediction that it will have a big impact on num­ ously. The theory of D-branes is a recent example. ber theory as the ideas flow across mathematics­ Often there is mathematics closely associated with on one extreme number theory, on the other these new insights. Through D-branes, K-theory physics, and in the middle geometry: the wind is entered string theory naturally and reshaped it. blowing, and it will eventually reach to the far­ We just have to wait and see what will happen. I thest extremities of number theory and give us a am quite confident that physics will come up new point of view. Many problems that are worked with some new ideas in string theory that will give upon today with old-fashioned ideas will be done us greater insight into the structure of the subject, with new ideas. I would like to see this happen: it and along with that will come new uses of mathe­ could be the Riemann hypothesis, it could be the matics. Langlands program, or a lot of other related things. Alain Connes's program is very natural- if you I had an argument with Andrew Wiles in which I want to combine geometry with quantum me­ claimed that physics will have an impact on his kind chanics, then you really want to quantize geome­ of number theory; he thinks this is nonsense, but try, and that is what noncommutative geometry we had a good argument. means. Noncommutative geometry has been used I would also like to make another prediction, effectively in various parts of string theory ex­ namely that fundamental progress on the physics/ plaining what happens at certain singularities, for mathematics front, string theory questions, etc., will example. I think it may be an interesting way of try­ emerge from a much more thorough understand­ ing to describe black holes and to explain the Big ing of classical four-dimensional geometry, of

FEBRUARY 2005 NOTICES OF THE AMS 229 Einstein's equations, etc. The hard part of physics .necessarily a fixed rigid object in that sense; I think in some sense is the nonlinearity of Einstein's equa­ it should develop and grow. I like to think of math­ tions. Everything that has been done at the moment ematics having a core, but I do not want it to be is circumventing this problem in lots of ways. They rigidly defined so that it excludes things that might haven't really got to grips with the hardest part. Big be interesting. You do not want to exclude some­ progress will come when people by some new tech­ body who has made a discovery saying: "You are niques or new ideas really settle that. Whether you outside, you are not doing mathematics, you are call that geometry, differential equations, or physics playing around." You never know! That particular depends on what is going to happen, but it could discovery might be the mathematics of the next be one of the big breakthroughs. century; you have got to be careful. Very often, These are of course just my speculations. when new ideas come in, they are regarded as Singer: I will be speculative in a slightly differ­ being a bit odd, not really central, because they look ent way, though I do agree with the number theory too abstract. comments that Sir Michael mentioned, particularly Singer: Countries differ in their attitudes about theta functions entering from physics in new the degree of specialization in mathematics and ways. I think other fields of physics will affect how to treat the problem of too much specializa­ mathematics-such as statistical mechanics and tion. In the United States I observe a trend toward condensed matter physics. For example, I predict early specialization driven by economic consider­ a new subject of statistical topology. Rather than ations. You must show early promise to get good count the number of holes, Betti numbers, etc., one letters of recommendations to get good first jobs. will be more interested in the distribution of You can't afford to branch out until you have es­ such objects on noncompact manifolds as one goes tablished yourself and have a secure position. The out to infinity. We already have precursors in the realities of life force a narrowness in perspective number of zeros and poles for holomorphic func­ that is not inherent to mathematics. We can counter tions. The theory that we have for holomorphic too much specialization with new resources that functions will be generalized, and insights will would give young people more freedom than they come from condensed matter physics as to what, presently have, freedom to explore mathematics statistically, the topology might look like as one more broadly, or to explore connections with other approaches infinity. subjects, such as biology these days in which there is lots to be discovered. Continuity of Mathematics When I was young the job market was good. It R & S: Mathematics has become so specialized, it was important to be at a major university, but you seems, that one may fear that the subject will break could still prosper at a smaller one. I am distressed up into separate areas. Is there a core holding things by the coercive effect of today's job market. Young together? mathematicians should have the freedom of choice Atiyah: I like to think there is a core holding we had when we were young. things together, and that the core is rather what I R & S: The next question concerns the continuity look at myself; but we tend to be rather egocentric. of mathematics. Rephrasing slightly a question that The traditional parts of mathematics, that evolved­ you, Professor Atiyah, are the originator of, geometry, calculus and algebra-all center on cer­ let us make the following gedanken experiment: tain notions. As mathematics develops, there are if, say, Newton or Gauss or Abel were to reappear new ideas, which appear to be far from the center in our midst, do you think they would understand going off in different directions, which I perhaps the problems being tackled by the present genera­ do not know much about. Sometimes they become tion of mathematicians-after they had been rather important for the whole nature of the math­ given a short refresher course? Or is present-day ematical enterprise. It is a bit dangerous to restrict mathematics too far removed from traditional the definition to just whatever you happen to un­ mathematics? derstand yourself or think about. For example, Atiyah: The point that I was trying to make there there are parts of mathematics that are very com­ was that really important progress in mathematics binatorial. Sometimes they are very closely related is somewhat independent of technical jargon. Im­ to the continuous setting, and that is very good: we portant ideas can be explained to a really good have interesting links between combinatorics and mathematician, such as Newton or Gauss or Abel, algebraic geometry and so on. They may also be re­ in conceptual terms. They are in fact coordinate­ lated to, e.g., statistics. I think that mathematics is free-more than that, technology-free and in a sense very difficult to constrain; there are also all sorts jargon-free. You don't have to talk of ideals, mod­ of new applications in different directions. ules or whatever-you can talk in the common lan­ It is nice to think of mathematics having a unity; guage of scientists and mathematicians. The really however, you do not want it to be a straitjacket. The important progress mathematics has made within center of gravity may change with time. It is not two hundred years could easily be understood by

230 NOTICES OF THE AMS VOLUME 52, NUMBER 2 people such as Gauss and Newton and Abel. Only ideas, we simplify lots of the constructions-we are a small refresher course in which they were told a very successful in mathematics and have been so few terms-and then they would immediately un­ for several hundred years. There is no evidence that derstand. this has stopped: in every new generation, there are Actually, my pet aversion is that many mathe­ mathematicians who make enormous progress. How maticians use too many technical terms when they do they learn it all? It must be because we have been write and talk. They were trained in a way that, if successful communicating it. you do not say it 100 percent correctly, like lawyers, Singer: I find it disconcerting speaking to some of you will be taken to court. Every statement has to my young colleagues, because they have absorbed, be fully precise and correct. When talking to other reorganized, and simplified a great deal of known people or scientists, I like to use words that are material into a new language, much of which I don't common to the scientific community, not neces­ understand. Often I'll finally say, "Oh; is that all you sarily just to mathematicians. And that is very meant?" Their new conceptual framework allows often possible. If you explain ideas without a vast them to encompass succinctly considerably more amount of technical jargon and formalism, I am than I can express with mine. Though impressed sure it would not take Newton, Gauss, and Abel with the progress, I must confess impatience be­ long-they were bright guys, actually! cause it takes me so long to understand what is Singer: One of my teachers at Chicago was Andre really being said. Weil, and I remember his saying: "If Riemann were R & S: Has the time passed when deep and im­ here, I would put him in the library for a week, and portant theorems in mathematics can be given short when he came out he would tell us what to do proofs? In the past, there are many such exam­ next." ples-e.g., Abel's one-page proof of the addition theorem of algebraic differentials or Goursat's proof Communication of Mathematics of Cauchy's integral theorem. R & S: Next topic: communication of mathematics. Atiyah: I do not think that at all! Of course, that Hilbert, in his famous speech at the International depends on what foundations you are allowed to Congress in 1900, in order to make a point about start from. If we have to start from the axioms of mathematical communication, cited a French math­ mathematics, then every proof will be very long. The ematician who said: "A mathematical theory is not common framework at any given time is constantly to be considered complete until you have made it advancing; we are already at a high platform. If we so clear that you can explain it to the first man are allowed to start within that framework, then at whom you meet on the street." In order to pass on every stage there are short proofs. to new generations of mathematicians the collective One example from my own life is this famous knowledge of the previous generation, how impor­ problem about vector fields on spheres solved by tant is it that the results have simple and Frank Adams, for which the proof took many hun­ elegant proofs? dreds of pages. One day I discovered how to write a Atiyah: The passing of mathematics on to sub­ proof on a postcard. I sent it over to Frank Adams sequent generations is essential for the future, and and we wrote a little paper which then would fit on this is only possible if every generation of mathe­ a bigger postcard. But of course that used some maticians understands what they are doing and dis­ K-theory; not that complicated in itself. You are tills it out in such a form that it is easily understood always building on a higher platform; you have by the next generation. Many complicated things get always got more tools at your disposal that are part simple when you have the right point of view. The first of the lingua franca which you can use. In the old proof of something may be very complicated, but days you had a smaller base: if you make a simple when you understand it well, you readdress it, and proof nowadays, then you are allowed to assume eventually you can present it in a way that makes it that people know what group theory is, you are look much more understandable-and that's the allowed to talk about Hilbert space. Hilbert space way you pass it on to the next generation! Without took a long time to develop, so we have got a much that, we could never make progress-we would have bigger vocabulary, and with that we can write more all this messy stuff. Mathematics does depend on a poetry. sufficiently good grasp, on understanding of the Singer: Often enough one can distill the ideas fundamentals so that we can pass it on in as simple in a complicated proof and make that part of a new a way as possible to our successors. That has been language. The new proof becomes simpler and done remarkably successfully for centuries. Other­ more illuminating. For clarity and logic, parts of the wise, how could we possibly be where we are? In the original proof have been set aside and discussed 19th century, people said: "There is so much math­ separately. ematics, how could anyone make any progress?" Atiyah: Take your example of Abel's Paris mem­ Well, we have-we do it by various devices, we gen­ oir: his contemporaries did not find it at all easy. eralize, we put all things together, we unify by new It laid the foundation of the theory. Only later on,

FEBRUARY 2005 NOTICES OF THE AMS 231 in the light of that theory, we can all say: "Ah, what when I try out my ideas, I'm wrong 99% of the time. a beautifully simple proof!" At the time, all the I learn from that and from studying the ideas, tech­ ideas had to be developed, and they were hidden, niques, and procedures of successful methods. My and most people could not read that paper. It was stubbornness wastes lots of time and energy. But on very, very far from appearing easy for his con­ the rare occasion when my internal sense of mathe­ temporaries. matics is right, I've done something different. R & S: Both of you have passed ordinary retire­ Individual Work Style ment age several years ago. But you are still very R & S: I heard you, Professor Atiyah, mention that active mathematicians, and you have even chosen one reason for your choice ofmathematics for your retirement or visiting positions remote from your career was that it is not necessary to remember a original work places. What are the driving forces for lot of facts by heart. Nevertheless, a lot of threads keeping up your work? Is it wrong that mathemat­ have to be woven together when new ideas are ics is a "young man's game" as Hardy put it? developed. Could you tell us how you work best, how Atiyah: It is no doubt true that mathematics is do new ideas arrive? a young man's game in the sense that you peak in Atiyah: My fundamental approach to doing re­ your twenties or thirties in terms of intellectual search is always to ask questions. You ask "Why is concentration and in originality. But later you this true?" when there is something mysterious or compensate for that by experience and other if a proof seems very complicated. I used to say­ factors. It is also true that if you haven't done any­ as a kind of joke-that the best ideas come to you thing significant by the time you are forty, you will during a bad lecture. If somebody gives a terrible not do so suddenly. But it is wrong that you have lecture-it may be a beautiful result but with to decline, you can carry on, and if you manage to terrible proofs-you spend your time trying to find diversify in different fields this gives you a broad better ones; you do not listen to the lecture. It is coverage. The kind of mathematician who has dif­ all about asking questions-you simply have to ficulty maintaining the momentum all his life is a have an inquisitive mind! Out of ten questions, person who decides to work in a very narrow field nine will lead nowhere, and one leads to some­ with great depths, who, e.g., spends all his life try­ thing productive. You constantly have to be in­ ing to solve the Poincare conjecture-whether you quisitive and be prepared to go in any direction. If succeed or not, after ten to fifteen years in this field you go in new directions, then you have to learn you exhaust your mind; and then, it may be too late new material. to diversify. If you are the sort of person that Usually, if you ask a question or decide to solve chooses to make restrictions to yourself, to spe­ a problem, it has a background. If you understand cialize in a field, you will find it harder and harder­ where a problem comes from, then it makes it easy because the only things that are left are harder for you to understand the tools that have to be used and harder technical problems in your own area, on it. You immediately interpret them in terms of and then the younger people are better than you. your own context. When I was a student, I learned You need a broad base, from which you can things by going to lectures and reading books­ evolve. When this area dries out, then you go to that after that I read very few books. I would talk with area-or when the field as a whole, internation­ people; I would learn the essence of analysis by ally, changes gear, you can change too. The length talking to Hormander or other people. I would be of the time you can go on being active within math­ asking questions because I was interested in a par­ ematics very much depends on the width of your ticular problem. So you learn new things because coverage. You might have contributions to make in you connect them and relate them to old ones, terms of perspective, breadth, interactions. A broad and in that way you can start to spread around. coverage is the secret of a happy and successful long If you come with a problem, and you need to life in mathematical terms. I cannot think of any move to a new area for its solution, then you have counterexample. an introduction-you have already a point of view. Singer: I became a graduate student at the Uni­ Interacting with other people is of course essential: versity of Chicago after three years in the U.S. Army if you move into a new field, you have to learn the during World War II. I was older and far behind in language, you talk with experts; they will distill the mathematics. So I was shocked when my fellow essentials out of their experience. I did not learn graduate students said, "If you haven't proved the all the things from the bottom upward; I went to Riemann hypothesis by age thirty, you might as well the top and got the insight into how you think commit suicide." How infantile! Age means little to about analysis or whatever. me. What keeps me going is the excitement of what Singer: I seem to have some built-in sense of how I'm doing and its possibilities. I constantly check things should be in mathematics. At a lecture, or [and collaborate!] with younger colleagues to be sure reading a paper, or during a discussion, I frequently that I'm not deluding myself-that what we are think, "that's not the way it is supposed to be." But doing is interesting. So I'm happily active in

232 NOTICES OF THE AMS VOLUME 52, NUMBER 2 mathematics. Another rea~n is, in a way, a joke. there was some pressure to get out and get in­ String theory needs us! String theory needs new volved in education, etc. The EMS took on this role ideas. Where will they come from, if not from Sir at a European level, and the EMS congresses-I was Michael and me? involved in the one in Barcelona-definitely made Atiyah: Well, we have some students .. .. an attempt to interact with the public. I think that Singer: Anyway, I am very excited about the these are additional opportunities over and above interface of geometry and physics and delighted the old-fashioned role of learned societies. There to be able to work at that frontier. are a lot of opportunities both in terms of the geography of Europe and in terms of the broader History ofthe EMS reach. R & S: You, Professor Atiyah, have been very much Europe is getting ever larger: when we started involved in the establishment of the European we had discussions about where were the borders Mathematical Society (EMS) around 1990. Are you of Europe. We met people from Georgia, who told satisfied with its development since then? us very clearly that the boundary of Europe is this Atiyah: Let me just comment a little on my in­ river on the other side of Georgia; they were very volvement. It started an awful long time ago, prob­ keen to make sure that Georgia is part of Europe. ably about thirty years ago. When I started trying Now, the politicians have to decide where the to get people interested in forming a European borders of Europe are. Mathematical Society in the same spirit as the It is good that the EMS exists; but you should European Physical Society, I thought it would be think rather broadly about how it is evolving as easy. I got mathematicians from different countries Europe evolves, as the world evolves, as mathe­ together and it was like a mini-UN: the French and matics evolves. What should its function be? How the Germans wouldn't agree; we spent years argu­ should it relate to national societies? How should ing about differences, and-unlike in the real UN, it relate to the AMS? How should it relate to the where eventually at the end of the day you are governmental bodies? It is an opportunity! It has dealing with real problems of the world and you a role to play! have to come to an agreement sometime-in math­ ematics, it was not absolutely essential. We went Apart from Mathematics ... on for probably fifteen years before we founded the R & S: Could you tell us in a few words about your EMS. main interests besides mathematics? On the one hand, mathematicians have much Singer: I love to play tennis, and I try to do so more in common than politicians. We are interna­ two to three times a week. That refreshes me, and tional in our mathematical life; it is easy to talk to I think that it has helped me work hard in mathe­ colleagues from other countries. On the other hand, matics all these years. mathematicians are much more argumentative. Atiyah: Well, I do not have his energy! I like to When it comes to the fine details of a constitution, walk in the hills, the Scottish hills-! have retired then they are terrible; they are worse than lawyers. partly to Scotland. In Cambridge, where I was be­ But eventually-in principle-the good will was fore, the highest hill was about this [gesture] big. there for collaboration. Of course you have got even bigger ones in Nor­ Fortunately, the timing was right. In the mean­ way. I spent a lot of my time outdoors, and I like time, Europe had solved some of its other problems. to plant trees, I like nature. I believe that if you do The Berlin Wall had come down-so suddenly there mathematics, you need a good relaxation that is was a new Europe to be involved in the EMS. This not intellectual-being outside in the open air, very fact made it possible to get a lot more people climbing a mountain, working in your garden. interested in it. It gave an opportunity for a broader But you actually do mathematics meanwhile. While base of the EMS, with more opportunities and also you go for a long walk in the hills or you work in relations to the European Commission and so on. your garden, the ideas can still carry on. My wife Having been involved with the setup, I withdrew complains, because when I walk she knows I am and left it to others to carry on. I have not followed thinking of mathematics. in detail what has been happening except that it Singer: I can assure you, tennis does not allow seems to be active. I get my newsletter, and I see that! what is going on. R & S: Thank you very much on behalf of the Roughly at the same time as the collapse of the Norwegian, the Danish, and the European Mathe­ Berlin Wall, mathematicians in general-both in matical Societies! Europe and in the United States-began to be more aware of their need to be socially involved and that mathematics had an important role to play in society. Instead of being shut up in their universi­ ties doing just their mathematics, they felt that fEBRUARY 2005 NOTICES OF THE AMS 233 Teachers, Exams, Standards: AMS Committee on Education Examines Issues

"It is almost a disaster." Irwin Kra's blunt words and institutes. MfA is his first large-scale venture summed up the basic impression that many math­ into mathematics education. ematicians have about the state of K-12 mathe­ Founded in February 2004, MfAhas already com­ matics education. The last several years have seen mitted over $2 5 million of private funds to improve a growing sense of urgency within the mathemat­ mathematicseducationinNewYorkCitypublichigh ical community about the poor quality of mathe­ schools over the next five years. With this commit­ matics instruction in the nation's schools, as well ment, MfA will award about forty Newton Fellowships as efforts on the part of mathematicians to help each year to mathematically sophisticated young address the problems. At the same time, mathe­ people and people who want to change careers, to matics departments today are taking seriously the enable them to enroll in MAT programs and become need to improve their own teaching. In particular, high school mathematics teachers inN ew York City. the role that math departments play in preparing The fellowships will pay for graduate mathematics future teachers of mathematics is increasingly education programs at partner universities, currently being seen as one of the keys to improving math­ Queens College and New York University, and will ematics education at all levels. also provide stipends, in addition to the regular salary As attention to education has increased within paid by the schools, during the fellows' first four years the mathematical community, the AMS Committee of teaching. In addition, for each of the next five on Education (COE) has become a focal point for years, the Newton Master Teacher Fellowship Pro­ discussions and debate. The COE is a policy com­ gram will award about ten four-year fellowships of mittee, not an action committee, so its primary $50,000 each to mathematics teachers in New York role is to stay abreast of developments in education City public schools to nurture them to become lead­ and to provide advice when needed. The annual COE ers in improving mathematics education. meetings, held each fall in Washington, DC, and The initial focus is on New York City simply arranged by the AMS Washington Office, are one of because the group behind MfA consists mainly the main venues for finding out about develop­ of New Yorkers, and they believe they can make ments in mathematics education that are pertinent progress in their home base. Plans call for expan­ to the interests of mathematicians. The most recent sion of the fellowship programs to other cities, COE meeting, held in October 2004, attracted about and MfA will eventually seek federal funding for a fifty representatives from mathematics depart­ national program. COE member Paul Sally of the ments all over the country. University of Chicago, who has led mathematics One of the most unusual developments discussed education improvement programs in Chicago for at the COE meeting came in the presentation by Kra, many years, commented that it could take MfA a who recently retired from the State University of decade to gain enough experience to expand its New York at Stony Brook and is currently the exec­ programs nationally. Kra did not disagree but utive director of a new organization called Math for added: "We think there is a crisis out there. We America (MfA). MfA was founded by James Simons, want to see change as quickly as possible. We are whose name is attached to the Chern-Simons in­ impatient." variants in geometry and who won the AMS Veblen Another group that is making a mark in mathe­ Prize in 1976. Simons, who used to be on the faculty matics education is Achieve, a nonprofit organiza­ at Stony Brook, made a fortune by establishing a suc­ tion that helps the states raise standards and cessful financial investment company and in recent improve assessment. Laura McGiffert, director of years has become a major financial supporter of Achieve's mathematics program, described the mathematics research at several major universities results of an Achieve study of high school exit

234 NOTICES OF THE AMS VOLUME 52, NUMBER 2 examinations. Twenty-four states now require that mathematics departments energize the teaching of students pass such exams in order to graduate, and graduate and undergraduate students and the train­ today there is a lot of pressure on schools to use this ing of postdocs. During "the panel, four representa­ kind of testing to show they are doing a good job. tives of mathematics departments spoke about What is the mathematical content of these exit exams? their VIGRE activities: University of Wisconsin at Achieve studied the exams in six states, looking at Madison, Texas A&M University, University of Cali­ the exams themselves rather than relying on what the fornia Los Angeles, and University of Arizona. Rep­ states said was on them. What it found is that the resentatives of the NSF's Division of Mathematical tests focus on material that students in most other Sciences (DMS) presented the disheartening news countries learn in the 7th or 8th grades rather than that, of the thirteen VIGRE grants that are expiring in high school. Most of the tests are multiple-choice, in 2005, at most five will be renewed. The DMS is are not very demanding, and do not probe very well aware of the pain the ending of these grants will deeply the students' reasoning and problem­ cause to the departments affected. However, that solving skills. The study concluded that, while the ex­ pain may be eased by two new programs that have ams are at a reasonable level, they should not be aims similar to VIGRE: Research Training Groups made any easier and should be strengthened over and Mentoring Through Critical Transition Points. time. DMS officials say that the total amount of funding Another study discussed at the COE meeting is DMS is now putting into such training programs has one conducted by the Mathematical Sciences Edu­ actually increased. cation Board of the National Academy of Sciences. On During the COE meeting, the president of the the committee preparing the study is Donald Saari American Mathematical Association of Two-Year of the University of California, Irvine, who made a Colleges (AMATYC), Susan Wood of]. Sargeant presentation before the COE. The study explored Reynolds Community College, described AMATYC's the question, Is the effectiveness of mathematics update of the "Crossroads" report, which lays out curricula being adequately evaluated? There was standards for two-year college mathematics. In no attempt to evaluate the curricula themselves; addition, former COE chair Roger Howe of Yale rather, the goal was to evaluate the evaluations of University described an effort by a small group of the curricula. The study focused on nineteen cur­ mathematicians who are working on a document ricula, thirteen of which were funded by the National that will provide guidance for development of Science Foundation (NSF) and the remainder of which mathematics standards. The meeting ended with were the products of commercial curriculum devel­ a panel in which four speakers representing a range opers. The committee began with a collection of of institutions discussed issues and challenges in seven hundred evaluations of these nineteen cur­ undergraduate education in mathematics. What ricula. Upon closer inspection, they found that around the COE meeting showed above all is that, unlike five hundred of those "evaluations" were really not in years past, it is now taken for granted that math­ evaluations at all but were such things as editorials, ematicians must pay attention to education. Future product descriptions, and progress reports. Of the students, future teachers, and the future of the field remaining two hundred evaluations, another fifty itself all depend on it. were eliminated as not being sufficiently rigorous -Allyn jackson and quantitative. The study concluded that these 150 evaluations Committee on Education are not adequate to say with certainty whether the Arthur Benjamin, Harvey Mudd College curricula are effective. Furthermore, the commit­ Sylvia T. Bozeman, Spelman College tee found that there are no standards for evaluat­ John B. Conway, National Science Foundation ing the effectiveness of mathematics curricula. The Robert Daverman, University of Tennessee (ex officio) report attempts to fill this gap by offering a frame­ David Eisenbud, Mathematical Sciences Research Institute work for curricular evaluation. One component of (ex officio) this framework is content analysis, in which the John H. Ewing, AMS (ex officio) disciplinary content of mathematics curricula is Robert Greene, University of California Los Angeles evaluated for clarity, accuracy, mathematical depth, Jane M. Hawkins, University of North Carolina and balance. Content analysis "is a place where we Roger Howe, Yale University mathematicians can and should have a voice," Saari Carole B. Lacampagne, National Research Council commented. The report, On Evaluating Curricular W. James Lewis, University of Nebraska William McCallum, University of Arizona (chair) Effectiveness: judging the Quality of K -12 Mathe­ Paul]. Sally Jr., University of Chicago matics Evaluations, is now available on the web at Michael Starbird, University of Texas at Austin http://www.nap.edu/books/0309092426/html. Alejandro Uribe, University of Michigan For its meeting the COE organized a panel on the Karen Vogtmann, Cornell University NSF's VIGRE (Vertical Integration of Research and Hung-Hsi Wu, University of California Berkeley Education) program. VIGRE has helped many

FEBRUARY 2005 NOTICES OF THE AMS 235 2004 Annual Survey of the Mathematical Sciences (First Report)

Report on the 2003-2004 New Doctoral Recipients Faculty Salary Survey

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

Report on the 2003-2004 New The First Report of the 2004 Annual Survey gives a broad picture of 2003-04 new doctoral recipients from U.S. departments in the math­ Doctoral Recipients ematical sciences, including their employment status in fall 2004. The This report presents a statistical profile of First Report also presents salary data for faculty members in U.S. de­ recipients of doctoral degrees awarded by partments of mathematical sciences in four-year colleges and uni­ departments in the mathematical sciences at versities. This report is based on information collected from two universities in the United States during the period questionnaires distributed to departments in May 2004. A follow-up July 1, 2003, through June 30, 2004. It includes a questionnaire was distributed to the individual new doctoral recipi­ preliminary analysis of the fall 2004 employment ents in October 2004. This questionnaire will be used to update and plans of 2003-04 doctoral recipients and a revise results in this report, which are based on information from the demographic profile summarizing characteristics of departments that produced the new doctorates. Those results will be published in the Second Report of the 2004 Annual Survey in the August citizenship status, sex, and racial/ethnic group. All 2005 issue of the Notices of the AMS. Another questionnaire concerned information came from the departments that gave with data on fall 2004 course enrollments, majors, graduate students, the degrees. and departmental faculty was distributed to departments in September 2004. Results from this questionnaire will appear in the Third Report Table l: Doctorates Granted Response Rates of the 2004 Annual Survey in the September 2005 issue ofthe Notices of the AMS. Group I (Pu) 24 of 25 including 0 with 0 degrees The 2004 Annual Survey represents the forty-eighth in an annual Group I (Pr) 22 of 23 including 0 with 0 degrees series begun in 1957 by the American Mathematical Society. The 2004 Survey is conducted by staff at the American Mathematical Society Group II 52 of 56 including 4 with 0 degrees with guidance from the Data Committee, a joint committee of the Group Ill 70 of 73 including 21 with 0 degrees American Mathematical Society, the American Statistical Association, Group IV 65 of 87 including 7 with 0 degrees the Institute of Mathematical Statistics, and the Mathematical Association of America. The current members of this committee are Group Va 20 of 23 including 1 with 0 degrees Amy Cohen-Corwin, Donald M. Davis, Nicholas M. Ercolani, J. Douglas See "Defm1t1ons of the Groups on page 251. Faires, Alexander Hahn, Naresh Jain, Stephen F. Kennedy, Ellen E. Table 1 provides the departmental response Kirkman (chair), David J. Lutzer, James W. Maxwell (ex officio), and rates for the 2004 Survey of New Doctoral Polly Phipps. The committee is assisted by AMS survey analyst Recipients. See page 2 51 for a description of the Colleen Rose. Comments or suggestions regarding this Survey Report groups. No adjustments were made in this report may be directed to the members of the Data Committee. for nonresponding departments. This preliminary report will be updated in the Second Report of the 2004 Annual Survey using information gathered from the new doctoral recipients. The Second Report will appear in the August 2005 issue of the Notices of the AMS.

236 NOTICES OF THE AMS VOLUME 52, NUMBER 2 2004 Annual Survey of the Mathematical Sciences

Changes in the Annual Survey occur over time, Highlights and these changes need to be considered when • There were 1 ,041 new doctoral recipients reported for 2003-04 by comparing results in this report to those in prior departments responding in time for the 2004 First Report. years. Information about changes that occurred in • Group I (Pu) reported the smallest number of new doctoral recipi­ 1997 or later can be found in the First Report for ents in the last 1 0 years (down 40% from 1995-96 figure). The the 2000 Annual Survey in the February 2001 issue number of new doctoral recipients from Groups I (Pu), I (Pr), and II of the Notices of the AMS. combined has increased from 566 in 2002-03 to 597 this year, an In this First Report's tables referring to new doc­ increase of 31 (5%) . toral recipients, "Fall" refers to results based on • Only 441 (42%) of the new doctoral recipients for 2003-04 are U.S. information about new doctoral recipients received citizens, a decrease of 48 (1 0%) from 2002-03 and down 145 (25%) from departments granting their degrees. This from 586 in 1997-98. The percentage of new doctoral recipients information is gathered in the first fall following who are U.S. citizens is the lowest percentage observed in the past nine years. the academic year in which the degrees were granted. "Final" refers to results based on supple­ • Based on responses from departments alone, the fall 2004 mental information received from the new doctoral unemployment rate for the 914 new doctoral recipients whose employment status is known is 5.7%, up from 5.1% for fall 2003. Table 2: New Doctoral Degrees Awarded • Fifty-eight new doctoral recipients hold positions at the institution by Group, Fall Count that granted their degree, although not necessarily in the same de­ partment. This is 7% of the new doctoral recipients who are currently Group I (Pu) I (Pr) II Ill IV Va TOTAL known to have jobs and 9% of those who have academic positions in the U.S. Nineteen new doctoral recipients have part-time positions. 1997-98 306 174 264 129 213 77 1163 • The number of new doctoral recipients employed in the U.S. is 739, 1998-99 292 152 241 136 243 69 1133 up 76 from last year. The number of new doctoral recipients em­ 1999-00 256 157 223 132 284 67 1119 ployed in academic positions in the U.S. increased to 614 (a nine­ 2000-01 233 129 203 125 237 81 1008 year high) from 534 last year (a 1 5% increase); there were increases in the categories of the doctoral-employing institutions (combined), 2001-02 218 139 164 124 222 81 948 but the Master's and Bachelor's institutions hired 2 fewer new doc­ 2002-03 258 138 170 121 239 91 1017 toral recipients than last year. 2003-04 195 187 215 111 243 90 1041 • Of the 739 new doctoral recipients taking positions in the U.S., 99 (1 3%) have jobs in business and industry; the number of new doc· toral recipients taking jobs in business and industry, after oscillat­ Figure 1: New Doctoral Degrees Awarded ing in the late 1990s, declined three consecutive years by 38 in fall by Combined Groups, Fall Count 2001, 45 in fall 2002, and 26 in fall 2003 before showing a slight _._. I (Pu), I (Pr), II, Ill, & Va increase of 2 in fall 2004. The number of new doctoral recipients taking jobs in government is down 6 (19%) over fall 2003. I (Pu), I (Pr), & II --<>-- • Among the 739 new doctoral recipients having employment in the 1000 U.S., 338 (46%) are U.S. citizens (down from 376 (57%) last year). 900 The number of non-U.S. citizens having employment in the U.S. is 401, up 40% from 287 last year. 800 • Among the 302 new doctoral recipients hired by U.S. doctoral­ 700 granting departments, 38% are U.S. citizens (down from 52% last year). Among the 312 having other academic positions in the U.S., 53% are 600 U.S. citizens. 500 • Of the 1 ,041 new doctoral recipients, 31 5 (30%) are females, up just 400 11 from fall 2003. Of the 441 U.S. citizen new doctoral recipients, 145 (33%) are females, down 12 from fall 2003. The all-time high 300 was 187 in fall 1998. 200 • Among the 441 U.S. citizen new doctoral recipients, 5 are American Indian or Alaska Native, 23 are Asian, 12 are Black or African Amer­ 100 ican, 13 are Hispanic or Latino, 386 are White, and 2 are Native Hawai­ 0 ian or Other Pacific Islander. • Group IV produced 243 new doctorates, of which 97 (40%) are 00 O'l 0 N m <:I" O'l O'l 0 0 0 0 0 females, compared to all other groups combined, where 218 (27%) I I I I I I I 00 O'l 0 N m O'l O'l O'l 0 0 0 0 are females. In Group IV; 81 (31%) of the new doctoral recipients "'O'l O'l O'l 0 0 0 0 N N N N are U.S. citizens (while in the other groups 45% are U.S. citizens). • Three hundred eighteen new doctorates had a dissertation in statistics/ biostatistics (289) and probability (29). The next highest Ellen E. Kirkman is professor of mathematics at the number was in algebra and number theory with 144. Those with dis­ Wake Forest University. ]ames W. Maxwell is AMS asso­ sertations in statistics/biostatistics and probability accounted for 31% ciate executive director for Membership, Meetings, and Programs. Colleen Rose is AMS survey analyst. of the new doctorates in 2003-04.

FEBRUARY 2005 NOTICES OF THE AMS 237 2004 Annual Survey of the Mathematical Sciences

Table 3: Full-Time Graduate Students in Groups I, II, Ill, & Va, Fall 1994 to Fall 2003

GRADUATE STUDENTS 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 Total full-time 10185 9761 9476 9003 8791 8838 9637 9361 9972 9731 First-year full-time 2668 2601 2443 2386 2458 2664 2839 2875 2996 3612 U.S. citizen full-time 5945 5623 5445 4947 4831 4668 5085 4631 5055 5168 First-year U.S. citizen full-time 1664 1551 1465 1316 1349 1401 1527 1517 1630 1426

(Data Reprinted from Table 6B in Third Report, 2003 Annual Survey) recipients themselves as well as additional new doc­ as many of the nomesponding departments as toral recipients not reported by departments in time possible. A careful look at the past history of the for publication in the First Report. These results are nomesponding departments makes it unlikely that published each August in the Second Report. the final count of new doctoral recipients will in­ crease by more than 35 . Doctoral Degrees Granted in 2003-04 From Table 2 we see that Group I (Pr) showed the Table 2 shows the number of new doctoral degrees largest increase (49) in the number of doctoral re­ granted by the different doctoral groups surveyed cipients from the previous year, while Groups II and in the Annual Survey for the past seven years. The IV also had an increase. Groups I (Pu), III, and Va 1,041 new doctorates granted by these depart­ showed decreases of 63, 10, and 1 respectively. ments in 2003-04 is an increase of 24 from the The total number in doctoral recipients in Group I (Pu) is the lowest number reported by this group fall count for 2002-03. Figure 1 presents the trends in ten years (down 40% from the 1995-96 number in doctorates granted for Groups I (Pu), I (Pr), II, III, of 325). Group III continues to decline slowly, down and Va combined and Groups I (Pu), I (Pr), and II 25 from its high in 1998-99, and Group Va dropped combined. slightly this year after reaching its highest level last The response rates were above 90% for all groups year. In addition, we see that Group I (Pr) reported except Groups IV and Va. Group IV historically has its highest number of doctoral recipients since had slightly lower response rates than the other 1997-98 with an increase of 49 over last year, groups. Overall, twelve fewer Group IV departments Group II increased by 45 but is still down 49 from responded in time for the First Report this year than its high in 1997-98, and Group IV for the second responded by this time last year. consecutive year shows an increase but is still The 1,041 new doctoral recipients is a prelimi­ down 41 from its high in 1999-2000. nary count. A final count will appear in the Second Table 3 gives historical information about var­ Report in the August 2005 issue of the Notices of ious types of full-time graduate students in Groups the AMS. Efforts are under way to obtain data from I, II, III, and Va combined. These data, gathered in the 2003 Departmental Profile Figure 2: Percentage of New Doctoral Recipients Unemployed survey, are reprinted from Table 6B of the (as reported in the respective Annual Survey Reports 1992-2003) Third Report of the 2003 Annual Survey -+-Faii....-<>-Final (Notices of the AMS, September 2004). It Report Fall Final 16.0 sheds some light on the downward trend 1992-93 12.0 8.9 in number of new doctorates as shown in 14.0 - 1993-94 14.0 11.0 Table 2 and Figure 1. Since 2000 the total number of full-time students has fluctuated 1994-95 15.0 11.0 12.0 in the 9,000s, with the fall 2003 count at 1995-96 9.4 8.1 9,731. The number of first-year full-time 10.0 1996-97 6.8 3.8 graduate students fell from 2,668 in 1994 1997-98 7.2 4.9 8.0 to 2,386 in 1997 before starting to increase in 1998, reaching a high of 3,612 for fall 1998-99 6.2 4.7 6.0 2003. Full-time first-year U.S. citizen grad­ 1999-00 4.6 3.3 uate students fell from 1,664 in 1994 to 2000-01 5.6 3.7 4.0 1,316 in 1997, then climbed to a high of 2001-02 4.3 2.9 1,630 for 2002 before declining to 1,426 for 2.0 fall2003. The increase in new doctoral re- 2002-03 5.1 5.0 cipients reported for 2003-04 continues 2003-04 5.7 * 0.0 what appears to be a moderate trend up­ M '

238 NOTICES OF THE AMS VOLUME 52, NUMBER 2 2004 Annual Survey of the Mathematical Sciences

Table 4A: Employment Status of 2003-04 U.S. New Doctoral Recipients in the Mathematical Sciences by Field of Thesis

FIELD OF THESIS

Real, Comp., Discr. Math./ Numerical Linear Differential, Algebra/ Funct., & Com bin./ Analysis/ Nonlinear Integral, & Number Harmonic Geometry/ Logic/ Statistics/ Applied Approxi· Optim./ Difference Math. Other/ TYPE OF EMPLOYER Theory Analysis Topology Comp. Sci. Probability Biostat. Math. mations Control Equations Educ. Unknown TOTAL Group I (Public) 18 5 8 6 3 2 11 7 1 8 0 0 69 Group I (Private) 10 8 19 3 2 0 7 0 0 8 0 0 57 Group II 15 7 12 6 2 4 5 3 0 7 0 0 61 Group Ill 4 2 5 4 2 10 4 0 0 1 3 0 35 Group IV 0 0 0 0 0 62 1 0 0 0 0 0 63 Group Va 1 0 0 3 0 1 4 5 0 3 0 0 17 Master's 10 7 4 7 2 14 3 7 3 3 2 0 62 Bachelor's 16 14 11 8 2 12 5 7 3 11 3 0 92 Two-Year College 3 3 4 0 0 1 0 1 0 2 0 0 14 Other Academic Dept. 4 4 5 6 2 56 19 8 3 3 5 0 115 Research Institute/ 2 2 4 3 2 8 3 2 0 3 0 0 29 Other Nonprofit Government 2 2 1 3 0 8 5 2 2 1 0 0 26 Business and Industry 6 1 5 7 3 55 13 5 1 3 0 0 99 Non-U.S. Academic 18 10 13 12 3 9 11 6 5 15 0 1 103 Non-U.S. Nonacademic 1 0 0 1 0 3 2 0 0 1 0 0 8 Not Seeking Employment 1 0 0 1 1 5 2 1 0 1 0 0 12 Still Seeking Employment 10 2 6 9 1 10 8 2 2 2 0 0 52 Unknown (U .S.) 12 7 4 6 2 18 6 7 2 4 2 0 70 Unknown (non-U.S.)* 11 7 5 9 2 11 5 3 0 3 1 0 57 TOTAL 144 81 106 94 29 289 114 66 22 79 16 1 1041 Column I Male 107 58 78 71 23 176 84 50 18 53 7 1 726 Subtotals I Female 37 23 28 23 6 113 30 16 4 26 9 0 315

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

Table 48: Employment Status of 2003- 04 U.S. New Doctoral Recipients in the Mathematical Sciences by Type of Degree-Granting Department

TYPE OF DOCTORAL DEGREE-GRANTING DEPARTMENT Group I Group I Row (Public) (Private) Group II Group Ill Group IV Group Va Subtotals TYPE OF EMPLOYER Math. Math. Math. Math. Statistics Applied Math. TOTAL Male Female Group I (Public) 29 25 9 0 1 5 69 53 16 Group I (Private) 15 32 6 0 0 4 57 46 11 Group II 20 17 16 2 4 2 61 4 1 20 Group Ill 5 9 5 10 6 0 35 22 13 Group IV 1 1 0 2 59 0 63 48 15 Group Va 0 3 1 0 0 13 17 13 4 Master's 8 1 25 18 9 1 62 42 20 Bachelor's 14 8 46 16 5 3 92 6 1 31 Two-Year College 4 0 2 7 1 0 14 9 5 Other Academic Dept. 6 10 16 15 48 20 115 69 46 Research Institute/ 8 7 4 0 9 1 29 17 12 Other Nonprofit Government 3 4 6 2 8 3 26 15 11 Bu siness and Industry 9 13 9 9 50 9 99 69 30 Non-U.S. Academic 3 1 22 24 9 7 10 103 78 2 5 Non-U.S. Nonacademic 0 4 0 0 3 1 8 6 2 Not Seeking Employment 0 1 6 2 3 0 12 4 8 Still Seeking Employment 8 11 15 6 7 5 52 40 12 Unknown (U.S.) 16 10 19 6 13 6 70 49 2 1 Unknown (non-U.S.)* 18 9 6 7 10 7 57 44 13 TOTAL 195 187 2 15 111 243 90 1041 726 315 Column I Male 151 137 152 72 146 68 726 Subtotals I Female 44 50 63 39 9 7 22 315 *Includes those w hose status is re ported as "unknown" or "still seeking employment".

F EBRUARY 2005 NOTICES OF THE AMS 239 2004 Annual Survey of the Mathematical Sciences

Table 4C: Field of Thesis of 2003-04 New Doctoral Recipients by Type of Degree-Granting Department FIELD OF THESIS TYPE OF DOCTORAL Real, Comp., Discr. Math./ Numerical Linear Differential, DEGREE-GRANTING Algebra/ Funct., & Combin./ Analysis/ Nonlinear Integral, & Number Harmonic Geometry/ Logic/ Statistics/ Applied Approxi- Optim./ Difference Math. Other/ DEPARTMENT Theory Analysis Topology Comp. Sci . Probability Bios tat. Math. mations Control Equations Educ. Unknown TOTAL Group I (Public) 52 28 32 21 8 3 20 10 1 20 0 0 195 Group I (Private) 43 15 36 23 9 5 31 4 1 19 0 1 187 Group II 34 30 29 25 3 11 23 27 12 17 4 0 215 Group Ill 1 5 8 9 17 2 19 8 10 2 9 12 0 111 Group IV 0 0 0 0 2 239 2 0 0 0 0 0 243 Group Va 0 0 0 8 5 12 30 15 6 14 0 0 90 Column Total 144 81 106 94 29 289 114 66 22 79 16 1 1041

Table SA: U.S. Employed 2003-04 New Doctoral Recipients tables will be revised using information from the by Type of Degree-Granting Department doctoral recipients themselves and will appear in the 2004 Second Report in the August 2005 issue U.S. EMPLOYER I (Pu) I (Pr) II Ill IV Va TOTAL of the Notices of the AMS. Groups I, II, Ill, IV, and Va 70 87 37 14 70 24 302 The last column (Total) in Table 4A can be used to find the overall unemployment rate. In this and Master's, Bachelor's, and 2-Year Colleges 26 9 73 41 1 5 4 168 other unemployment calculations in this report, the individuals whose employment status is not Other Academic and Research Institutes 14 17 20 1 5 57 21 144 known (Unknown (U.S.) and Unknown (non-U.S.)) are first removed, and the unemployment fraction Government 3 4 6 2 8 3 26 is the number still seeking employment divided Business and Industry 9 13 9 9 50 9 99 by the total number of individuals left after the TOTAL 122 130 145 81 200 61 739 "Unknowns" are removed. The overall unemploy- Table SC: Number of New Doctoral sex, in later sections of this report. The names of Recipients Taking U.S. Academic Positions by the 1,041 new doctoral recipients are found on Type of Degree-Granting pages 264-82 of this issue of the Notices. Department, Fall 2000 to Fall 2004 Group I (Pu) I (Pr) II Ill IV Va TOTAL Employment Status of 2003-04 New Doctoral Recipients Fall 2000 133 78 112 75 126 27 551 Tables 4A, 4B, and 4C each provide a different Fall 2001 146 70 109 74 84 27 510 cross-tabulation of the 1,041 new doctoral recipi­ Fall 2002 120 83 91 86 92 31 503 ents in the mathematical sciences. These tables Fall 2003 123 76 117 60 118 40 534 contain a wealth of information about these new doctoral recipients, some of which will be dis­ Fall 2004 110 113 130 70 142 49 614 cussed in this report. Note that these tables give a breakdown by sex for type of employer, type of ment rate for these data is 5.7%. This figure will degree-granting department, and field of thesis. be updated later with information gathered from Keep in mind that the results in this report come the individual new doctoral recipients. The figure from the departments giving the degrees and not for fall 2003 was 5.1%. Figure 2 shows how this from the degree recipients themselves. These unemployment rate compares with other years over the past decade. The unemployment rates, cal­ Table 58: Number of New Doctoral culated using Table 4B, vary from group to group, Recipients Taking Positions in Business and with a high of 7.9% for Group II and lows of 3.2% Industry in the U.S. by Type of Degree­ and 5.0% for Groups IV and I (Pu) respectively. Granting Department, Fall 2000 to Fall 2004 There are 739 new doctoral recipients employed in the U.S. Table SA gives a breakdown of type of Group I (Pu) I (Pr) II Ill IV Va TOTAL employer by type of degree-granting department Fall 2000 31 23 34 25 79 14 206 for these 73 9 new doctoral recipients. Of these, 614 Fall 2001 24 1 5 25 21 59 24 168 (83%) hold academic positions, 26 (4%) are em­ ployed by government, and 99 (13%) hold posi­ Fall 2002 1 5 12 19 6 56 1 5 123 tions in business and industry. Fall 2003 19 13 5 8 45 7 97 In the First Report for 2002-03, there were 663 Fall 2004 9 13 9 9 50 9 99 new doctoral recipients employed in the US, of which

240 NOTICES OF THE AMS VOLUME 52, NUMBER 2 2004 Annual Survey of the Mathematical Sciences

Table 50: U.S. Academic Positions Filled Among the 739 new doctoral recipients known by New Doctoral Recipients by Type of to have employment in the U.S. in fall 2004, Group Hiring Department, Fall 2000 to Fall 2004 II has the smallest percentage taking jobs in busi­ ness and industry at 6% and Group IV the highest Group 1-111 IV Va M&B Other TOTAL at 25%. Fall 2000 209 46 13 158 125 551 Table SC shows the number of new doctoral Fall 2001 199 41 12 161 97 510 recipients who took academic positions in the U.S. by type of department granting their degree for fall Fall 2002 213 46 7 138 99 503 2000 to fall 2004. It shows a moderate rebound Fall 2003 203 39 9 156 127 534 in the total number of new doctoral recipients tak­ Fall 2004 222 63 17 154 158 614 ing academic employment in fall 2004, compared with the previous nine years. This year's number 534 (81%) held academic positions, 32 (5%) were in is up 15% over last year. Among the 739 new doc­ government, and 97 (15%) were in business and toral recipients employed in the U.S. in fall 2004, industry. The number of new doctoral recipients 83% have academic positions. This percentage is employed in the U.S. increased in all categories of highest for Groups I (Pu) and II at 90% and lowest Table SA except "Government". for Groups Nat 71%. Table SD shows the number of positions filled with new doctoral recipients for each type of aca­ Table 5E: Females as a Percentage of 2003-04 demic employer. Increases in positions filled by New Doctoral Recipients Produced by and new doctoral recipients were realized by all groups Hired by Doctoral-Granting Groups except Group M & B. Infall2004, 58 new doctoralrecipientsheldposi­ Percent I (Pu) I (Pr) II Ill IV Va TOTAL tions in the institution that granted their degree, Produced 23 27 29 35 40 24 30 although not necessarily in the same department. Hired 23 19 33 37 24 24 26 Table 5G: 2003-04 New Doctoral Table SB shows the number of new doctoral Recipients Having Employment in the U.S. recipients who took positions in business and by Type of Employer and Citizenship industry by the type of department granting their CITIZENSHIP degree for fall 2000 to fall 2004. The number of U.S. EMPLOYER U.S. Non-U.S. TOTAL new doctoral recipients taking jobs in business and industry, after oscillating in the late 1990s, de­ Academic, Groups I- Va 116 186 302 clined three consecutive years (by 38 in fall 2001, Academic, Other 164 148 312 45 in fall 2002, and 26 in fall 2003) before show­ Nonacademic 58 67 125 ing a slight increase of 2 in fall2004. The fall2004 number is down 52% from the fall 2000 number. TOTAL 338 401 739

Table SF: Employment Status of 2003-04 U.S. New Doctoral Recipients by Citizenship Status

CITIZENSHIP NON-U.S. CITIZENS TYPE OF EMPLOYER U.S. CITIZENS Permanent Visa Temporary Visa Unknown Visa TOTAL U.S. Employer 338 so 326 25 739 U.S. Academic 280 36 278 20 614 Groups I, II , Ill, and Va 96 16 11 9 8 239 Group IV 20 5 34 4 63 Non-Ph.D. Department 155 15 106 7 283 Research Institute/Other Nonprofit 9 0 19 1 29 U.S. Nonacademic 58 14 48 5 125 Non-U.S. Employer 23 2 84 2 111 Non-U.S. Academic 21 2 78 2 103 Non-U.S. Nonacademic 2 0 6 0 8 Not Seeking Employment 9 0 3 0 12 Still Seeking Employment 24 7 21 0 52 SUBTOTAL 394 59 434 27 914 Unknown (U.S.) 44 5 19 2 70 Unknown (non-U.S.)* 3 0 46 8 57

TOTAL 441 64 499 37 1041

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

f EBRUARY 2005 NOTICES OF THE AMS 241 2004 Annual Survey of the Mathematical Sciences

Table 6: Sex, Race/Ethnicity, and Citizenship of 2003-04 U.S. New Doctoral Recipients

MALE FEMALE NON-U.S. CITIZENS NON-U.S. CITIZENS u.s. Permanent Temporary Unknown Total u.s. Permanent Temporary Unknown Total RACIAL/ETHNIC GROUP CITIZENS Visa Visa Visa Male CITIZENS Visa Visa Visa Female TOTAL American Indian or 3 0 0 0 3 2 0 0 0 2 5 Alaska Native Asian 13 17 187 13 230 10 11 86 0 107 337 Black or African 7 5 10 0 22 5 1 3 1 10 32 American Hispanic or Latino 11 1 25 1 38 2 1 4 1 8 46 Native Hawaiian or 2 0 1 0 3 0 0 0 0 0 3 Other Pacific Islander White 260 14 137 8 419 126 11 46 1 184 603 Unknown 0 1 5 3 9 0 1 0 5 6 15 TOTAL 296 38 365 25 724 145 25 139 8 317 1041

This represents 7% of new doctoral recipients who Later sections in this First Report give more in­ are currently employed and 9% of the U.S. academic formation about the female new doctoral recipients positions held by new doctoral recipients. Infall2003 by citizenship and the female new doctoral recip­ there were 60 such individuals making up 8% of the ients in Group IV. new doctoral recipients who were employed at the time of the First Report. Nineteen new doctoral re­ Employment Information about 2003-04 cipients have taken part-time positions in fall2004 New Doctoral Recipients by Citizenship compared with 10 infall2003. and Type of Employer Table SF shows the pattern of employment within Information about 2003-04 Female employer categories broken down by citizenship New Doctoral Recipients status of the new doctoral recipients. Tables 4A and 4B give male and female breakdowns The unemployment rate for the 441 U.S. citizens of the new doctoral recipients in 2003-04 by Field of is 6.1% compared to 5.1% in fall 2003. The unem­ Thesis, by Type of Degree-Granting Department, and ployment rate for non-U.S. citizens is 5.4%. This by Type of Employer. varies by type of visa. The unemployment rate for Overall, 315 (30%) of the 1,041 new doctoral non-U.S. citizens with a permanent visa is 11.9%, recipients in 2003-04 are female. In 2002-03, 304 while that for non-U.S. citizens with a temporary (30%) of the new doctoral recipients were female. visa is 4.8%. Among U.S. citizens whose employ­ This percentage varies over the different groups, ment status is known, 86% are employed in the U.S. and these percentages are given in the first row of Among non-U.S. citizens with a permanent visa Table SE. This year the percentage of females whose employment status is known, 85% have jobs produced is highest for Group IV at 40%, while last in the U.S. (last year the percentage was 81%), while year it was highest in Group III. While the lowest the percentage for non-U.S. citizens with a tempo­ percentage last year was for Group I (Pr) at 19%, this rary visa is 75% (last year the percentage was 68%). year it is for Group I (Pu) at 23%. The number of non-U.S. citizens having employ­ The second row of Table SE gives the percent­ ment in the U.S. is 401, up 40% from 287last year. age of the new doctoral recipients hired who are Table SG is a cross-tabulation of the 739 new female for each of the Groups I, II, III, IV, and Va. doctoral recipients who have employment in the In addition, 32% of the new doctoral recipients U.S. by citizenship and broad employment cate­ hired in Group M, master's departments, are gories, using numbers from Table SF. Of the 739 female; 34% of the new doctoral recipients hired new doctoral recipients having jobs in the U.S., in Group B, bachelor's departments, are female; 46% are U.S. citizens. Of the 302 new doctoral re­ and 30% of new doctoral recipients hired in cipients who took jobs in U.S. doctoral-granting business and industry are female. departments, 38% are U.S. citizens (down from 52% The unemployment rate for female new doc­ last year). Of the 312 who took other academic po­ toral recipients is 4% compared to 6% for males and sitions, 53% are U.S. citizens. Of the 125 who took 5.7% overall. nonacademic positions, 46% are U.S. citizens. Of the The percentage of female new doctoral recipi­ 338 U.S. citizens employed in the U.S., 34% have jobs ents within fields of thesis ranged from 18% in in a doctoral-granting department, 49% are in other optimization/ control to 39% in statistics and 56% academic positions, and 17% are in nonacademic in mathematics education. positions. For the 401 non-U.S. citizens employed

242 NOTICES OF THE AMS VOLUME 52, NUMBER 2 2004 Annual Survey of the Mathematical Sciences

Table 7: U.S. Citizen Doctoral Recipients Figure 3: U.S. Citizen Doctoral Recipients ---+- Total Doctorates Granted by U.S . Institutions Total Doctorates Total U.S. --o--- Total U.S. Citizen Doctoral Recipients Granted by U.S. Citizen Doctoral 1300 Year Institutions Recipients % 1200 1980-81 839 567 68 1100 1985-86 755 386 51 1990-91 1061 461 43 1000 1996-97 1158 516 45 900 1997-98 1216 586 48 800 1998-99* 1133 554 49 700 1999-00 1119 537 48 600 2000-01 1008 494 49 500 2001-02 948 418 44 2002-03 1017 489 48 400 2003-04 1041 441 42 300 * Prior to 1998-99, the counts include new doctoral recipients from 200 Group Vb. In addition, prior to 1982- 83, the counts include recipients 100 from computer science departments. 0 N «:!" l!l 00 0 N «:!" l!l 00 0 N «:!" in the U.S., the analogous percentages are 46%, 00 00 00 00 0\ 0\ 0\ 0\ 0\ 0 0 0 I I I I I I I I I I I I 3 7%, and 17% respectively. m LJ"\ r-.. 0\ m LJ"\ r-.. 0\ m 00 00 00 00 00 0\ 0\ 0\ 0\ 0\ 0 0 0\ 0\ 0\ 0\ 0\ 0\ 0\ 0\ 0\ 0\ 0 0 N N Sex, Race/Ethnicity, and Citizenship Status of 2003-04 New Doctoral Recipients Asians, 20 Blacks or African Americans, 33 Hispan­ Table 6 presents a breakdown of new doctoral ics or Latinos, 1 Native Hawaiian or Other Pacific Is­ recipients according to sex, racial/ethnic group, and lander (male), 217 Whites, and 15 other. citizenship status. The information reported in Table 7 (and Figure 3) gives the number of new this table was obtained in summary form from the U.S. doctoral recipients and the number of U.S. cit­ departments granting the degrees. izens back to 1980-81. The 441 U.S. citizen new Therewere441 (42%)U.S.citizensamongthe 1,041 doctoral recipients is down by 145 (25%) since new doctoralrecipients in 2003-04. Among U.S. cit­ 1997-98. The percentage of U.S. citizens is the izens, 5 are Americanlndian or Alaska Native (3 males lowest percentage (42%) reported since 1995-96 and2 females), 23 areAsian(13malesand lOfemales), (43%). 12 are Black or African American (7 males and 5 fe­ Females make up 33% of the 441 U.S. citizens males), 13 are Hispanic or Latino (11 males and 2 receiving doctoral degrees in the mathematical females), 2 are Native Hawaiian or Other Pacific Is­ lander (males), and 386 are White (260males and 126 Figure 4: Females as a Percentage of U.S. Citizen females). Among non-U.S. citizens, there are 314 New Doctoral Recipients 40% ------Table 8: U.S. Citizen Doctoral Recipients by Sex 35% ------Total U.S. Citizen Doctoral % 30% Year Recipients Male Female Female 1980-81 567 465 102 18 25% 1985-86 386 304 82 21 1990-91 461 349 112 24 1996-97 516 368 148 29 1997-98 586 423 163 28 15% ------1998-99* 554 367 187 34 1999-00 537 379 158 29 10% ------2000-01 494 343 151 31 2001-02 418 291 127 30 5% ------2002-03 489 332 157 32 2003-04 441 297 144 33 0% N «:!" l!l 00 0 N «:!" l!l 00 0 N «:!" 00 00 00 00 0\ 0\ 0\ 0\ 0\ 0 0 0 * Prior to 1998- 99, the counts include new doctoral recipients from I I I I I I I I I I I I LJ"\ m Group Vb. In addition, prior to 1982- 83 , the counts include recipients m LJ"\ 1'- 0\ m 1'- 0\ 00 00 00 00 00 0\ 0\ 0\ 0\ 0\ 0 0 from computer science departments. 0\ 0\ 0\ 0\ 0\ 0\ 0\ 0\ 0\ 0\ 0 0 N N

fEBRUARY 2005 NOTICES OF THE AMS 243 2004 Annual Survey of the Mathematical Sciences

Table 9: Sex and (:itizenship of 2003-04 New Doctoral Recipients by Granting Department

GROUP I (Pu) I (Pr) II Ill IV Va TOTAL CITIZENSHIP Male Female Male Female Male Female Male Female Male Female Male Female Male Female u.s. 67 22 55 23 76 33 29 20 43 38 27 8 297 144 Non-U.S. 84 22 82 27 76 30 43 19 103 59 41 14 429 171 TOTAL 1 51 44 137 50 152 63 72 39 146 97 68 22 726 315

sciences in 2003-04. This is the second highest new doctoral recipients with dissertations in statis­ percentage of females among U.S. citizen new doc­ tics/biostatistics and probability. The other groups toral recipients reported since 198 5-86,when it was produced 77 new doctoral recipients with disserta­ 34%, the highest ever reported by the Annual Sur­ tions in statistics/biostatistics and probability in vey. Last year this percentage was 32%. Among the 2003-04 and have averaged 75 per year over the past 600 non-U.S. citizen new doctoral recipients, 29% seven years. Information about these 77 new doc­ (172) are female, up from last year's 28%. toral recipients and the 243 new doctoral recipients Table 8 (and Figure 4) gives the historical in Group IV is found in this section of the report. record of U.S. citizen new doctoral recipients, For nine years substantial effort has gone into broken down by male and female for past years, making Group IV an appropriate set of depart­ going back to 1980-81. The number of female ments for the Annual Survey and increasing the U.S. citizen new doctoral recipients is down 43 number of Group IV departments that respond to (23%) from an all-time high of 187 in 1998-99. the Annual Survey. Table 10 contains information Table 9 gives a sex and citizenship breakdown about new doctoral recipients in Group IV as well of the new doctorates within each of the six groups as those with dissertations in statistics/biostatis­ of doctoral-granting departments. Among all1,041 tics and probability in other groups for the past new doctoral recipients, 41% of the males and 46% seven years. The last two rows of Table 10 give of the females are U.S. citizens. Within the groups a split of the 2003-04 results between the 56 the percentage of the new doctoral recipients who statistics departments and the 31 biostatistics and are U.S. citizens is lowest in Group IV at 33% and biometrics departments in Group IV. Quite a bit of highest in Group II at 50%. Groups II is the only the variation in numbers from year to year in this group to have more U.S. citizen than non-U.S. citi­ table is due to the changes made in the departments zen new doctoral recipients in 2003-04. in Group IV over the nine years and to the relatively low response rate for this group. At the time of the 2003-04 New Doctoral Recipients with Second Report last year, 77 of 86 (90%) of Group Dissertations in Statistics/Biostatistics IV departments had responded, which is the largest and Probability percentage ever. Group IV contains U.S. departments (or programs) Group IV has 87 departments for 2003-04, 14 of statistics, biostatistics, and biometrics reporting more than the next largest doctoral group. It con­ a doctoral program. In the Annual Survey Reports, tains 30% of all doctoral departments surveyed, and Group IV is referred to as the Statistics Group. In the 65 Group IV departments responding to the An­ addition, other groups in the Annual Survey produce nual Survey reported 243 new doctoral recipients,

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

New Doctoral Recipients in Statistics/ Biostatistics New Doctoral Recipients New Doctoral Recipients in Group IV and Probability Hired by Group IV Depts Depts Responding Female Jobs in Percentage Other Percentage Year Surveyed (percent) Total (percent) Bus & lnd Unemployed Total Group IV Groups Unemployed Male Fem ale 1997-98 82 59 (72) 213 73 (34) 70 3.2 294 199 95 3.7 25 10 1998-99 91 72 (79) 243 87 (36) 57 4.9 320 240 80 5.8 29 20 1999-00 89 75 (84) 284 110 (39) 79 2.4 351 278 73 2.0 24 22 2000-01 86 70 (81) 237 98 (41) 59 5.1 289 221 68 5.3 27 14 2001-02 86 72 (84) 222 92 (41) 56 6.0 288 221 67 5.4 31 15 2002-03 86 74 (86) 239 98 (41) 45 2.1 302 234 68 3.3 20 19 2003-04 87 65 (75) 243 97 (40) 50 3.0 318 241 * 77** 4.0 48 15 Statistics 56 44 (79) 180 63 (35) 38 3.0 28 10 Biostatistics 31 21 (68) 63 34 (54) 12 3.0 20 5 * Of 241, there were 239 in statistics/ biostatistics and 2 in probability. For complete details, see Table 4C. ** Of 77, there were 50 in statistics/ biostatistics and 27 in probability. For complete details, see Table 4C.

244 NOTICES OF THE AMS VOLUME 52, NUMBER 2 2004 Annual Survey of the Mathematical Sciences

23% of all new doctoral recipients in 2003-04. The number of new doctoral recipients in Group IV is up Faculty Salary Survey four from the number reported at this time last year, The charts on the following pages display faculty while the number of departments responding is salary data for Groups I (Pu), I (Pr), II, III, IV down nine from the number responding by this time (Statistics), IV (Biostatistics), Va, M, and B: faculty last year. salary distribution by rank, mean salaries by rank, Because of its size, the data from Group IV have information on quartiles by rank, and the number a large effect on the results when all doctoral groups of returns for the group. Results reported here are are combined. Furthermore, Group IV results are of­ summaries based on the departments who re­ sponded to this portion of the Annual Survey. This ten quite different from those for Groups I (Pu), I is the third year that salary information has been (Pr), II, III, and Va. Group IV results can mask im­ reported separately for statistics departments and portant changes in the other doctoral groups. In the biostatistics and biometrics departments in Group following paragraphs some of these differences IV. are presented. The trends noted below have also Table 11 provides the departmental response been observed in past reports. rates for the 2004 Faculty Salary Survey. Depart­ Table 9 shows that for the Group IV new doctoral ments were asked to report for each rank the recipients, 97 of 243 (40%) are female, while 218 of number of tenured and tenure-track faculty whose 798 (27%) are female in the other doctoral groups. 2004-05 academic-year salaries fell within given Among U.S. citizens, females accounted for 38 of salary intervals. Reporting salary data in this the 81 (47%) Group IV new doctoral recipients, fashion eliminates some of the concerns about while for the other groups 106 of 360 (29%) were confidentiality but does not permit determination of actual quartiles. Although the actual quartiles can­ female. Overall, 144 of 441 (33%) U.S. citizen new not be determined from the data gathered, doctoral recipients were female. these quartiles have been estimated assuming that In Group IV, 81 of 243 (33%) new doctoral recipi­ the density over each interval is uniform. ents are U.S. citizens, while in other groups 360 of Since departments in Groups I, II, and III were 798 (45%) are U.S. citizens. changed in 1995-96 (see definitions of the groups Of the 200 new doctoral recipients from Group IV who found employment in the U.S., 50 (2 5%) took Table 11: Faculty Salary Response Rates jobs in business or industry. From the other groups, 539 new doctoral recipients found employment in Department Number Percent the U.S., of which 49 (9%) took jobs in business or in­ Group I (Public) 21 of 25 84 dustry. Group I (Private) 17 of 23 74 The employment status for 220 Group IV new 48 of 56 86 doctoral recipients is known, and 7 (3.2%) are unem­ Group II ployed. For the other groups, the employment Group Ill 62 of 73 85 status of 694 is known, and 45 (6.5%) are unemployed. Group IV (Statistics) 39 of 56 70 Fifteen of 63 (24%) new doctoral recipients hired by Group IV (Biostatistics) 20 of 31 65 Group IV departments were female, down from last Group Va 8 of 18* 44 year's 49%, the lowest percentage of female hires re­ Group M 104 of 192 54 ported since 1999-2 000. The other doctoral groups reported that 64 of 2 3 9 (2 7%) new doctoral recipients Group B 350 of 1020 34 hired were female, the same percentage as reported • The population for Group Va is slightly less than for the Doctorates last year, significantly more than the 16% reported in Granted Survey, because some departments grant degrees but do not for­ mally "house" faculty and their salaries. 1999-2000. Group IV had 241 new doctoral recipients with on page 251), comparisons are possible only to fields of thesis in statistics/biostatistics (239) and the last eight years' data. In addition, prior to the probability (2), and the other doctoral departments 1998 survey Groups Va and Vb were reported had 77 with field of thesis in statistics/biostatistics together as Group V. When comparing current (50) and probability (2 7). The distribution of these 77 and prior year figures, one should keep in mind that degrees among the various groups can be found in differences in the set of responding departments Table 4C. The number of new doctoral recipients with may be a significant factor in the change in the re­ theses in statistics/biostatistics and probability (318) ported mean salaries. is substantially larger than any other field, withal­ gebra and number theory next with 144.

fEBRUARY 2005 NOTICES OF THE AMS 245 2004 Annual Survey of the Mathematical Sciences

Group I (Public) Faculty Salaries Doctoral degree-granting departments of mathematics (25) 21 responses (84%) 2004-05 2003-04 70 Rank No. Reported Q, Median Q, Mean Mean l : Assistant Professor 116 60,730 63,060 65,960 63,129 60,483 65 .I ~ Associate Professor 158 64,120 69,730 76,250 70,671 67,619 s::: ru 60 I J Full Professor 749 87,060 100,910 123,420 105,529 102,5 19 ~ s::: 55 - ~ - ..s::: IJ w Assistant ... 50 - ·~ i >- 45 111 Associate - ~ ::I u 40 • Full ru 1- LL. 35 -;II iU 30 ~-~ ~ t ...0 1- ..... 25 ~ 0 ~ '\ ... 20 s::: '· C1l ~-~~ ...u 1 5 .- ·~ ~ - c..C1l ~ . 10 ~1 ~ r- - 1---

5 ~ ~- I ~ t-- l.· rc~. 1 - 1--- ~,~ .!---:;:;;::_ 11 [± 0 - I--"- .----= 1--- tl=t - 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 - 0 0 0 '¢ Ln <.0 ...... 00 a> 0 N m '¢ Ln <.0 ...... 00 a> a> I I I I I I 0 0 0 0 0 0 I I I I I I I I I I A m '¢ Ln <.0 ...... 00 0 0 0 0 0 0 0 0 0 0 a> 0 N m '¢ Ln <.0 ...... 00

2004-05 Academic-Year Salaries (in thousands of dollars)

Group I (Private) Faculty Salaries Doctoral degree-granting departments of mathematics (23) 17 responses (74%) 2004-05 2003-04 70 Rank No. Reported Q, Median Q, Mean Mean 65 Assistant Professor 68 56,430 61,070 67,180 60,176 60,027 ~ Associate Professor 83 68,980 75,920 82,600 76,528 73,357 s::: 60 ru Full Professor 317 98,320 113,900 133,140 116,379 11 5,455 ~ 55 s::: ..s:::... 50 ·~ L Assistant 45 >- ~ 111 Associate ::I 40 u ru i I '<~ LL. 35 ' • Full ·,---I. iU 30 -· - . ...0 ' 1- ..... 25 ·'-- ·- -- 0 i 20 1 ... ,--' s::: r""" C1l u 1 5 -- r--- 01 I-- ... ' C1l r ' i c.. 10 -- H . - I-- - ··d .___~ 1 !)'", 1 • 5 ,ttl I--[ - I-- - ~ 0 h ·- ·-=~ tc .---- LC .---- t:ltt=t • - 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 '¢ Ln <.0 ...... 00 a> 0 N m '¢ Ln <.0 ...... 00 a> a> I I I I I I 0 0 0 0 0 0 I I I I I I I I I I 'A m '¢ Ln <.0 ...... 00 0 0 0 0 0 0 0 0 0 0 a> 0 N m '¢ Ln <.0...... 00

2004-05 Academic-Year Salaries (in thousands of dollars)

246 NOTICES OF THE AMS VOLUME 52, NUMBER 2 2004 Annual Survey of the Mathematical Sciences

Group II Faculty Salaries Doctoral degree-granting departments of mathematics (56) 48 res nses (86%)

70 Rank Assistant Professor 240 52 ,7 50 56,860 61,170 56 ,862 54,870 65 ~ Associate Professor 401 59,470 64,070 69,860 65,385 62,256 1:ns 60 Full Professor 942 74,500 86,350 100,360 89,664 86,368 c.:: 1: 55 ..s::: t"' Assistant .... 50 '3: • Associate >. 45 ~ ::l 40 \j • Full ns LL. 35 iii .... 30 0 1- ...... 25 0 .... 20 1: Ql \j.... 1 5 Ql c.. 10 5 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 '¢ LJ"\ <.D I'- 00 O'l 0 N m '¢ LJ"\ <.D I'- 00 O'l O'l I I I I I I 0 0 0 0 0 0 I I I I I I I I I I A m '¢ LJ"\ <.D I'- 00 0 0 0 0 0 0 0 0 0 0 O'l 0 N m '¢ LJ"\ <.D I'- 00

2004-05 Academic-Year Salaries (in thousands of dollars)

Group Ill Faculty Salaries Doctoral degree-granting departments of mathematics (73) 62 res (85%)

70 Rank Assistant Professor 290 48,380 53,630 59,310 54,349 52,796 65 ~ Associate Professor 414 53 ,650 59,530 69,470 63,297 61,639 1:ns 60 Full Professor 639 67,980 76,940 90,600 79,756 80,221 c.:: 1: 55 ~ Assistant ..s:::.... so '3: • Associate >. 45 ~ ::l \j 40 • Full ns LL. 35 iii.... 0 30 1- ...... 25 ....0 c 20 Ql \j.... 1 5 Ql c.. 10 5 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 '¢ LJ"\ <.D I'- 00 O'l 0 N m '¢ LJ"\ <.D I'- 00 O'l O'l I I I I I I 0 0 0 0 0 0 I I I I I I I I I I A m '¢ LJ"\ <.D I'- 00 0 0 0 0 0 0 0 0 0 0 O'l 0 N m '¢ LJ"\ <.D I'- 00 2004-05 Academic-Year Salaries (in thousands of dollars) fEBRUARY 2005 NOTICES OF THE AMS 247 2004 Annual Survey of the Mathematical Sciences

Group IV (Statistics) Faculty Salaries Doctoral degree-granting departments of statistics (56) 39 responses (68%) 2004--05 2003-04 Rank No. Reported Q, Median Q, Mean Mean Assistant Professor 138 60,900 65,100 68,480 64,975 65,656 ~ c Associate Professor 139 63,810 71 ,200 79,760 73 ,275 72,557 tU 70 Full Professor 315 87,310 103,070 122,420 107,297 105,164 D::: c 65 .s:::...., 60 H '3: 55 I ! - I l Assistant .::::>- 50 - :I J I.J 45 I 1111 Associate - tU u... 40 I 1 - iii • Full ...., 35 j.l - 0 ~ 30 I .... I ~ ....,0 25 - c I Cl) 20 ...I.J _I ~ - ~ ~ Cl) 1 5 c.. 10 - 1--- 5 ;-l;ffi - 1--- 'l-t- ... ._ bi 0 1 ~ 1--- 3=-=::. - • 0 0 0 0 0 0 0 0 0 0 0 0 0 -- 0 0 0 0 "

2004-05 Academic-Year Salaries (in thousands of dollars)

Group IV ( Biostatistics) Faculty Salaries Doctoral degree-granting departments of biostatistics and biometrics (31) 20 responses (65%) 2004-05 2003-04 70 Rank No. Reported Q l Median Q, Mean Mean Assistant Professor 88 61 ,950 66,710 69,850 66,129 64,048 65 Associate Professor 62 72,330 77,500 86,750 81,209 79,598 ~ c 60 Full Professor 108 93,890 110,630 129,280 113,396 113,090 tU D::: 55 Ill c .s:::...., 50 I Assistant f- '3: 45 I. 1}. >- 1111 Associate f- .:::: ~ -- :I 40 II 1- I.J • Full tU u... 35 ! - iii ...., 30 I 0 ~ r- I• .... 25 ;."t- ....,0 20 I __!- ~ · -_ 1---- c b p Cl) ...I.J 1 5 I l l!,, Cl) c.. I r- · r; 10 pil _j r- ,...., - 1--- - 1--- Il l~---~ ~ ~" f ·. ·1 5 I-I:·. - 1--- - 1--- r ·~rn- , !1-i·',ii ~~- i:·l ' 0 ,__ ~ .--- ~ .--- r--- =I • eo- • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 "

248 NOTICES OF THE AMS VOLUME 52, NUMBER 2 2004 Annual Survey of the Mathematical Sciences

Group Va Faculty Salaries Doctoral degree-granting departments of applied mathematics (18) 8 re nses (44%) 70 Rank 65 Assistant Professor 24 4 6,670 52,500 63,000 54,418 56,005 ~ Associate Professor 29 46,250 58,130 67,750 59,123 65,699 s:: 60 tU Full Professor 61 71,570 90,830 11 5,930 97,784 100,720 c::: 55 s:: Assistant ..s::.... 50 • Associate '3: 45 >- !: • Full :::l 40 IJ tU Ll.. 35 ~.... 30 0 ....1- 25 0 .... 20 s:: Q) IJ... 15 Q) Q, 10 5 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 '

2004-05 Academic-Year Salaries (in thousands of dollars)

Group M Faculty Salaries Master's degree-granting departments of mathematics (192) 1 04 res ponses (54%) 2004-05 2003-04 Rank No. Reported Q, Median Q, Mean Mean 55 Assistant Professor 523 45,420 48,690 53,700 51,972 53,320 or 550 53,060 58,730 65,620 61,603 63,984 ~ Associate Profess s:: 50 Fu ll Professor 724 66,870 75,760 85,830 81,785 81,205 tU c::: s:: 45 ..s:: .... 40 '3: Assistant >- !: 35 r-- :::l • Associate IJ • tU 30 r-- Ll.. •Full ~.... 25 r-- 0 ! 1- ....._ .... 20 ·-· ~ ....0 s:: 1 5 - - ....._ - Q) ! IJ... ' Q) 10 - - - Q, 5 ·- 1- : .. - - ~ ~ ~~ ~ ' f~. ' n I r r I ~ 0 t r • • - 0 Lrl 0 Lrl 0 Lrl 0 Lrl 0 Lrl 0 Lrl 0 Lrl 0 Lrl 0 Lrl 0 Lrl 0 Lrl 0 0 m M '

FEBRUARY 2005 N OTICES OF THE AMS 249 2004 Annual Survey of the Mathematical Sciences

Group B Faculty Salaries Bachelor's degree-granting departments of mathematics (1 020) 3 50 responses (34%) 55 2004- 05 2003-04 Rank No . Reported Q1 Median _33_ Mean Mean 50 Assistant Professor 961 42,630 47,310 53,640 48,511 47,570 ~ c Associate Professor 898 49,540 55,990 64,050 57,542 56,161 I'd cc:: 45 Full Professor 1,010 61,190 70,640 83,580 73,745 71,917 c .s:::.... 40 "§: ~- Assistant 35 I-- .:::>- :I • Associate 1.1 30 1--- I'd Ll.. • Full ~.... 25 I-- 0 .....1- 20 ....0 c 1 5 Ql ...1.1 Ql 10 '----- l!i' c.. 5 f"ll _.1" • ~i' [ I r,. .~~ t;frtli l ~ i I 0 FC ~1 .. J • • - • 0 Ln 0 Ln 0 Ln 0 Ln 0 Ln 0 Ln 0 Ln 0 Ln 0 Ln 0 Ln 0 Ln 0 0 M M 0'> 0 0 N N M M Ln 0 Ln 0 Ln 0 Ln 0 Ln 0'> 0 0 N N M M

2004-05 Academic-Year Salaries (in thousands of dollars)

Previous Annual Survey Reports Other Data Sources The 2003 First, Second, and Third Annual Survey American Association of University Professors, The Annual Reports were published in the Notices of the AMS Report on the Economic Status of the Profession in the February, August, and September 2004 issues 2003-2004, Academe: Bull. AAUP (March/April2004), respectively. These reports and earlier reports, as Washington, DC. well as a wealth of other information from these Commission on Professionals in Science and Technology, surveys, are available on the AMS website at Professional Women and Minorities, 15th ed., CPST, www.ams.org/employment/surveyreports.html. Washington, DC, 2004. __, Salaries of Scientists, Engineers, and Technicians: A Acknowledgments Summary of Salary Surveys, 20th ed., CPST, Wash­ ington, DC, 2003. The Annual Survey attempts to provide an accurate appraisal and analysis of various aspects of the aca­ __, Employment of Recent Doctoral Graduates in S&E: demic mathematical sciences scene for the use and Results ofProfessional Society Surveys, CPST, Washing­ benefit of the community and for filling the infor­ ton, DC, 1998. mation needs of the professional organizations. _ _ , Employment Outcomes ofDoctorates in Scie nce and Every year, college and university departments Engineering: Report of a CPST Workshop, CPST, Wash­ in the United States are invited to respond. The ington, DC, 1998. Annual Survey relies heavily on the conscientious __, Supply and Demand Indicators for New Science and efforts of the dedicated staff members of these Engineering Doctorates: Results of a Pilot Study, CPST, departments for the quality of its information. On Washington, DC, 1997. behalf of the Annual Survey Data Committee Conference Board of the Mathematical Sciences, Statisti­ and the Annual Survey Staff, we thank the many cal Abstract of Undergraduate Programs in the Math­ secretarial and administrative staff members in ematical Sciences in the United States: Fall 2000 CBMS the mathematical sciences departments for their Survey, American Mathematical Society, Providence, cooperation and assistance in responding to the RI, 2002. survey questionnaires. __, Statistical Abstract of Undergraduate Programs in the Mathematical Sciences in the United States: Fal/1995 CBMS Survey, MAA Reports No.2, 1997.

250 NOTICES OF THE AMS VOLUME 52, NUMBER 2 2004 Annual· Survey of the Mathematical Sciences

National Opinion Research Center, Doctorate Recipients from United States Universities: Summary Report 2002, Definitions ofthe Groups Survey of Earned Doctorates, Chicago, IL, 2003. As has been the case for~ number of years, much of the data in these National Research Council, Strengthening the Linkages reports is presented for departments divided into groups according between the Sciences and the Mathematical Sciences, to several characteristics, the principal one being the highest degree National Academy Press, Washington, DC, 2000. offered in the mathematical sciences. Doctoral-granting departments _ _ , U.S. Research Institutes in the Mathematical Sciences: of mathematics are further subdivided according to their ranking of National Academy Press, Assessment and Perspectives, "scholarly quality of program faculty" as reported in the 1995 publi­ Washington, DC, 1999. cation Research-Doctorate Programs in the United States: Continuity _ _ , Research-Doctorate Programs in the United States: and Change.l These ran kings update those reported in a previous study Continuity and Change, National Academy Press, Wash­ published in 1982.2 Consequently, the departments which now com­ ington, DC, 1995. pose Groups I, II, and Ill differ significantly from those used prior to National Science Board, Science and Engineering Indica­ the 1 996 survey. tors-2004 (NSB 04-01), National Science Foundation, The subdivision of the Group I institutions into Group I Public and Arlington, VA, 2004. Group I Private was new for the 1996 survey. With the increase in num­ National Science Foundation, Characteristics ofDoctoral ber of the Group I departmen_ts from 39 to 48, the Annual Survey Data Scientists and Engineers in the United States: 2001 Committee judged that a further subdivision of public and private (NSF 03-310), Detailed Statistical Tables, Arlington, would provide more meaningful reporting of the data for these de­ VA, 2003. partments. __,Emigration of U.S.-Born S&E Doctorate Recipients Brief descriptions of the groupings are as follows: (NSF 04-327), Arlington, VA, June 2004. Group I is composed of 48 departments with scores in the 3.00-5.00 __, Graduate Students and Postdoctorates in Science and range. Group I Public and Group I Private are Group I departments Engineering: Fall 2001 (NSF 03-320), Arlington, VA, at public institutions and private institutions respectively. 2003. Group II is composed of 56 departments with scores in the 2.00-2.99 --• Gender Differences in the Careers of Academic Sci­ range. entist and Engineers (NSF 04-323), Arlington, VA, 2004. Group Ill contains the remaining U.S. departments reporting a doc­ - - · Plans for Postdoctoral Research Appointments toral program, including a number of departments not included Among Recent U.S. Doctorate Recipients (NSF 04-308), in the 1995 ranking of program faculty. Arlington, VA, 2004. Group IV contains U.S. departments (or programs) of statistics, bio­ __ ,Science and Engineering Degrees: 1966-2000 (NSF statistics, and biometrics reporting a doctoral program. 02-327), Detailed Statistical Tables, Arlington, VA, 2002. Group V contains U.S. departments (or programs) in applied mathe­ __, Science and Engineering Degrees, by Race/Ethnic­ matics/applied science, operations research, and management ity ofRecipient: 1992-2001 (NSF 04-318), Detailed Sta­ science which report a doctoral program. tistical Tables, Arlington, VA, 2004. Group Va is applied mathematics/applied science; Group Vb, which __ ,Science and Engineering Doctorate Awards: 2002 was no longer surveyed as of 1998-99, was operations research (NSF 04-303), Detailed Statistical Tables, Arlington, and management science. VA, 2003. Group M contains U.S. departments granting a master's degree as __, Women, Minorities, and Persons with Disabilities in the highest graduate degree. Science and Engineering: 2004 (NSF 004-317), Arling­ Group B contains U.S. oepartments granting a baccalaureate degree ton, VA, 2004. only. --· Statistical Profiles of Foreign Doctoral Recipients in Listings of the actual departments which campo se these groups are Science and Engineering: Plans to Stay in the United available on the AMS website at www. ams. erg/employment/. States (NSF 99-304), Arlington, VA, 1998. lResearch-Doctorate Programs in the United States: Continuity and __, Who Is Unemployed? Factors Affecting Unemploy­ Change, edited by Marvin L. Goldberger, Brendan A. Maher, and Pamela ment among Individuals with Degrees in Science and Ebert Flattau, National Academy Press, Washington, DC, 1995. Engineering, Higher Education Surveys Report (NSF 97-336), Arlington, VA, 1997. 2 These findings were published in An Assessment of Research­ Doctorate Programs in the United States: Mathematical and Physical Sciences, edited by Lyle V. ]ones, Gardner Lindzey, and Porter E. Coggeshall, National Academy Press, Washington, DC, 1982. The information on mathematics, statistics, and computer science was presented in digest form in the Apri/1983 issue of the Notices of the AMS, pages 257-67, and an analysis of the classifications was given in the June 1983 Notices of the AMS, pages 392-3.

FEBRUARY 2005 NOTICES OF THE AMS 251 Mathematics People

Green was recognized for his joint work with Terence Tao on arithmetic progressions of prime numbers. These Baiiuelos Awarded Blackwell­ are equally spaced sequences of primes such as 31, 3 7, 43 or 13, 43, 73, 103. Results in the area go back to the work TapiaPrize of Lagrange and Waring in the 1770s. A breakthrough came in 1939 when the Dutch mathematician Johannes van RODRIGO BANuELOS of Purdue University has been awarded der Corput showed that there are an infinite number of the 2004 Blackwell-Tapia Prize. His research focuses on three-term arithmetic progressions of primes. Green and probability and its connections to harmonic analysis, par­ Tao showed that for any n there are infinitely many n-term tial differential equations, spectral theory, and geometry. progressions of primes. Their proof, which relies on results The prize, which honors David Blackwell and Richard A. Tapia, is presented every two years to a mathematical of Szemeredi (1975) and of Goldston and Yildirim (2003), scientist who has contributed significantly to his or her uses ideas from combinatorics, ergodic theory, and the field of expertise and who has served as a role model for theory of pseudorandom numbers. The Green-Tao result mathematical scientists and students from underrepre­ is a major advance in our understanding of the primes. sented minority groups or has contributed in other Lauman and Ng6 were recognized for their proof of the significant ways to addressing the problem of the under­ fundamental lemma for unitary groups. The lemma is a representation of minorities in mathematics. The prize conjectured identity between orbital integrals for two amount, contributed this year by Cornell University, is $3,000. groups, for example, the unitary groups U(n) and The prize is cosponsored by the Mathematical Sciences Re­ U(p) x U(q), where p + q = n. Combined with the Arthur­ search Institute (MSRI), the Institute for Pure and Applied Selberg trace formula, it enables one to prove relations be­ Mathematics (IP AM), and Cornell University, with additional tween automorphic forms on different groups and is a key support from Arizona State University. step toward proving links between certain automorphic The organizing committee for the 2004 prize consisted forms and Galois representations. This is one of the aims of Carlos Castilla-Chavez (Arizona State University and Cor­ of the Langlands program, which seeks a far-reaching nell University), Mark Green (IP AM), William Massey (Prince­ unification of ideas in number theory and representation ton University), Robert Megginson (MSRI), and Richard theory. The result of Lauman and Ng6 uses the equivari­ Tapia (Rice University). ant cohomology approach introduced by Goresky, Kottwitz, and MacPherson, who proved the lemma in the -Mark Green, Institute for Pure and Applied split and equal valuation case. The proof for the unitary Mathematics case, which is significant for applications, requires many new ideas, including Lauman's deformation strategy and Ng6's purity result, which is based on a geometric inter­ Clay Research Award Winners pretation of the endoscopy theory of Langlands and Kottwitz in terms of the Hitchin fibration. Announced Green was named a Clay Research Fellow for a term of The Clay Mathematics Institute (CMI) has announced the two years. Lauman and Ng6 were named Clay Research recipients of the 2004 Clay Research Awards. The awards, Scholars for a period of one year. Each awardee received which recognize major research breakthroughs, were pre­ a bronze replica of the CMI icon by sculptor Helaman sented to BEN GREEN of Trinity College, Cambridge, and to Ferguson. Former recipients of the Clay Research Award GERARD LAUMON and BAO-CHAU NGO, both of the Universite are Andrew Wiles, Laurent Lafforgue, Alain Cannes, Paris-Sud and the Centre Nationale de Recherche Scien­ tifique (CNRS).

252 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Mathematics People

Stanislav Smirnov, Edward Witten, Oded Schramm, Marrin­ Universitii.t Munster under the direction of H. Behnke and dr a Agrawal, Richard Hamilton, and Terence Tao. also studied with Heinz Hopf at the Eidgenossische Tech­ Ben Green was born in 19 77 in Bristol, England. He nische Hochschule in Zurich. After serving as an assistant was educated at Trinity College, Cambridge, first as an at the Universitat Erlangen, Hirzebruch spent two years undergraduate and later as a research student of Fields (1952-54) at the Institute for Advanced Study in Prince­ Medalist Timothy Gowers. Since 2001 he has been a ton. After a year in Miinster he went to Princeton Univer­ Fellow of Trinity College, and in that time he has made sity for a year. In 19 56 he became a professor at the extended research visits to Princeton University, the Renyi Universitat Bonn. Hirzebruch is perhaps most famous for Institute in Budapest, the University of British Columbia, proving what is now known as the Hirzebruch-Riemann­ and the Pacific Inst;itute of Mathematics (PIMS), where he Roch Theorem and for developing the theory of charac­ was a postdoctoral fellow. In January 2005 he will take up teristic classes around it. Together with M. F. Atiyah and a chair in pure mathematics at the University of Bristol. A. Grothendieck, Hirzebruch was one of the main archi­ Gerard Lauman, born in 1952, received his These d'Etat tects of K-theory. In later years he made significant from the Universite de Paris-Sud, Orsay, in 1983 under the contributions to the theory of algebraic surfaces and direction of Luc Illusie. In 1987 Lauman was awarded 3-folds. Hirzebruch also had an important influence on the Silver Medal of CNRS. In 1992 he was awarded the the mathematical life in Germany by organizing the famous E. Dechelle Prize of the French Academy of Sciences. Arbeitstagung meetings since 1957 and by founding the Bao-ChauNg6, born in 1972 in Hanoi, Vietnam, received Max-Planck-Institut fiir Mathematik in Bonn in 1981. He his Ph.D. at the Universite de Paris-Sud, Orsay, in 1997 under the direction of Gerard Lauman. He has held visit­ served as director of that institute until1995. ing positions at the Max Planck Institute in Bonn, the -Allyn jackson Universities of Toronto, Sydney, and Chicago, and the Institut des Hautes Etudes Scientifiques. He has held a CNRS position at the Universite de Paris 13 since 1998, and Izumi Awarded Operator he assumed a professorship at the Universite de Paris-Sud in the fall of 2004. Algebra Prize -From a CMI announcement MAsAKI IzUMI of Kyoto University has been awarded the second Operator Algebra Prize for his outstanding con­ tributions to the theory of subfactors and the classifica­ Hirzebruch tion of automorphisms of C* -algebras, and thus to the advancement of operator algebra theory. The prize con­ Awarded Cantor sists of a cash award of about US$3,000, a prize certifi­ Medal cate, and a medal. The Operator Algebra Prize was established in 1999 by The Deutsche Mathematiker initiatives and contributions from some senior Japanese Vereinigung (DMV, German researchers in operator algebra theory and related fields Mathematical Society) has to encourage young researchers in these fields. The prize awarded the 2004 Georg Cantor is awarded every four years to a person under forty years Medal to FRIEDRICH HIRZEBRUCH. of age either of Japanese nationality or principally based The medal was presented dur­ in a Japanese institution for outstanding contributions to ing the DMV meeting in operator algebra theory and related areas. Heidelberg in September 2004. -Huzihiro Araki, Kyoto University Friedrich Hirzebruch The citation reads: "In recog­ nition of his remarkable achievements the Deutsche Mathematiker Vereinigung be­ stows the Georg Cantor Medal on Prof. Dr. Friedrich Hirze­ NRC -Ford Foundation Minority bruch. With this distinction the DMV honors a mathe­ matician of worldwide reputation whose path-breaking Fellowships Awarded works have substantially furthered mathematics. His ideas Scorr Izu of New Mexico State University has been awarded and discoveries-particularly in connection with Riemann an NRC-Ford Foundation Predoctoral Fellowship for 2004. Roch theorems, characteristic classes, and K-theory- have He is a student in the field of analytical mathematics. contributed to the instigation of one of the most impor­ The NRC-Ford Foundation Minority Fellowships pro­ tant developments in mathematics in the second half of grams are administered by the National Research Council the 20th century. He has contributed more than anyone for the purpose of increasing the presence of underrep­ else to the international integration of German mathe­ resented groups among faculty members in colleges and matics and to the absorption of east and west German universities. The recipients were selected on the basis of mathematicians into a common organization." Friedrich Hirzebruch was born in Hamm, Westphalia, merit and promise of future achievement. on October 17, 1927. He received his Ph.D. from the -From an NRC announcement

FEBRUARY 2005 NOTICES OF THE AMS 253 Mathematics People

or graduate students specializing in mathematics and/or Papikian Awarded Emil Artin computer science) the opportunity to spend a semester in Moscow studying mathematics. The fifteen-week program Junior Prize is similar to the Research Experiences for Undergraduates The 2005 Emil Artin Junior Prize in Mathematics has been programs that are held each summer across the United awarded to MiHRAN PAPIKIAN of Stanford University. Papikian States. Math in Moscow draws on the Russian tradition was chosen for his paper "On the degree of modular of teaching mathematics, which emphasizes creative parametrizations over function fields", which appeared approaches to problem solving and in-depth understand­ in the journal of Number Theory 97 (2002), 317-349. ing. All instruction is in English. Established in 2001, the Emil Artin Junior Prize in Math­ Each semester since 2001 the AMS has awarded several ematics carries a cash award of US$500 and is presented scholarships of approximately$ 5,000 each for U.S. students usually every year to a student or former student of an to attend the Math in Moscow program. The scholarships Armenian university who is under the age of thirty-five, are made possible through a grant from the National Sci­ for outstanding contributions to algebra, geometry, topol­ ence Foundation (NSF). Information about how to apply may ogy, and number theory-the fields in which Emil Artin be found in the August 2004 issue of the Notices, page 805, made major contributions. Previous awardees were Vahagn or on the webpage http: I /www. ams. org/careers-edu/ Mikaelian (2001), Artur Barkhudaryan (2002), and Gurgen mi moscow. html. For more information about Math in Asatryan (2004). Moscow, consult http: I /www. me erne. ru/mathi nmoscow The prize committee consisted of A. Basmajian, Y. Mov­ and the article "Bringing Eastern European Mathematical sisyan, and V. Pambuccian. Traditions to North American Students", Notices, Novem­ ber 2003, pages 1250-54. -Artin Prize Committee announcement -Allyn jackson DMV Awards Media and Journalism Prizes In October 2004 in Berlin, the Deutsche Mathematiker Vereinigung (DMV, German Mathematical Society) awarded two prizes recognizing outstanding contributions to rais­ ing public awareness of mathematics. The DMV Media Prize was awarded to CHRISTOPH POPPE, a writer and editor for the magazine Spektrum der Wissenschaft. The DMV Jour­ nalist Prize went to HUBERTUS BREUER for his article "Der mit den Falten rechnet" ("He who computes with the folds"), which appeared in the newspaper Die Zeit. The DMV Media Prize of 5,000 euros (approximately US$6,500 is presented every two years to recognize out­ standing activities to popularize mathematics within the general public. The first recipient of the prize was Gero von Randow (2002)

-Allyn jackson

Math in Moscow Scholarships Awarded The AMS has made awards to four undergraduate stu­ dents to attend the Math in Moscow program in spring 2005. The names of the students and their institutions are: CHRISTOPHER E. BIERMANN, Dartmouth College; BRENDAN MATTHEW CREUrz, California Polytechnic State University, San Luis Obispo; VICTOR KOSTYUK, Rochester Institute of Tech­ nology; JOEL LOUWSMA, University of Michigan; and ADRIENNE RAu, Barnard College/Columbia University. Math in Moscow is a program of the Independent Univer­ sity of Moscow that offers foreign students (undergraduate

254 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Mathematics Opportunities

will be published by the American Mathematical Society, NSF Integrative Graduate by the Society for Industrial and Applied Mathematics, or jointly by the American Statistical Association and the Education and Research Institute of Mathematical Statistics. Training Support is provided for about thirty participants at each conference, and the conference organizer invites The Integrative Graduate Education and Research Training both established researchers and interested newcomers, (IGERT) program was initiated by the National Science including postdoctoral fellows and graduate students, to Foundation (NSF) to meet the challenges of educating Ph.D. attend. scientists and engineers with the interdisciplinary back­ The proposal due date is April 8, 2005. For further grounds and the technical, professional, and personal information on submitting a proposal, consult the CBMS skills needed for the career demands of the future. The website, http: I lwww. cbms . o rg, or contact: Conference program is intended to catalyze a cultural change in grad­ Board of the Mathematical Sciences, 1529 Eighteenth Street, uate education for students, faculty, and universities by NW, Washington, DC 20036; telephone: 202-293-1170; establishing innovative models for graduate education in fax: 202-293-3412; email: ko l be@math. georgetown. edu a fertile environment for collaborative research that tran­ or rosi er@math. georgetown. edu. scends traditional disciplinary boundaries. It is also intended to facilitate greater diversity in student participation and -From a CBMS announcement to contribute to the development of a diverse, globally aware science and engineering workforce. Supported pro­ jects must be based on a multidisciplinary research theme National Academies Research and administered by a diverse group of investigators from U.S. Ph.D.-granting institutions with appropriate research Assodateship Programs and teaching interests and expertise. The preproposal deadline for the 2005 IGERT compe­ The Policy and Global Affairs Division of the National tition is February 4, 2005. Further information may be Academies is sponsoring the 2005 Postdoctoral and Senior found at the website http: I lwww. nsf. gov lpubsl 2005l Research Associateship Programs. The programs are meant nsf05517l nsf05517.htm. to provide opportunities for Ph.D., Sc.D., or M.D. scientists and engineers of unusual promise and ability to perform - From an NSF announcement research at more than 100 research laboratories through­ out the United States and overseas. Full-time associateships will be awarded for research in the fields of mathematics, chemistry, earth and atmos­ Call for Proposals for 2006 NSF­ pheric sciences, engineering, applied scien ces, life sciences, space sciences, and physics. Most of the labora­ CBMS Regional Conferences tories are open to both U.S. and non-U.S. nationals and to To stimulate interest and activity in mathematical re­ both recent doctoral recipients and senior investigators. search, the National Science Foundation (NSF) intends to Awards are made for one or two years, renewable for a support up to seven NSF-CBMS Regional Research Con­ maximum of three years. Annual stipends for recent Ph.D. ferences in 2006. A panel chosen by the Conference Board recipients range from $30,000 to $50,000, depending on of the Mathematical Sciences will make the selections from the sponsoring laboratory; the awards for senior recipients among the submitted proposals. will be higher. Support is also provided for allowable Each five-day conference features a distinguished lec­ relocation expenses and for limited professional travel turer who delivers ten lectures on a topic of important during the period of the award. current research in one sharply focused area of the math­ Awards will be made four times during the year, in ematical sciences. The lecturer subsequently prepares February, May, August, and November. The deadline for an expository monograph based on these lectures, which application materials to be postmarked or for electronic is normally published as a part of a regional conference submissions for the February 2005 review is series. Depending on the conference topic, the monograph February 1, 2005.

F EBRUARY 2005 NOTICES OF THE AMS 255 Mathematics Opportunities

For further information and application materials, Designed for graduate students and mathematicians see the National Academies website at http: I lwww4. nas . within five years of receipt of the Ph.D., the program is edulpgal rap. nsfIWebDocumentsiHome+Page, or con­ organized around Ricci flow and the geometrization of tact Research Associateship Programs, Keck Center of the 3-manifolds, particularly the recent work of Grisha National Academies, 500 Fifth Street, NW, GR322A, Wash­ Perelman. Topics covered will include an introduction to ington, DC 20001; telephone 202-334-2760; fax 202-334- geometrization, Ricci flow (both geometric and analytic 2759; email: rap@nas. edu. aspects), minimal surfaces, and various fundamental results in topology and differential geometry. Courses will be - From an NRC announcement dedicated to Perelman's work on general Ricci flow, as well as some results and applications in 3 dimensions. There will be three weeks of foundational courses and one National Academies Graduate week of minicourses focusing on more advanced topics. Lecturers include Jeff Cheeger, Bennett Chow, Tobias Fellowship Program Colding, Richard Hamilton, Bruce Kleiner, John Lott, John Morgan, Gang Tian, and others. The organizing committee The Christine Mirzayan Science and Technology Policy for the summer school consists of Gang Tian, John Lott, Graduate Fellowship Program of the National Academies John Morgan, Bennett Chow, Tobias Colding, Jim Carlson, is designed to engage graduate science, engineering, David Ellwood, and Hugo Rossi. medical, veterinary, business, and law students in the Funding is available to graduate students and post­ analysis and creation of science and technology policy doctoral fellows who are within five years of receipt of the and to familiarize them with the interactions of science, Ph.D. Standard support amounts will include funds for local technology, and government. As a result, students develop expenses and accommodations plus economy travel. essential skills different from those attained in academia The deadline for application is February 28, 2005. and make· the transition from graduate student to pro­ Application forms are available at http: I lwww. fessional. In 2005 programs will be held in the summer from cl aymath. orglsummerschoo l. For more information, see June 6 through August 12, and in the fall from September the website http: I lwww. cl aymath. o rgl summe rschoo l; 12 through November 18. telephone: 617-995-2600; email: summerschool@ Applications for the fellowships are invited from cl aymath. org. scholars from graduate through postdoctoral levels in any physical, biological, or social science field or any field of -From a CMI announcement engineering, medicine and health, or veterinary medicine, as well as business, law, education, and other graduate and professional programs. Postdoctoral scholars should have received their Ph.D.'s within the past five years. NSF-CBMS Regional The stipend for both 10-week programs is $4,800. The Conferences, 2005 fellowship stipend is intended to cover all living expenses for the period. In addition, a travel stipend of up to $500 With funding from the National Science Foundation (NSF), will be provided. the Conference Board of the Mathematical Sciences (CBMS) Deadlines for receipt of materials for the summer pro­ will hold three NSF-CBMS Regional Research Conferences gram is March 1, 2005, and for the fall program, June 1, during the spring and summer of 2005. 2005. More information and application forms and These conferences are intended to stimulate interest and instructions can be found on the website http: I lwww7. activity in mathematical research. Each five-day conference nationalacademies.orglpolicyfellows or by con­ features a distinguished lecturer who will deliver ten tacting National Academies Christine Mirzayan Science lectures on a topic of important current research in one and Technology Policy Graduate Fellowship Program, 500 sharply focused area of the mathematical sciences. The lec­ 5th Street, NW, Room 508, Washington, DC 20001; turer subsequently prepares an expository monograph telephone: 202-334-2455; fax: 202-334-1667. based on these lectures. Depending on the conference topic, the monograph will be published by the American -From a National Academies announcement Mathematical Society, by the Society for Industrial and Applied Mathematics, or jointly by the American Statistical Association and the Institute of Mathematical Statistics. Clay Mathematics Institute Support for about thirty participants will be provided 2005 Summer School for each conference. Established researchers and interested newcomers, including postdoctoral fellows and graduate The Clay Mathematics Institute (CMI) Summer School on students, are invited to attend. Ricci Flow, 3-Manifolds, and Geometry will be held at the Information about an individual conference may be Mathematical Sciences Research Institute (MSRI) in Berke­ obtained by contacting the conference organizer. The ley, California, June 20-July 15, 2005. three conferences to be held in 2005 are listed below.

256 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Mathematics Opportunities

New Perspectives for Boundary Value Problems and Workshops will enable many others to join in the effort. Their Asymptotics, Athanassios Fokas, lecturer. May 16-20, Every SAMSI program will have at least an opening and a University of Texas-Pan American. Organizers: Lokenath closing workshop, allowing for broad participation of Debnath, telephone 956-381-3459, email: debnath1@ individuals who cannot spend part of the year at SAMSI. utpa.edu; and Andras Balogh, telephone 956-381-2119, New researchers and members of underrepresented groups email: aba1 ogh@utpa. edu; website: http: I /www. math. are especially encouraged to participate in SAMSI work­ panam.edu/cbms2005.htm. shops and programs. Nonlinear Dispersive and Wave Equations, Terence Tao, SAMSI is very interested in obtaining proposals for fu­ lecturer. June 13-18, New Mexico State University. Orga­ ture research programs. Anyone with an idea for a future nizers: Joseph Lakey, telephone 505-646-2417, email: program should contact Jim Berger (berge r@samsi . info). j 1 akey@nmsu. edu; Tiziana Giorgi, telephone 505-646- Such ideas can also be communicated to the other mem­ 2323, email: tgi orgi @nmsu. edu; Cristina Pereyra, tele­ bers of the SAMSI directorate-Tom Banks (htbanks@eos. phone 505-277-4147, email: cri sp@math. unm. edu; Adam ncsu. edu), Alan Karr (karr@ni ss. org), and Young Truong Sikora, telephone 505-646-6269, email: asi kora@nmsu. (truong@bi os. unc. edu)-or to the SAMSI National Advi­ 505-646-2884, email: edu; and Robert Smits, telephone sory Committee, chaired by Peter Bickel and Margaret rsmi ts@nmsu. edu; website: http: I /www. math. nmsu. Wright. edu/-jlakey.cbms.html. Brief descriptions of the upcoming Fourth Year SAMSI Algebraic and Topological Combinatorics of Ordered programs follow. A program on Financial Mathematics, Sets, Anders Bjorner, lecturer. August 8- 12, San Francisco State University. Organizers: Joseph Gubeladze, telephone Statistics and Econometrics will run from September 2005 415-338-7722, email: soso@math. sfsu. edu; and Serkan through December 2005. This program, being led by Jean­ Hosten, telephone 415-338-7723, email: serkan@math. Pierre Fouque and Eric Ghysels, has the goal of bringing sfsu. edu; website http: I /www. sfsu. edu/gube l adze/ together the three disciplines of mathematics, statistics, cbms. htm1. and econometrics to focus on the major challenges in the three essential tasks: modeling, data analysis, and com­ - From a CBMS announcement putation in applications ranging from financial and energy derivatives to real options and defaultable securities. A program on National Defense and Homeland Secu­ SAMSI rity will run from September 2005 through May 2006. News from This program, being led by Lawrence Cox and Nell The Statistical and Applied Mathematical Sciences Institute Sedransk, will emphasize biointelligence, which intersects (SAMSI) has entered its third year of operation. SAMSI is the planned development of a CDC Biointelligence Center; a national NSF institute in the mathematical sciences whose real time inference, involving data streams; anomaly de­ mission is to forge a new synthesis of the statistical tection, with particular attention to high-dimensional data, sciences with the applied mathematical sciences and extremely rare events, and false positives; data integration, disciplinary science to confront the very hardest and most including integration of new forms of data such as images important data- and model-driven scientific challenges. or biometric identification; and dynamics of massive SAMSI is housed in the NISS building in Research Triangle databases, which is in part a fundamental issue of data Park, North Carolina. quality. After a very successful second year, with well over 700 The third program is Astrostatistics, to be conducted participants in SAMSI activities, the current year has an from January to June 2006. This program, being led by exciting slate of programs, on Computational Biology of Jogesh Babu, will address a range of statistical and math­ Infectious Diseases, Latent Variable Models in the Social ematical problems that arise in modern astronomical and Sciences, and Data Assimilation for Geophysical Systems. space sciences research, particularly due to the flood of Some opportunities for participation in these programs still data produced by space-based astronomical surveys at remain, especially in the latter program, which begins Jan­ many wave-bands. The program will especially emphasize uary 2005. See the SAMSI website (http: I / www. samsi . collaborations involving astronomers, mathematicians, info) for further information about these programs. Plans are well under way for SAMSI's 2006-07 pro­ and statisticians on novel problems facing upcoming grams (discussed below), and numerous opportunities astronomy missions. exist for participation by AMS members. Visiting young and In addition to these three major programs, SAMSI will senior researchers will be resident at SAMSI for periods of conduct planning or hot topics workshops, undergradu­ one month to one year. Several postdoctoral positions will ate and graduate outreach workshops, summer schools be funded for each SAMSI program. Special programs exist (as part of programs), and several interdisciplinary courses for graduate and upper-level undergraduate students to associated with ongoing programs. For more information initiate their involvement in cross-disciplinary and team about any of the SAMSI activities and the possibilities for research. New researchers will have special opportunities, participating in them, go to the SAMSI website, http: I I from both the SAMSI environment and from financial sup­ www. samsi . info. port. Senior researchers will have the chance for serious broadening of their interests and skill sets. - ]ames Berger, SAMSI director f EBRUARY 2005 NOTICES OF THE AMS 257 For Your Information

further suggestions from the mathematics and statistics Return of the CBMS Survey community about important issues that might become The Conference Board of the Mathematical Sciences (CBMS) part of the 2005 survey. Please send suggestions to David is an umbrella organization whose members are the Lutzer at Lutzer@math. wm. edu. presidents of sixteen professional associations in the Increased coordination with the Joint Data Committee mathematical and statistical sciences (these associations of the AMSIASAIIMSIMAA will allow considerable simpli­ are listed at http: I lwww. cbmsweb. o rgiMembe rsl fication of the questionnaires used in CBMS200 5 compared member _societies. htm). Every five years since 1965 the to previous years. Survey questionnaires will be mailed to CBMS has sponsored a national survey of undergraduate selected departments and programs in September 2005. mathematical and statistical sciences in the nation's uni­ There will be an intense follow-up effort in the fall of 2005 versities and colleges, both four-year and two-year. With in the hope of matching the roughly 65 percent response National Science Foundation support, there will be a new rate for the CBMS2000 project. Responses will be analyzed CBMS survey in 2005, called CBMS2005. in the spring and summer of 2006, and the final CBMS2005 The CBMS2005 project is supervised by a steering com­ report will be published by the AMS in the spring of 2007. mittee with members representing the AMATYC (Ameri­ can Mathematical Association of Two-Year Colleges), the -David Lutzer, College of William and Mary AMS, the ASA (American Statistical Association), and the MAA (Mathematical Association of America). CBMS2005 will use carefully designed random sampling to study cur­ Mathematics Awareness Month riculum, pedagogy, enrollment levels, number of bachelor's graduates, and faculty in the nation's undergraduate 2005 mathematical and statistical sciences departments and programs. In addition to continuing numerous long-term The AMS, the American Statistical Association (ASA), the studies, CBMS2005 will investigate certain "topics of Mathematical Association of America (MAA), and the opportunity", i.e., issues identified as being of timely Society for Industrial and Applied Mathematics (SIAM) interest to the national mathematical and statistical com­ announce that the theme for Mathematics Awareness munity. The final survey report will follow the general Month 2005 is Mathematics and the Cosmos. pattern of the CBMS2000 report (available for free down­ Mathematics is at the core of our attempts to understand load at the website http: I lwww. ams. o rgl cbmsl). the universe at every level, from the most theoretical to The CBMS2005 steering committee will finalize the list the most mundane. Modern cosmology is based on the of topics of opportunity early in 2005. Professional soci­ ideas of Riemann regarding the nature of space, along ety committees and officers have suggested several top­ with the notion of curved spaces of three and more di­ ics as deserving of further study, including: the growing mensions, adapted by Einstein to four-dimensional space dichotomy (detected in CBMS2000) between doctoral and time, and encapsulated in Einstein's fundamental insight bachelor's-only mathematics departments in the avail­ that gravity is geometry. From this and his justly famous ability of advanced undergraduate courses, growth and field equations, Einstein deduced on theoretical grounds quality control issues associated with dual-enrollment the bending of light as it passes a massive object, the courses, changes in calculus pedagogy, the mathematical precise amount of precession of Mercury's perihelion, the education of preservice K-8 teachers, the statistical back­ expansion of the universe, the existence of black holes, the ground of faculty who teach statistics in mathematics behavior of binary stars, and the existence of gravitational departments, the apparent shift away from tenure-stream waves, all of which led to experiments to confirm their appointments in mathematical sciences departments and validity. toward faculty appointments outside of the tenure stream, In cases not subject to direct experimentation, other and self-assessment methods used by mathematical sci­ mathematical methods are vital for carrying out simula­ ence departments. The steering committee welcomes tions of the motions within galaxies and star clusters, the

258 NOTICES OF THE AMS VOLUME 52, NUMBER 2 For Your Information Universitat Ulm collision of galaxies and black holes, and other large-scale gravitational interactions. At the level of the solar system, the mathematical methods initiated by Newton and continually elaborated over the ensuing centuries have The Faculty of Mathematics and Economics explained or predicted the action of the tides; the bulge at the University of Ulm invites applications for a of the Earth around the equator; the existence of previously unknown planets; the orbits and return times of comets; Professorship in Algebra/ and, just in the past decade, the existence of planets orbiting other stars. Discrete Mathematics (W3) In the realm of practical space exploration, mathemat­ ical techniques allow the planning of efficient trajectories to commence in October 2005. to reach the Moon, Mars, and the outer planets and the Candidates should have an excellent research means to communicate with those satellites, both for record in Algebra/Discrete Mathematics and be navigation and to encode, compress, and transmit images able to both contribute to the research activities across many hundreds of millions of miles of space, as in within the mathematics group and to strengthen the recent spectacular photographs from the Cassini the interdisciplinary research activities within the mission to Saturn. University. The applicants work should be well Mathematics departments may find on the Mathematics connected with an applied area of algorithmic Awareness Month website, http: I jwww. mathaware. org, a sample press release that can be adapted for public mathematics such as e.g. Information and Cod­ awareness activities. ing Theory, Cryptography or Complexity Theory. Each year in April the Joint Policy Board for Mathematics We expect that the applicant participates actively sponsors Mathematics Awareness Month to recognize the in our interidisciplinary graduate college Mathe­ importance of mathematics through written materials and matical Evolution, Information and Complexity. an accompanying poster that highlight mathematical Successful candidates will be teaching at all lev­ developments and applications in one particular area. els both for students of our faculty as well as The Mathematics Awareness Month 2005 advisory com­ other faculties of the University of Ulm . mittee members are: Robert Osserman (chair), Mathematical Sciences Research Institute; Douglas N. Arnold, Institute Applicants are expected to have a doctorate in for Mathematics and Its Applications; Jonathan Borwein, mathematics and a Habilitation or must other­ Dalhousie University; Tony Chan, University of California, wise present evidence of excellence in research Los Angeles; Charles Elachi, Jet Propulsion Laboratory, and teaching. California Institute of Technology; and Sarah]. Greenwald, Appalachian State University. The position is an established (permanent) Pro­ fessorship. However, in the case of a first ap­ -AMS announcement pointment the employment is initially temporary. Exceptions may be made for applications form abroad or from outside academia. No new appli­ TV Program Featuring cation process is required if it is decided to con­ tinue the employment permanently after the ini­ Mathematician tial appointment. A new television series called NUMB3RS will feature a The University of Ulm is committed to increase mathematician as a main character. According to the the percentage of women in research and teach­ webpage for the series (http: I /ki dk. cbs now. com/ ing. We therefore affirmatively encourage female pri meti me/numb3 rs/), the story revolves around an FBI scientists to apply. agent who recruits his "mathematical genius brother" to help solve a wide range of crimes in Los Angeles. "From Applications with the usual documents (including two very different perspectives, the brothers take on reprints of the three most important publications) the most confounding criminal cases," the webpage states. are due four weeks after publication of the ad­ "Inspired by actual events, the series will depict how vertisement to the Dean of the Faculty of Mathe­ the confluence of police work and mathematics provides matics an Economics, University of Ulm, unexpected revelations and answers to the most perplex­ D-89069 Ulm (Phone ++49-731-5023500, ing criminal questions." Telefax ++49-7 31-5 02 36 10). For further infor­ The premiere episode of NUMB3RSwill be broadcast on mation about the Faculty consult our homepage: CBS on Friday, January 21, 2005, at 10:00 p.m. EST. www.mathematik.uni-ulm.de

-Allyn jackson Equally qualified individuals with disabilities will be considered with priority.

FEBRUARY 2005 NOTICES OF THE AMS 259 Reference and Book List

The Reference section of the Notices fgalfellowships_grantsl February 1, 2005: Applications for is intended to provide the reader with selected. cfm or contact the AAUW February review for National Acade­ frequently sought information in Educational Foundation, 1111 Six­ mies Postdoctoral and Senior Re­ an easily accessible manner. New teenth St. N.W., Washington, DC search Associateship Programs. See information is printed as it becomes 20036; telephone 800-326-2289 "Mathematics Opportunities" in this available and is referenced after the issue. first printing. As soon as information (AAUW); fax 202-872-1425; email: i nfo@aauw. org. February 1, 2005: Applications for is updated or otherwise changed, it AWM Collaborative Research Grants January 13, 2005: Proposals for will be noted in this section. for Women. See http: I lwww. ONR Young Investigator Program. See Contacting the Notices awm-math.orgltravelgrants. http:llwww.onr.navy.mill html#collaborative; telephone The preferred method for contacting sci_techlindustriall363lyip. the Notices is electronic mail. The 301-405-7892; email: awm@math. asp. umd. edu. editor is the person to whom to send January 31, 2005: Applications for articles and letters for consideration. February 1, 2005: Applications for Articles include feature articles, postdoctoral fellowships at the Mittag­ AWM Travel Grants and AWM Men­ memorial articles, communications, Leffler Institute. See http: I lwww. ml . taring Travel Grants. See the AWM opinion pieces, and book reviews. The kva. selgrants. website, http:llwww.awm-math. editor is also the person to whom to send news of unusual interest about Where to Find It other people's mathematics research. A brief index to information that appears in this and previous issues of the The managing editor is the person Notices. to whom to send items for "Mathe­ matics People", "Mathematics Op­ AMS Bylaws-November 2003, p. 1283 portunities", "For Your Information", AMS E-mail Addresses-December 2004, p. 1365 "Reference and Book list", and "Math­ AMS Ethical Guidelines-june/July 2004, p. 675 ematics Calendar". Requests for AMS Officers 2002 and 2003 (Council, Executive Committee, · permissions, as well as all other Publications Committees, Board of Trustees)-May 2004, p. 566 inquiries, go to the managing editor. AMS Officers and Committee Members-October 2004, p. 1082 The electronic-mail addresses are Conference Board of the Mathematical Sciences-September 2004, noti ces@math. ou. edu in the case of p. 921 the editor and noti ces@ams. org in Information for Notices Authors-June/July 2004, p. 670 the case of the managing editor. The fax numbers are 405-325-7484 for Mathematics Research Institutes Contact Information-August 2004, p. 810 the editor and 401-331-3842 for the managing editor. Postal addresses National Science Board-january 2005, p. 76 may be found in the masthead. New journals for 2003-]une/]uly 2004, p. 672 NRC Board on Mathematical Sciences and Their Applications-March 2004, p. 350 NRC Mathematical Sciences Education Board-April 2004, p. 446 Upcoming Deadlines NSF Mathematical and Physical Sciences Advisory Committee-February January 10, 2005: Applications for 2005, p. 261 AAUW Selected Professions Fellow­ Program Officers for Federal Funding Agencies-October 2004, ships. See http: I lwww. aauw. orgl p. 1078 (DoD, DoE); December 2004, p. 1368 (NSF)

260 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Reference and Book List orgltrave l grants. html; telephone: nsf.govlpubsyslodslgetpub. Pacific Northwest National 301-405-7892; email: awm@math. cfm?nsf05504. Laboratory umd. edu. June 30, 2005: Nominations for February 4, 2005: Preproposals the 2005 Fermat Prize. See http: I I Peter F. Green (10105) for NSF IGERT competition. See "Math­ www.ups-tlse.friACTUALITESI Department of Chemical ematics Opportunities" in this issue. Sciences1Prix_Fermat_2004l Engineering February 15, 2005: Nominations Aregl ement. html. University of Texas, Austin for Clay Mathematics Institute Liftoff January 1, 2006: Applications for Program. See the website http: I I ICM 2006 Travel Grants. See Sol M. Gruner (10107) claymath.orglfaslliftoff_ http: I lwww. i cm2006. org or email: Department of Physics fell owsl. [email protected]. Cornell University February 28, 2005: Applications for Clay Mathematics Institute 2005 MPS Advisory Committee Frances Hellman (10106) Summer School. See "Mathematics Op­ Following are the names and affilia­ Department of Physics portunities" in this issue. tions of the members of the Advisory University of California, Berkeley March 1, 2005: Applications for Committee for Mathematical and summer program of the Christine Physical Sciences (MPS) of the National John Huchra (10106) Mirzayan Science and Technology Pol­ Science Foundation. The date of the Harvard-Smithsonian Center for icy Graduate Fellowship Program of expiration of each member's term is Astrophysics the National Academies. See "Mathe­ given after his or her name. The web­ Harvard University matics Opportunities" in this issue. site for the MPS directorate may be March 1, 2005: Applications for found at http: I lwww. nsf. gov I Raymond L. johnson (10106) Summer Program for Undergraduate homelmpsl. The postal address is Department of Mathematics Women in Mathematics at George Directorate for the Mathematical and University of Maryland, College Park Washington University. See http: I I Physical Sciences, National Science www.gwu.edul~mathlspwm.html. Foundation, 4201 Wilson Boulevard, ]on R. Kettenring (10106) March 1, 2005: Applications for Arlington, VA 22230. Charles A. Dana Research Institute Drew University EDGE Summer Program. See website Shenda Baker (10105) athttp:llwww.edgeforwomen.orgl Department of Chemistry Robert V. Kahn (10107) index. html. Harvey Mudd College March 1, 2005: Applications for Courant Institute New York University IMA New Directions visiting profes­ Lars Bildsten (10107) sorships at IMA. See http: I lwww. KITP Steven E. Koonin (10107) ima.umn.eduldocslmembership. University of California, Chief Scientist html. Santa Barbara April1, 2005: Applications for IMA BP, plc New Directions Short Course. See Janet AI. Conrad(10I 06) W Carl Lineberger (chair) (10106) http:llwww.ima.umn.edulnew­ Department of Physics Department of Chemistry and directionsi2005NDshort-coursel Columbia University NDcourse-app.php. Biochemistry Joint Institute for Laboratory April 8, 2005: Proposals for 2005 Susan Coppersmith (10107) Astrophysics NSF-CBMS Regional Conferences. See Department of Physics University of Colorado at Boulder "Mathematics Opportunities" in this University of Wisconsin issue. David R. A1orrison (10105) May 1, 2005: Applications for AWM Luis Echegoyen (10106) Department of Mathematics Travel Grants. See the AWM website, Department of Chemistry Duke University http:llwww.awm-math.orgl Clemson University travel grants. html; telephone: 301- Venkatesh Narayanamurti (10106) 405-7892; email: awm@math. umd. edu. Aiostafa El-Sayed (10106) Division of Engineering and Applied June 1, 2005: Applications for fall School of Chemistry and Sciences program of the Christine Mirzayan Biochemistry Harvard University Science and Technology Policy Grad­ Georgia Institute of Technology uate Fellowship Program of the Na­ Claudia Neuhauser (10105) tional Academies. See "Mathematics Lucy Fortson (10106) Professor and Director of Graduate Opportunities" in this issue. Department of Astronomy Studies june 2, 2005: Applications for NSF Adler Planetarium Ecology, Evolution and Behavior University-Industry Cooperative Re­ University of Minnesota search Programs in the Mathematical Jean H. Futrell (10105) Sciences (UICRP). See http: I lwww. Director

FEBRUARY 2005 NOTICES OF THE AMS 261 Reference and Book list

Eve Ostriker (10/07) Watkins. Princeton University Press, Wallace. W. W. Norton, October 2003. Department of Astronomy April 2004. ISBN 0-691-11503-6. ISBN 0-393-00338-8. (Reviewed University of Maryland Adam Spencer's Book of Numbers, June/July 2004.) by Adam Spencer. Four Walls Eight The Fabric of the Cosmos, by Brian David W Oxtoby (10/07) Windows, January 2004. ISBN 1-568- Greene. Knopf, February 2004. ISBN 0- Office of President 58289-7. 375-41288-3. Pomona College Alan Turing: Life and Legacy of a Fields Medalists' Lectures, edited Great Thinker, edited by Christof by Sir Michael Atiyah and Daniel Marcia]. Rieke (10/07) Teuscher. Springer, 2004. ISBN 3-540- Iagolnitzer. World Scientific, 2nd Steward Observatory 262 20020-7. edition, December 2003. ISBN 9-812- University of Arizona ''Alfred Tarski: Life and Logic, by 38259-3. Anita Burdman Feferman and * From Eudoxus to Einstein: A His­ Gary Sanders (10/05) Solomon Feferman. Cambridge Uni­ tory of Mathematical Astronomy, by Thirty Meter Telescope Project versity Press, October 2004. ISBN 0- C. M. Linton. Cambridge University California Institute of Technology 521-80240-7. Press, August 2004. ISBN 0-521- Alpha and Omega: The Search for 82750-7. Elizabeth H. Simmons (10/07) the Beginning and End of the Universe, From Newton to Hawking: A History Department of Physics by Charles Seife. Viking, July 2003. of Cambridge University's Lucasian and Astronomy ISBN 0-670-03179-8. Professors of Mathematics, edited by Michigan State University Automated Reasoning and the Dis­ Kevin C. Knox and Richard Noakes. covery of Missing and Elegant Proofs, Cambridge University Press, Novem­ Book list by Larry Wos and Gail Pieper. Rinton ber 2003. ISBN 0-521-66310-5. The Book List highlights books that Press, December 2003. ISBN 1-58949- Gamma: Exploring Euler's Constant, 023-1. have mathematical themes and are by Julian Havil. Princeton University Beyond Coincidence, by Martin aimed at a broad audience potentially Press, May 2003. ISBN 0-691-09983-9. Plimmer and Brian King. Icon Books, including mathematicians, students, (Reviewed August 2004.) March 2004. ISBN 1-840-46534-4. and the general public. When a book Geometry: Our Cultural Heritage, The Changing Shape of Geometry: has been reviewed in the Notices, a ref­ by Audun Holme. Springer, April Celebrating a Century of Geometry erence is given to the review. Gener­ 2002. ISBN 3-540-41949-7. (Reviewed and Geometry Teaching, edited by ally the list will contain only books May 2004.) published within the last two years, Chris Pritchard. Cambridge Univer­ sity Press, January 2003. ISBN 0-521- G6del's Proof, by Ernest Nagel and though exceptions may be made in James R. Newman. New York Univer­ cases where current events (e.g., the 53162-4. Cogwheels of the Mind: The Story of sity Press, revised edition, February death of a prominent mathematician, 2002. ISBN 0-8147-5816-9. (Reviewed coverage of a certain piece of mathe­ Venn Diagrams, by A. W. F. Edwards. March 2004.) matics in the news) warrant drawing Johns Hopkins University Press, April The Golden Ratio: The Story ofPhi, readers' attention to older books. Sug­ 2004. ISBN 0-801-87434-3. the World's Most Astonishing Number, gestions for books to include on the list Constantin Caratheodory: Mathe­ may be sent to notices-book- matics and Politics in Turbulent Times, by Mario Livia. Broadway Books, 1 i st@ams. org. by M. Georgiadou. Springer, Septem­ October 2002. ISBN 0-767-90815-5. *Added to "Book List" since the ber 2004. ISBN 3-540-44258-8. A Handbook of Mathematical Dis­ list's last appearance. The Constants of Nature: From course, by Charles Wells. Infinity Alpha to Omega-The Numbers That Publishing Company, 2003. ISBN 1089 and All That. A journey into Encode the Deepest Secrets of the Uni­ 0-7414-1685-9. (Reviewed September Mathematics, by David Acheson. Ox­ verse, by John D. Barrow. Jonathan 2004.) ford University Press, July 2002. ISBN Cape, September 2002. Pantheon * The Heart ofMathematics: An In­ 0-19-851623-1. (Reviewed in this Books, January 2003. ISBN 0-375- vitation to Effective Thinking, by Ed­ issue.) 42221-8. (Reviewed November 2004.) ward B. Burger and Michael Starbird. * 13: The Story of the World's Most Count Down: Six Kids Vie for Glory Key College Publishing (Springer-Ver­ Popular Superstition, by Nathaniel at the World's Toughest Math Compe­ lag), April 2000. ISBN 0-555953- Lachenmeyer. Thunder's Mouth Press, tition, by Steve Olson. Houghton Mif­ 407-9. (Reviewed in this issue.) October 2004. ISBN 1-568-58306-0. flin, April2004. ISBN 0-618-25141-3. Karl Pearson: The Scientific Life in Abel's Proof: An Essay on the (Reviewed August 2004.) a Statistical Age, by Theodore M. Sources and Meaning ofMathematical The Curious Life of Robert Hooke, Porter. Princeton University Press, Unsolvability, by Peter Pesic. MIT the Man Who Measured London, by February 2004. ISBN 0-691-11445-5. Press, May 2003. ISBN 0-262-16216-4. Lisa Jardine. HarperCollins, February Kepler's Conjecture: How Some of (Reviewed March 2004.) 2004. ISBN 0-060-53897-X. the Greatest Minds in History Helped Across the Board: The Mathematics Everything and More: A Compact Solve One of the Oldest Math Prob­ of Chessboard Problems, by John]. History of Infinity, by David Foster lems in the World, by George G. Szpiro.

262 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Reference and Book List

Wiley, January 2003. ISBN 0-471- H0yrup. Birkhauser, December 2003. Mathematics, by Karl Sabbagh. Farrar 08601-0. (Reviewed January 2005.) ISBN 3-764-31634-9. Straus & Giroux, April 2003. ISBN 0- '' The Knot Book: An Elementary In­ Mathematics, Art, Technology, and 374-25007-3. troduction to the Mathematical Theory Cinema, edited by Michele Emmer and The Saga of Mathematics: A Brief of Knots, Colin C. Adams. AMS, Sep­ Mirella Manaresi. Springer, 2003. ISBN History, by Marty Lewinter and William tember 2004. ISBN 0-8218-3678-1. 3-540-00601-X. Widulski. Prentice Hall, January 2002. * The Liar Paradox and the Towers Mathematics in Nature: Modeling ISBN 0-130-34079-0. of Hanoi: The Ten Greatest Math Puz­ Patterns in the Natural World, by John Shooting the Sun, by Max Byrd. zles of All Time, by Marcel Danesi. Adam. Princeton University Press, No­ Bantam, December 2003. ISBN 0-553- Wiley, August 2004. ISBN 0-471- vember 2003. ISBN 0-691-11429-3. 80208-9. 64816-7. Meta Math! The Quest for Omega, Signs of the Inka Khipu: Binary Cod­ Masters of Theory: Cambridge and by Gregory ]. Chaitin. April 2004. ing in the Andean Knotted-String the Rise of Mathematical Physics, by Available at http: I jwww. cs. Records, by Gary Urton. University of Andrew Warwick. University of umaine.edu/-chaitin/omega.html. Texas Press, August 2003. ISBN 0-292- Chicago Press, July 2003. ISBN 0-226- More Mathematical Astronomy 78540-2. 87375-7. Morsels, by Jean Meeus. Willmann-Bell Strange Curves, Counting Rabbits, *Math Magic: How to Master Every­ Inc., 2002. ISBN 0-943396-743. and Other Mathematical Explorations, day Math Problems, by Scott Flansburg. The Music of the Primes: Searching by Keith Ball. Princeton University Perennial Currents, revised edition, to Solve the Greatest Mystery in Press, November 2003. ISBN 0-691- August 2004. ISBN 0-060-72635-0. Mathematics, by Marcus Du Sautoy. 113 21-1. (Reviewed in December Math through the Ages: A Gentle HarperCollins, April 2003. ISBN 0- 2004.) History for Teachers and Others, by 066-21070-4. Sync: The Emerging Science of WilliamP. Berlinghoff and Fernando Q. Newton's Apple: Isaac Newton and Spontaneous Order, by Steven Stro­ Gouvea. Oxton House, 2002. ISBN 1- the English Scientific Renaissance, by gatz. Hyperion, February 2003. ISBN 0-786-86844-9. (Reviewed March 881929-21-3. (Reviewed October 2004.) Peter Aughton. Weidenfeld & Nicolson, The Mathematical Century: The 30 October 2003. ISBN 0-297-84321-4. 2004.) Towards a Philosophy ofReal Math­ Greatest Problems of the Last 100 The Number rr, by Pierre Eymard ematics, by David Corfield. Oxford Years, by Piergiorgio Odifreddi, trans­ and Jean-Pierre Lafon. AMS, 2004. University Press, April 2003. ISBN 0- lated by Arturo Sangalli. Princeton ISBN 0-8218-3246-8. 521-81722-6. University Press, May 2004. ISBN 0- Number Theory from an Analytic '' The Universal Book of Mathe­ Point of View, by Badih Ghusayni. 691-09294-X. matics: From Abracadabra to Zeno's Mathematical journeys, by Peter D. Komati, December 2003. ISBN 9953- Paradoxes, by David Darling. Wiley, Schumer. Wiley-Interscience, Febru­ 0-0282-7. July 2004. ISBN 0-471-27047-4. ary 2004. ISBN 0-471-22066-3. Phase Change: The Computer Rev­ *You Can Do the Math: Overcome A Mathematician's Survival Guide: olution in Science and Mathematics, Your Math Phobia and Make Better Graduate School and Early Career De­ by Douglas S. Robertson. Oxford Financial Decisions, by Ron Lipsman. velopment, by Steven G. Krantz. AMS, University Press, March 2003. ISBN Praeger Publishers, November 2004. August 2003. ISBN 0-8218-3455-X. 0-195-15748-6. ISBN 0-275-98341-2. (Reviewed April 2004.) Portraits of the Earth: A Mathe­ Mathematicians as Enquirers: Learn­ matician Looks at Maps, by Timothy G. ing about Learning Mathematics, edited Feeman. AMS, September 2002. ISBN by Leone Burton. Kluwer, April 2004. 0-8218-3255-7. Hardbound, ISBN 1-4020-7853-6; pa­ Prime Obsession: Bernhard Rie­ perback, ISBN 1-4020-7859-5; eBook, mann and the Greatest Unsolved ISBN 1-4020-7908-7. Problem, by John Derbyshire. Joseph Mathematicians under the Nazis, Henry Press, March 2003. ISBN 0- by Sanford L. Segal. Princeton Uni­ 309-08549-7. versity Press, July 2003. ISBN 0-691- Probability Theory: The Logic of 00451-X. Science, by E. T. Jaynes, edited by G. Mathematics: A Very Short Intro­ Larry Bretthorst. Cambridge Univer­ duction, by Timothy Gowers. Oxford sity Press, April 2003. ISBN 0-521- University Press, October 2002. ISBN 59271-2. 0-192-85361-9. (Reviewed in this The Reader of Gentlemen's Mail: issue.) Herbert 0. Yardley and the Birth of Mathematics and Culture I, edited American Codebreaking, by David by Michele Emmer. Springer, January Kahn. Yale University Press, March 2004. ISBN 3-540-01770-4. 2004. ISBN 0-300-09846-4. Mathematics and War, edited by The Riemann Hypothesis: The Bernhelm Booss-Bavnbek and ]ens Greatest Unsolved Problem in fEBRUARY 2005 NoTICES OF THE AMS 263 Doctoral Degrees Conferred 2003-2004

ALABAMA Do, Younghae, Chaotic transient behavior Piatek-]imenez, Katrina, Undergraduate of dynamical systems under random mathematics students' understanding University of Alabama, perturbations. of mathematical statements and proofs. Birmingham (4) Ephrem, Menassie, Characterizing liminal Pierce, Virgil, The asymptotic expansion and type I graph C*-algebras and C*­ of the partition function of random BIOSTATISTICS algebra of the Z2 -tree. matrices. Li, Yufeng, Parameter estimation for a Hirman, joseph, The role of variance: an Rasmussen, Christopher, Jacobians of proposed joint distribution of multi­ extension of small area estimation. etale covers of the projective line minus variate Bernoulli trials. Kim, Bong-Sik, Alpha models for rotating three points. Zhang, Yuting, A pattern mixture model Navier-Stokes equations in geophysics Selden, jeffrey, The density of states in a for censored binary longitudinal data. with nonlinear dispersive regulariza­ quasi-gap. tion. Wootton, Aaron, Defining algebraic poly­ MATHEMATICS Larsem, Sean, Supporting the guided nomials for cyclic prime covers of the reinvention of the concepts of group Malaugh, ]ames M., Rotational sets of the Riemann sphere. and isomorphism: a developmental re­ circle under zd. search project. Yan, Aimin, An inverse goundwater Negoita, Cristina, Global kinetic imag­ ARKANSAS model. ing using dynamic positron emission tomography data. University of Arkansas (3) University of Alabama, Smith, Shelly, A discrete homotopy theory Tuscaloosa (4) for graphs, with application to order MATHEMATICAL SCIENCES complexes of lattices. Hughes, Kimberly, Variations on general­ INFORMATION SYSTEMS, STATISTICS, AND Yang, Daqing, Extension of the game col­ ized logit models: alternative links and MANAGEMENT SCIENCE oring number and some results on the stepwise selection. Flynn, Timothy, Sequencing mixed-model choosability of complete multipartite Reed, Michael, Symbolic blow-ups and assembly lines in a lean environment. graphs. generation in degree four. Ybarra, Lynn, Small area estimation using Wu, Hsing-Yen, Tight congruences on MATHEMATICS data from multiple surveys. semigroups. Bunnag, Dhiranuch, Stochastic algo­ rithms for global optimization. University of Arizona (11) Cheng, Kang-Ping, Three numerical APPLIED MATHEMATICS CALIFORNIA schemes for solving nonlinear partial Hoppin, John, Ranking estimation meth­ California Institute of differential equations. ods in medical imaging without the use Sukantamala, Nattakorn, Area operator of a gold standard. Technology (15) on Hardy spaces. Kuecken, Michael, On the formation of APPLIED MATHEMATICS fingerprints. ARIZONA Lane, Emily, Wave-current interactions in Camp, Charles David, Temporal and coastal waters and their application to spatial patterns of the interannual shore-connected bars. variability of stratospheric ozone and Arizona State dynamics. Lo, Arthur, Theoretical simulation of University (12) metabolic mechanisms for regulating Chaubell, Mario julian, Low-coherence interferometric imaging: solution of MATHEMATICS AND STATISTICS capillary perfusion in working skeletal muscle. the one-dimensional inverse scattering Boerner, Rochus, problem. Wavelets with integer Parra, Mario, Filter-bank transforms with dilation factors larger than two. exact inverses. Burke, John, Mathematical models of CONTROL AND DYNAMICAL SYSTEMS metabolic cascades and gene regulation. MATHEMATICS Dunbar, William, Distributed receding Chidambaram, Rama, Modeling and deci­ Hoffman, Thomas, Constructing basic horizon control of multiagent systems. sion making in a semiconductor supply algebras for the principal block of Leok, Melvin, Foundations of computa­ chain. sporadic simple groups. tional geometric mechanics.

The above list contains the names and thesis titles of recipients of contains the name of the recipient and the thesis title. The number doctoral degrees in the mathematical sciences (July 1, 2003, to June 30, in parentheses following the name of the university is the number of 2004) reported in the 2004 Annual Survey of the Mathematical Sciences degrees listed for that university. A supplementary list containing names by 221 departments in 152 universities in the United States. Each entry received since compilation of this list will appear in a summer 2005 issue of the Notices.

264 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Doctoral Degrees Conferred

Ross, Shane, Cylindrical manifolds and Harvey, Nathaniel, Finitary codes on Edens, Thaddeus, A new large total vari­ tube dynamics in the restricted three­ Bernoulli shifts. ation stability result for the quadratic body problem. Horowitz, jason, Linearizing countably nonlinear system associated with the West, Matthew, Variational integrators. infinite partial orders. compressible Euler equations by eigen­ value methods. MATHEMATICS ]ung, Kenley, Fractal entropies and di­ mensions for microstate spaces. Grishin, Denis, Fast and efficient methods Bartroff, jay, Asymptotically optimal for multi-dimensional scattered data multistage hypothesis tests. Kalman, Tamas, Contact homology and approximation. one parameter families of Legendrian Ishkhanov, Tigran, Legendrian knots: Colwell, jason, The conjecture of Birch knots. and Swinnerton-Dyer elliptic curves equivalence of normal rulings and with complex multiplication by a non­ Karaali, Gizem, r-matrices on Lie super­ augmentations of Chekanov-Eliashberg maximal order. algebras. algebra. Daftuar, Sumit, Eigenvalue inequalities in Latremoliere, Frederic, Finite dimensional Peirce, ]ames, Well-posedness of the quantum information processing. approximations of quantum tori for the three dimensional Lagrangian averaged Gupta, Vineet, Conformal laminations. quantum Gromov-Hausdorff distance. Navier-Stokes equations. Lin, Qiang, Bloch-Kato conjecture for the Miller, Benjamin, Full groups, classifica­ Wolowski, Lech, Noise induced dissipation adjoint of H' (X0 (N)) with integral Heeke tion, and equivalence relations. in discrete-time classical and quantum algebra. Myers, Robert, Global transverse disks dynamical systems. Martin, Kimball, Four-dimensional Galois and suspendibility criteria. Yoshida, Ruriko, Barvinok's rational func­ representations of solvable type and Nemyrovska, Nina, On atypical represen­ tions: algorithms and applications to automorphic forms. tations of classical Lie superalgebras of optimization, statistics, and algebra. Vasylkevych, Sergiy, Poisson structures defect one. STATISTICS for PDEs associated with diffeomor­ Proudfoot, Nicholas, Hyper-Kahler ana­ phism groups. logues of Kahler quotients. Leng, Xiaoyan, Functional linear discrim­ ination analysis. Vessenes, Rebecca, Generalized Foulkes' Purbhoo, Kevin, Vanishing and non­ conjecture and tableaux construction. vanishing criteria for branching Schu­ Senturk, Dam/a, Covariate adjusted re­ Zhan, Dapeng, Random Loewner chains bert calculus. gression and correlation. in Riemann surfaces. Yao, Fang, Functional data analysis for Sandman, Nirit, Tamari lattices and a longitudinal data. Claremont Graduate geometric problem in antitrust. Tang, Xiang, Quantization of noncom­ University of California, University (3) mutative Poisson manifolds. los Angeles (17) MATHEMATICS Viswanath, Sankaran, Stabilization of Bhan, Ashish, Topological structure of tensor products in Kac-Moody algebras. MATHEMATICS networks derived from micro array time­ Zambon, Marco, Submanifold averaging Balbas, jorge, Non-oscillatory central series data. in Riemannian, symplectic and contact schemes for the equations of ideal Eyadat, Mohammad, Comparative per­ geometry. magnetohydrodynarnics in one- and formance evaluation of practical digital Zhu, Chenchang, Integrating Lie alge­ two-space dimensions. watermarking embedded schemes. broids via stacks and applications to Cecil, Thomas, Numerical methods for Orrala, Carlos, Numerical and experimen­ Jacobi manifolds. partial differential equations involving tal investigations of two side-by-side discontinuities. turbulent jets in a cross flow. STATISTICS Chaudhary, Suneal, Acceleration of Monte University of California, Ge, Yongchao, Multiple testing in mi­ Carlo methods using low discrepancy croarrays. sequences. Berkeley (28) Choi, Yohann, Kechris, Katherina, Statistical methods Computation of ordinal­ invariant trajectory solutions to multi­ BIOSTATISTICS for discovering features in molecular sequences. person bargaining problems. Bolstad, Benjamin, Low-level analysis of Daileda, Ryan, Extremal class numbers high-density oligonucleotide array data: Nacu, Serban, On the simulation of of non-Abelian number fields. background, normalization and sum­ certain random systems. marization. Davey, Owen, On the existence of alge­ Popovic, Lea, Asymptotic genealogy of braic oriented equivariant cohomology Molinaro, Annette, Novel approaches to a branching process and a model of theories. prediction to survival in cancer re­ macroevolutions. search: focus on genomics. Forbes, Brian, Open string mirror maps Schafer, Chad, Constructing confidence from Picard-Fuchs equations on relative regions of optimal expected size: theory MATHEMATICS cohomology. and application to cosmic microwave Gutars, Baris/ava, The inverse boundary Alexandrova, Ivana, Structure of the inference. semi-classical amplitude for general value problem in anisotropic media. scattering. University of California, Kao, Chiu-Yen, Fast sweeping methods Dasgupta, Samit, Gross-Stark units, Stark­ for static Hamilton-Jacobi equation. Heegner points, and class fields of real Davis (12) Lee, Arthur, Symplectic integration of nonlinear Hamiltonian dynamics. quadratic fields. MATHEMATICS Datta, Ruchira S., Algebraic methods in Min, Cho-Hong, A computational frame­ game theory. Ahmed, Maya, Algebraic combinatorics work tracking a moving interface in Giaimo, Daniel, On the Castelnuovo­ of magic squares. arbitrary dimension and codimension. Mumford regularity of curves and re­ Ballinger, Brad, Length-preserving trans­ Moelich, Mark, Logic models in segmen­ duced schemes. formations in polygons. tation and tracking. Graf, Peter, Optimization of model re­ Beaver, Scott, Banach algebras of integral Nicoara, Remus, Some finiteness results duction for linear ordinary differential operators, off-diagonal decay, and ap­ for commuting squares of finite dimen­ equations. plications in wireless communications. sional von Neumann algebras.

FEBRUARY 2005 NOTICES OF THE AMS 265 Doctoral Degrees Conferred

Soderlund, Christina, Characterizing fixed COLORADO Brown, David, Variations on interval point sets. graphs. Tan, Chong Hui, Equivariant K-theories, Colorado School of Uiyyasathian, Chariya, Maximal-clique equivariant cycle theories and equivari­ Mines (I) partitions. ant motivic homotopy theory. Zhu, Wei, Illusory contours and shape MATHEMATICAL AND COMPUTER SCIENCES based segmentation. Yang, Yongjun, A new discontinuous CONNECTICUT finite element method based on a least­ STATISTICS squares stabilization for elliptic and University of Yuan, Shin-Sheg, Some contributions in convection-diffusion problems. Connecticut (8) computational biology. Colorado State MATHEMATICS University of California, University (4l Bulancea, Gabriela, Sequence algebras of continuous functions. Riverside

266 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Doctoral Degrees Conferred

DELAWARE Florida State University csJ GEORGIA University of Delaware C5l MATHEMATICS Emory University C7l ]ones, Deborah, Intersection numbers of MATHEMATICAL SCIENCES divisors in graph varieties. BIOSTATISTICS Chandler, David, The Smith normal forms Lengfield, Marc, Envelopes, duality, and Davis, Xiaohong, Estimating vaccine effi­ of design with classical parameters. multipliers for certain non-locally con­ cacy from household data. Dmytrenko, Vasyl, Classes of polynomial vex Hardy-Lorentz spaces. MATHEMATICS AND COMPUTER SCIENCE graphs. Montin, Benoit, A stock market agent­ based model using evolutionary game Glimm, Tilmann, Supersymplectic reduc­ Fiedler, Frank, Maximal arcs in P G(2, 2, m ). tion. Muniz, Wagner, A modified linear sam­ theory and quantum mechanical for­ malism. Palmer, Katrina, Regularization of quasi­ pling method valid for all frequencies. Newton methods: Applied to image Williford, jason, Constructions in finite Vogeler, Roger, On the geometry of Hurwitz surfaces. restoration. geometry with application to graphs. Perrone, Lisa, Kronecker products in STATISTICS image restoration. Schacht, Mathias, On the regularity DISTRICT OF Kitsanta, Panagiota, Assessing adverse birth outcomes via classification trees. method for hypergraphs. COLUMBIA Sissokho, Papa, Light spanners and sparse Liu, Dacheng, Mixed-effects state space pseudorandom graphs. models for longitudinal data analysis. American University C3l Whalen, Thor, Degree conditions and Pu, Wenji, Selecting mixed-effects models MATHEMATICS AND STATISTICS relations to distance, extendability, and based on a generalized information levels of connectivity in graphs. Dickens, ]ames, An analysis of the impact criterion. and focus of preparation efforts to Smith, Michael, A framework for using Georgia Institute of improve performance on the Stanford multi-modal sensors to estimate target nine mathematics test. locations and identities in a battlefield Technology C7l Dweik, Bashir, Mixtures of Erlang distri­ scene. MATHEMATICS butions and renewal processes based Curran, Sean, Independent trees in 4- on them. University of Central connected graphs. Hill, Vicki, Constantin Caratheodory: Florida (5l Day, Sarah, A rigorous numerical method 1873-1950. MATHEMATICS in infinite dimensions. Figueroa-Lopez, jose Enrique, Nonpara­ George Washington Boncek, John, Studies in tight frames and metric estimation of Levy processes University C4l polar derivatives. with a view towards mathematical fi­ Korotkova, Olga, A model for a partially nance. MATHEMATICS coherent Gaussian beam in atmospheric Kreslavskiy, Dmitry, Lorentz lattice gases Dabkowski, Mieczyslaw, Cubic skein mod­ turbulence with applications for Laser­ on graphs. ules and Burnside groups. com and Lidar systems. Ohoudjou, Kassa, Characterization of Muise, Robert, Quadratic filters for auto­ function spaces and boundedness of bi­ STATISTICS matic pattern recognition. linear operators through Gabor frames. Christophi, Costas, Distances in random VanDeCar, Ida (Sidra), Inequalities in­ Rasmussen, Bryan, Numerical methods tries via analytic probability: The oscil­ volving complex rational functions. for the continuation of invariant tori. latory distribution. Zamyatin, Alexander, Mathematics of Sheppardson, Laura, Disjoint paths in El-Baz, Abeer, Some contributions to cone-beam transform in computer to­ planar graphs. statistical prediction theory. mography. Fan, ]iaquan, Short-term cancer inci­ University of Georgia C9l University of Florida C1l dence prediction. MATHEMATICS MATHEMATICS Howard University C1l A wanou, Gerard, Energy methods in 3D Griffiths, William, On integer solutions to spline approximations of the Navier MATHEMATICS systems of linear equations. Stokes equations. Beck, Michael, Square dependence in Diatta, Bassirou, Quivers, representation theory, non-commutative symplectic University of Miami C2l random integers. Donnelly, Steve, Finding elements of geometry, stratification and singular MATHEMATICS symplectic quotients. given order in Tate-Shafarevich groups Canas, Carlos, Multiserver cyclic queue­ of elliptic curves. ing networks with discrete time: Exact Pine, Eric, Sums of integer cubes. FLORIDA results and approximations. Vologodsky, Vitali, The extended Torelli Kolacinski, joseph Franke, Mathematics and Prym maps. Florida Institute of anxiety and learned helplessness. STATISTICS Technology C2l University of South Lee, ]aechoul, Linear trends, periodicities, MATHEMATICAL SCIENCES Florida (2) and extremes. Dontha, Satyanarayana, Variational Lya­ Wang, Lihua, Parameter estimation for punov method for differential equa­ MATHEMATICS mixtures of generalized linear mixed­ tions. Abdallah, Ahmed, Global dynamics of effects model. Martinez-Garza, Cesar, Impulsive hybrid damped Boussinesq equations. Xiao, YuanHui, Shot noise processes. differential systems with invisible solu­ Al-Najjar, Hasan, Tridiagonal pairs in Zhou, ]in, Non-Gaussian bifurcating mod­ tions. representation theory. els.

FEBRUARY 2005 NOTICES OF THE AMS 267 Doctoral Degrees Conferred

HAWAII Devadoss, Divya E., Mathematical model­ Crisman, Karl-Dieter, Chow groups of ing of polymerization waves. zero-cycles relative to hyperplane ar­ University of Hawaii (1) Montgomery, Kimberley, Feedback con­ rangements. MATHEMATICS trol of traveling wave solutions to the Guay, Nicolas, Representation theory of complex Ginzburg Landau equation and rational Cherednik algebras. Wills, Luis, Finite group graded Lie alge­ a nonlinear analysis of the amplification Holmer, justin, Uniform estimates for braic extensions and trefoil symmetric properties of auditory hair cells. the Zakharov system and the initial­ relativity, standard model, Yang Mills boundary value problem for the and gravity theories. Moroz, Vadim, Rotating non-Boussinesq Rayleigh-Benard convection. Korteweg de Vries and nonlinear Schro­ Perry, Michael F., Mathematical analysis dinger equations. IDAHO of two monomer systems of frontal Johnson, Brian, Factoring Cartan matrices polymerization. of group algebras. Idaho State University (1l Ritter, Laura R., On initiation of polymer­ Lucarelli, Catherine, A converse to Mazur's MATHEMATICS ization waves in thermal free-radical inequality for split classical groups. frontal polymerization. Potter, Russell, Further results on the Lucarelli, Vincent, Affine pavings for Siler cones and related cone theory. Roxin, Alexander C., Five projects in affine Springer fibers for split elements pattern formation, fluid dynamics and inPGL(3). University of Idaho (1l computational neuroscience. Maher, joshua, The geometry of dilata­ Wahle, Christopher W., Gas-solid nonequi­ tion and distortion. MATHEMATICS librium in filtration combustion. Mehta, Mridul, Birational equivalence of Zhang, Danhong, Disjoint cycles in Higgs moduli. graphs and directed graphs. MATHEMATICS Rodriguez, Andres, Prequantization of Fisher, Todd, On the structure of hyper­ moduli of G-bundles. ILLINOIS bolic sets. Rogale Plazonic, Kristina, Limits of invari­ Perepelitsa, Mikhail, Global existence of ants of algebraic cycles in a geometric Illinois Institute of solutions with large, discontinuous ini­ degeneration. Technology nl tial data for the Navier-Stokes equations Shapiro, Ilya, ERST reduction of the chiral for compressible fluid flows. Heeke algebra. APPLIED MATHEMATICS Phelps, Kathleen, A study on the rela­ Sigurdsson, Johann, The homotopy the­ Miranda, jesus, Incorporating R-functions tionship between the cohomology of ory of ex-spaces. into the theory of positive definite func­ 2-groups and certain subalgebras of the Spallone, Steven, Arthur's trace formula tions to solve elliptic partial differential mod-2 Steenrod algebra. for S0(5) and individual discrete series equations. Pribble, Ethan, Algebraic stacks for stable matrix coefficients. homotopy theory and the algebraic Vandervelde, Samuel, The Mahler mea­ Illinois State University (7) chromatic convergence theorem. sure of parametrizable polynomials. MATHEMATICS Renze, John, Perverse sheaves on affine Yan, Chao-Ping, A new angle on the tilt Bower, Michelle (Wallace), Characteriza­ Grassmannians of type Al. illusion. tion of high school mathematics and Schemmerhom, Kristen, Unstable opera­ Yeap, Lay May, Reversible normal forms physics language genres. tions and the Bousfield-Kuhn functor. and nonlinear development of elliptical Foster, Halcyon, Already left behind: instability. What can be done for low achieving Southern Illinois STATISTICS high school mathematics students. University, Carbondale (5) Johnson, Yolanda, Come home, then: An Bouman, Peter, Statistical and computa­ exploration of the past and present MATHEMATICS tional methods for complex multicenter experiences of two 8th grade black Aimanassra, Mahmoud, Estimation of data analysis. females in one mathematics classroom. survival and cumulative hazard func­ Dolgoarshinnykh, Regina, Epidemic mod­ Nugent, Patricia, Using a webboard as an tions of restricted quality adjusted elling: SIRS models. asynchronistic community to facilitate lifetime. Kordzakhia, George, The problem of first year secondary mathematics teach­ Hjouj, Fawaz, Identification of reflected, coexistence in multi-type competition ers as they move from apprenticeship dilated, translated and rotated objects models. status to effective teacher status. from their Radon projections. Romero, Martin, On two topics with no Olson, ]o, Teachers' acceptance of new Ibrahim, Haslinda, A family of designs bridge: Bridge sampling with depen­ leadership roles and changes in class­ for triads and related factorizations. dent draws and bias of the multiple room practices. imputation variance estimator. Pennisi, Sarah-Jean, Making improving McCreight, Jeff, Generalized Fourier trans­ forms. Song, ]ongwoo, A sequential clustering practice part of teachers' practice in the algorithm with applications to gene Staples, George, Clifford algebras, combi­ context of teaching geometry. expression data. natorics, and stochastic processes. Yimer, Asmamaw, Metacognitive and cog­ Tan, Zhiqiang, Likelihood approach for nitive functioning of college students Monte Carlo integration. during mathematical problem solving. University of Chicago (26) Welty, Leah, Spatial statistics for model- Northwestern MATHEMATICS ing phytoplankton. University (14) Barnhill, Angela, Fixed point theorems for actions of Coxeter groups on non­ University of Illinois, ENGINEERING SCIENCE AND APPLIED positively curved singular spaces. Chicago (9) MATHEMATICS Belkin, Mikhail, Problems of learning on EPIDEMIOLOGY AND BIOSTATISTICS Cui, Changrong, Hydrodynamic and dif­ manifolds. ferential-diffusion effects on premixed Calta, Kariane, Veech surfaces and com­ Liu, Li, A mixed effects model for flame propagation. plete periodicity in genus two. longitudinal multivariate ordinal data.

268 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Doctoral Degrees Conferred

MATHEMATICS, STATISTICS AND Wei, Ying, Longitudinal growth charts University of Notre COMPUTER SCIENCE based on semiparametric quantile re­ Dame (9) gression. Budur, Nero, Multiplier ideals and Hodge MATHEMATICS theory. Xu, Xueli, Computerized adaptive testing and equating methods with nonpara­ Arana, Andrew, Arithmetical investiga­ Dominici, Diego, Asymptotic analysis of metric IRT models. a data handling system and its general­ tions: A study of models of arithmetic ization. and purity of methods. Chernysh, Vladislav, Egorin, Vladimir, Characteristic varieties On the homotopy INDIANA type of the space of positive scalar of algebraic curves. curvature metrics. Florek, Wojciech, Foliations: A probabilis­ Indiana University, tic potential theory approach. Dekker, Michael, A new proof of the Bloomington (4) bordism invariance of the index. Goncharov, Yevgeny, Mathematical the­ MATHEMATICS Carla, Elisa, Lifting properties from the ory of mortgage and modeling. general hyperplane section of a projec­ Klaff, Benjamin, Boundary slopes of Chung, Min, Local sine and cosine bases tive scheme. of Coifman and Meyer type and the knots in closed 3 manifolds with cyclic Gorsky, jennifer, On the Cauchy problem fundamental groups. construction of smooth wavelets. for a KdV type equation on the circle. Kim, Kyounghee, Integrals of exponential Nguyen, Nghiem, Higher order stability Han, Guangyue, Space time coding with theory of solitary waves. Brownian motion and derivative pricing multiple antenna systems. in the log-normal bond model. Ping, Zhihong, Measures of importance Harrington, Phillip, Compactness and with applications to inspection policies. Shiu, ji-Liang, The H 1 -closure of the Haar system and its dual space. subellipticity for the aNeumann prob­ lem on domains with minimal smooth­ University of Illinois, Tsyganov, Eugene, Global existence for ness. Urbana-Champaign (20) systems of mixed hyperbolic-parabolic type, with discontinuous initial data. Kiskowski, Maria, Discrete stochastic MATHEMATICS models of morphological pattern for­ Indiana University-Purdue mation in biology. Al-Fadhel, Tariq, Rates of convergence of Weber, Rebecca, A definable relation continued fractions and an approxima­ University, Indianapolis (1) between c. e. sets and ideals. tion theorem. MATHEMATICAL SCIENCES Avramidou, Parthena, Ergodic theory and harmonic analysis. Di, Xiaojun, Real zeros of random poly­ IOWA Bush, Michael, p-Class towers of imagi­ nomials: Scaling and universality. nary quadratic fields. Iowa State University (13) Purdue University (12) Denne, Elizabeth, Alternating quadrise­ MATHEMATICS cants of knots. MATHEMATICS Calhoun-Lopez, Marcus, Numerical solu­ Gage/man, jerry, Stability in geometric Di, Xiaojun, Real zeros of random poly­ tions of hyperbolic conservation laws: theories. nomials: Scaling and universality. Incorporating multi-resolution viscos­ Kim, Seog-jin, Problems in graph coloring Hosseini, Majid, Ratio inequalities for ity methods into the finite element and graph structure. heat kernels. framework. Kongsiriwong, Sarachai, Theta functions janakiraman, Prabhu, Weak-type esti­ Kwon, Hee-Dae, Analysis and approxima­ and related infinite series. mates for singular integral and maximal tion of terminal-state tracking optimal Li, Hui, Semi-free Hamiltonian circle operators. control problems and controllability problems constrained by linear and actions on 6-dimensional symplectic joo, Sookyung, The phase transition be­ manifolds. nonlinear parabolic partial differential tween chiral nematic and smectic C* equations. Li, Xiaosheng, Quasi conformal groups. liquid crystals. Tuncay, Candan, Oscillatory behavior Martin-Pizarro, Amador, Algebraic curves Merenkov, Sergiy, Determining biholo­ over supersimple fields. of higher order functional differential morphic type of a manifold using equations with distributed deviating Minasian, Vahagn, On THH and TAQ of combinatorial and algebraic structures. argument. commutative S-algebras. Yu, Xiaoxiang, Finiteness of orbits and Yang, Sung-Dae, Shooting methods for Musa, Mona, On dihedral codes and poles of intertwining operators. numerical solutions of control prob­ the double circulant conjecture for Zhang, Ning, Holomorphic line bundles lems constrained by linear and non­ extended quadratic residue codes. on the loop space of the Riemann linear hyperbolic partial differential Petracovici, Lia, Cremer fixed points and sphere. equations. critical points in complex dynamics. Rohwer, Thomas, Modules over valued STATISTICS STATISTICS fields with an endomorphism. , Annis, David H., A new statistical model De Cock, Dean, Kriging as an alternative Spiro({, Sandra, Limiting behavior on combining strength and binary choice to polynomial regression in response restriction of divisor classes to hyper­ with applications to paired comparison surface analysis. surfaces. problems. Drignei, Dorin, Statistical analysis of Yeap, Boon Pin, Contributions to trigono­ Cao, Dachuang, Quantitative trait locus multivariate computer output. metric sums and mock theta functions. analysis in polyploids. Fridley, Brooke, Data augmentation for Grevstad, Nels, Statistical analysis of the handling of censored spatial data. STATISTICS medical images. Ilk, Ozlem, Exploratory multivariate lon­ Georgescu, Constantin, Quantile estima­ Lin, Xiaodong, Finite mixture for cluster­ gitudinal data analysis and models for tors for finite populations. ing, dimension reduction and privacy multivariate longitudinal binary data. Lin, Nan, Three statistical problems with preserving data mining. Kim, ji-Yeon, Nonparametric regression imprecisely or incompletely observed Ma, Ping, Nonparametric mixed-effect estimation under complex sampling data. models. designs.

FEBRUARY 2005 NOTICES OF THE AMS 269 Doctoral Degrees Conferred

Lee, Eun-Kyung, Projection pursuit meth­ KANSAS LOUISIANA ods for exploratory supervised classifi­ cation. Kansas State University (5) Louisiana State Silva, Damiao Nobrega Da, Adjustments University, Baton for survey unit nonresponse under MATHEMATICS nonparametric response mechanisms. Rouge (5) Onofrei, Silvia, A characterization of two Wang, Jing, Interval mapping of QTL with classes of locally truncated diagram MATHEMATICS selective DNA pooling data. geometries. Zhang, Hongmei, Probability models for Blankenship, Robin, Book embeddings of graphs. design and analysis of genetic data. STATISTICS Harris, john, The Kauffman bracket skein Lee, Eun-joo, Statistical analysis software University of Iowa (18) module of the quaternionic manifold. for multiplicative interaction models. Holcomb, Michael, On the geometry and APPLIED MATHEMATICAL AND Shanga, Gilbert, Analysis of crossover topology of moduli spaces of multi­ COMPUTATIONAL SCIENCES designs when treatments have unequal polygonal linkages. variances. Jiang, Hong, Exploring algorithms for Kanno, jinko, Splitter theorems for 3- network capacity dimensioning and Su, Zhaohui, Inference on some lin­ and 4-regular graphs. traffic modeling. ear mixed-effect models and testing Wang, Hao-Hao, Equations of parametric for lack-of-fit for experiments without Kim, Changki, Modeling surrender/lapse surfaces with base points via syzygies. rates and valuing surrender options in replication. Korean interest indexed annuities. Taylor, Veronica, Use of three partial Louisiana Technical areas for establishing bioequivalence Leem, Koung-Hee, Solving linear systems University (4) for meshfree discretizations. and estimation of sample size for equivalence studies. MATHEMATICS AND STATISTICS PROGRAM BIOSTATISTICS University of Kansas (3) Hu, Jing, Mathematical and empirical Wang, Deli, Robust estimation of a two­ modeling of chemical reactions in a way sernilinear model with applications MATHEMATICS microreactor. to microdata normalization and analy­ Arana, Luis, The C* -algebra of Lie semidi­ Kaba, Ibrahima, A numerical method sis. to solve the two-step parabolic heat rect products of the form Rn X a R. Wang, Wenquan, Estimating and testing transfer equations in a microsphere treatment effects on two binary end­ Bach, Kelly, A cancellation problem for subjected to an ultrafast laser pulse. quantum spheres. points and association between end­ Shen, Lixin, A three-level finite difference points in clinical trials. Mir, Ellen, Relative topological properties scheme for solving a dual-phase-lagging of Hausdorff spaces. heat transport equation in spherical MATHEMATICS coordinates. Ahn, jeongho, Dynamic frictionless con­ Wichita State University (1) Zhen, Peng, Modeling of the inverse heat­ tact problems with linearly elastic bod­ conduction problem with application ies. MATHEMATICS AND STATISTICS to laser chemical vapor deposition and Ahn, Myung-sook, Weekly clean rings and Benchama, Noureddine, A simplified bioheat transfer. almost clean rings. Fornberg-like method for the conformal Clarke, Sharon, Star-operations induced mapping of multiply connected regions. University of Louisiana at by overrings. Lafayette (3) Hidayat, Dylmoon, Continuously trans­ lated framelets and wavelets. KENTUCKY MATHEMATICS Oshima, Chihiro, Characterization theo­ Guo, Huizhen, Inference on quantiles of rems in infinitary languages. University of Kentucky (7) some parametric models. Robeson, John, Irredundant generating Lu, Yang, Inferences on the common sets for modalities. MATHEMATICS mean of normal populations: The cor­ Svidersky, nona, Lifting schemes for Bendall, Gareth, Domination analysis be­ related and uncorrelated cases. wavelets. yond the traveling salesman problem. Sonnier, William joshua, Mathematical Ugalde, William, Conformal invariants Goodloe, Mary, Hadamard products of modeling of coupled nonlinear Schroe­ and the Wodzicki residue. convex harmonic mappings. dinger systems using conservation schemes. Waters, Gavin, W2·P estimates for para­ Ishizuka, Wataru, The weak compactness bolic equations. and regularity of weakly harmonic Yoon, jasang, Structure and spectral maps on Riemannian manifolds with theory of multivariable weighted shifts bounded measurable metrics. MARYLAND of hyponormal operators. Kovacs, Steve, Invertibility preserving Johns Hopkins Youn, Eun-Jung, Essential laminations maps of C*-algebras. and Dehn surgery on Montesinos knots. Menzel, Matthew, Generalized sewing University (9) constructions for polytopes. STATISTICS AND ACTUARIAL SCIENCE APPLIED MATHEMATICS AND STATISTICS Mueller, Stacey, Harmonic mappings and Christ, Aaron, An animal movement solutions of a differential equation Cope, Leslie, Some asymptotic properties model incorporating resource·selection related to the de la Vallee Poussin of smooth quantile ratio estimation. and home range. means. Yuan, Weishi, Asymptotic properties and Lin, Yu-jau, The Bayesian analysis of Riehemann, Robert, Subset takeaway on inferences for varying coefficient re­ threshold autoregressive models. graphs. gression with longitudinal variables.

270 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Doctoral Degrees Conferred

BIOSTATISTICS MEASUREMENT, STATISTICS AND Retina Rabbee, Nusrat, Power studies: I. Power and sample size for ordered cat­ Chen, Weimin, Robust quantitative trait EVALUATION egorical data. II. Power calculations for linkage analysis in extended human Koenig, judith, Comparison ofcharacter­ pedigrees. familial aggregation studies. III. Power istic curve methods for linking param­ calculations for selective genotyping in Eddings, Wesley, Topics in the philosophy eters estimated with the generalized QTL mapping in backcrosses. of statistics: Methods, data, and theory. graded unfolding model. Roberts, Kevin, Latent predictor models Gupte, Nikhil, Statistical models and with applications to asthma. methods for mother to infant HIV transmission studies. MASSACHUSETTS Scholtens, Denise, Studies in multidimen­ sional data: Estimation of the bivariate MATHEMATICS Boston University C?l survival curve, analysis of factorial designed microarray experiments, iden­ Dean, Brian, Some results on stable BIOSTATISTICS tification of protein complex member­ compact embedded minimal surfaces ship. in 3-manifolds. Govindarajulu, Usha, The selection of frailty models and the development Wilkins, Kenneth, Marginally-specified con­ Lee, Seok-Min, On certain cohomological of a frailty model for unexplained ditional models for longitudinal out­ invariants of quadratic number field. heterogeneity in the Framingham heart comes with possibly non-ignorable non­ Xu, Xiangjin, Eigenfmiction estimates on study. response. compact manifolds with boundary and Guo, Chao-Yu, Extensions of family­ Zhao, Yihua (Mary), General design Hormander multiplier theorem. based genetic tests of linkage and/or Bayesian generalized linear mixed mod­ Zhang, Sirong, Curvature estimates for association for a dichotomous trait. els with applications to spatial statis­ constant mean curvature surfaces in tics. three manifolds. MATHEMATICS AND STATISTICS ENGINEERING AND APPLIED SCIENCES University of Maryland, Andonova jaeger, Savina, Theoretical and experimental analysis of the gen­ Ashmore, Jacqueline, Free-surface and Baltimore C2l eralization ability of some statistical coating flows. Cettei, Kim, Code cache management in MATHEMATICS AND STATISTICS learning algorithms. Chazaro, Irmarie, A comparison of dynamic optimization systems. Webster, Samuel, Stability and conver­ family-based association test for quan­ Ellard, Daniel, Trace-based analyses and gence of a spectral Galerkin method for titative traits. optimizations for network storage ser­ the linear Boltzmann equation. Macabea, Joyce, Dynamics of Shepherd vers. Zhao, Qing, Correlation machines and moon ring systems. Fischer, Robert, Web applications with their applications. Vierling, Angela, Linear systems on ruled client-side storage. University of Maryland, surfaces and moduli of vector bundles Mansouri, Abdol, Sub-elliptic diffusions, over curves. geometry, and control. College Park CBJ Zompatori, Marina, Curves of high genus Rauenbusch, Timothy, Measuring infor­ MATHEMATICS in projective space. mation transmission for team decision making. Calcut, jack, Torelli actions and smooth Brandeis University csJ Schechter, Stuart, Computer security structures on 4-manifolds. strength and risk: A quantitative ap­ Eikenberg, Edward, Rational points on MATHEMATICS proach. some families of elliptic curves. Bone, Eric, A generalization of Pohlig­ Sullivan, David, Using probabilistic rea­ ]ones, Catherine, Pyramids of properness: Hellman simplification in elliptic curve soning to automatic software tuning. Proving the properness conjecture. cryptography. Valente, Andre, Symmetries and geomet­ Kolesar, joseph, Sigma delta modulation Bourgoin, Mario, Immersed curves and rical ansatze in dynamical systems: and correlation criteria for the con­ links in oriented thickenings. Hybrid dynamics, control with mov­ struction of finite frames arising in Kim, Hee-]ung, Modifying surfaces in ing averages, microflows, and network communication theory. 4-manifolds by twist spinning. robustness problem. Kollar, Richard, Existence and stability Varvak, Anna, Encoding properties of MATHEMATICS of vortex solutions of certain nonlinear lattice paths. Schrodinger equations. Coskun, Izzet, Degenerations of scrolls Xin, Gouce, The ring of Malcev-Neumann Ott, William, Infinite-dimensional dynam­ series and the residue theorem. and Del Pezzo surfaces and applications ical systems and projections. to enumerative geometry. Perlitz, Michael, Explaining the emergence Harvard University C28l Dumas, David, Complex projective struc­ of cooperation: An axiomic theory of tures, grafting, and Teichmuller theory. accumulation. BIOSTATISTICS Manolescu, Ciprian, A spectrum valued Ridley, Ahmad, Performance analysis of Arroyo, Cassandra, High dimensional TQFT from the Seiberg-Witten equa­ multiclass preemptive-resume priority data analysis with applications to dia­ tions. call center with time-varying arrivals. betes prevention and physical activity Marian, Alina, Intersection theory on the Snitz, Kobi, Theta correspondence of data. moduli space of stable bundles via automorphic characters. Ding, Beiying, Analysis of high dimen­ morphism spaces. Tang, Zhihui, Fast transforms based on sional data: Classification, measure­ Mirzakhani, Maryam, Simple geodesics structured matrices with applications ment error model and graph based on hyperbolic surfaces and volume of to the fast multiple method. association measures, with application the moduli space of curves. Wu, Chin-Tien, On implementation of to microarray data. Plamenevskaya, Olga, Contact structures an accurate and efficient solver for O'Brien, Liam, Methods for the analysis and Floer homology. convection-diffusion equations. longitudinal multiple source data and Ramsey, Nicholas, Geometric and p-adic Zheng, Shijun, Besov spaces for the multiple predictor data. modular forms of half-integral weight. Schrodinger operator with barrier po­ Park, Yuhyun, Semiparametric statistical Rauch, Daniel, Perturbations of the d-bar tential. inference in survival analysis. operator.

FEBRUARY 2005 NOTICES OF THE AMS 271 Doctoral Degrees Conferred

Rogers, Nicholas, Elliptic curves x 3 + y 3 = Northeastern Redett, David, Invariant vector sub spaces k with high rank. University (6) of LP with applications. Yang, Stephanie, Special linear series in Sa/divia, Luis, Topological transitivity of p2. MATHEMATICS bounded linear operators. Dubrovskiy, Stanislav, Differential invari­ Sword, Sarah, Intermediate domains be­ Massachusetts Institute ants of geometric structures. tween a local ring and its completion: Conditions for normality and factorial­ of Technology (24l Keng, Shengli, The geometry of Gz mani­ folds. ity. MATHEMATICS Kreiman, Victor, Monomial bases and STATISTICS AND PROBABILITY applications for Richardson and Schu­ Blanchette, Fran(:ois, Sedimentation in a Li, Fang, Testing for the equality of two stratified ambient. bert varieties in ordinary and affine Grassmannians. autoregressive and regression func­ Bozin, Vladimir, Geometry of Ricci flat tions. Kahler manifolds and some counterex­ Scott, Joshua, Grassmannians and cluster algebras. Stepanov, Alexey G., Optimal control of amples. dynamical systems with jump Markov Silantyev, Valentin, Clifford, Peter, Algebraic and combinato­ Kirchhoff and Ria­ perturbations. rial properties of minimal border strip bouchinsky models with semiperme­ tableaux. able obstacles. Michigan Technological Wang, Erxiao, Submanifold geometries Costeanu, Viorel, On the 2-typical deRham­ and integrable systems. University (2) Witt complex. MATHEMATICAL SCIENCES Early, Edward, Chain and antichain enu­ Tufts University (2l meration in posets, and b-ary partitions. Nicko/ov, Rados/av, Association tests for MATHEMATICS candidate genes based on Gibbs random Elizalde, Sergi, Statistics on pattern­ field models. avoiding permutations. Cowan, John David, A billiard model of a gas of rigid particles. Sarami, Chekad, Topics in coding theory Ganter, Nora, Orbifold genera, product and combinatorial structures. formulas and power operations. Pedroza, Andres, Cohomology and locali­ Hou, Zuoliang, Local complex singularity sation formulas. Oakland University (2) exponents for isolated singularities. University of MATHEMATICS AND STATISTICS Korn, Michael, Geometric and algebraic properties of polyomino tilings. Massachusetts, Ghosh, Pulak, A Bayesian approach to bioequivalence trials. Latour, Frederic, Representations of Cher­ Amherst (2) ednik algebras in positive charac­ Kikas, Lazaros, Interconnection networks teristic. MATHEMATICS AND STATISTICS and the k-disjoint paths problem. Lieblich, Max, Moduli of twisted sheaves Garibotti, Gilda, Estimation of the sta­ University of Michigan, and generalized Azumaya algebras. tionary distribution of Markov chains. Ann Arbor (31) Luo, Wei, On contact homology of the Otto, Peter, Study of equilibrium macro­ unit cotangent bundle of a Riemann states for two models in statistical BIOSTATISTICS mechanics. surface with genus greater than one. Carlson, Nichole, A bivariate model of Lurie, Jacob, Derived algebraic geometry. two pulsatile hormones: A Bayesian Mahdian, Mohammad, Facility location MICHIGAN approach. and analysis of algorithms through Feng, Shibao, Relative risk model analysis factor-revealing programs. Central Michigan of multivariate survival data. Osserman, Brian, Limit linear series in University (2) Hayasaka, Satoru, Validating and im­ positive characteristic and Frobenius­ proving cluster size influence in brain unstable vector bundles on curves. MATHEMATICS image analysis. Popescu, lone/, Morse inequalities, a prob­ Maynard, jacinth, A class of beta­ Hsu, Chiu-Hsieh, Survival analysis via abilistic approach. exponential distributions: Properties, nonparametric multiple imputation. estimation and applications. Radoicic, Rados, Extremal problems in Huang, Chiang-Ching, Markov model for combinatorial geometry and Ramsey Sadir, Dawn, Circular symmetry of spec­ defining genomic changes using gene theory. tra of composition operators. expression profiling. Isaman, Deanna, Use of indirect transi­ Ragharsson, Kari, Frobenius transfers Michigan State and p-local finite groups. tion estimates in discrete-state multiple­ University (10l stage models. Rassart, Etienne, Geometric approaches Li, Yisheng, Bayesian inference in gener­ to computing Kostka numbers and MATHEMATICS alized additive mixed models. Littlewood-Richardson coefficients. Cheng, Szu-En, Generating function proofs Liu, Fang, Bayesian methods for statisti­ Sankar, Arvind, Smoothed analysis of of identities and congruences. cal disclosure control in microdata. Gaussian elimination. Cheng, Wen-Chiao, Relations among con­ Patil, Sujata, Latent trajectory models for Sesum, Natasa, Limiting behaviour of ditional entropy, topological entropy longitudinal data: A Bayesian approach. Ricci flows. and pointwise preimage entropy. Wang, Yue, Statistical methods utiliz­ Usher, Michael, Relative Hilbert scheme Furaidan, Monther Rashed, Imprimitive ing biomarkers in clinical trials and methods in pseudoholomorphic geom­ distance-transitive graphs. screening studies. etry. Kwon, Seongchun, Real aspects of the Yu, ]ian, Prosper function analysis for Wang, Lijing, Bergman kernel and stabil­ moduli space of stable maps of genus organ allocation, a counting process ity of holomorphic vector bundles with zero curves. and Martingale approach. sections. Morgan, Charles, Decay of correlations Yu, Menggang, Joint longitudinal-survival­ Yee, Wai Ling, On the signature of the for piecewise smooth mappings with cure model with application in prostate Shapovalov form. unbounded distortion. cancer studies.

272 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Doctoral Degrees Conferred

MATHEMATICS Western Michigan Portal, Pierre, Harmonic analysis of Ba­ University (1) nach space valued functions in the Aubrey, Jason, Pseudo-dominating fami­ study of parabolic evolution equations. lies of functions. MATHEMATICS Elitzur, Haggai, Tight closure in Artinian Weinhold, Marcia, How secondary school STATISTICS modules. mathematics teachers construct an un­ Lee, Suhwon, Nonparametric Bayesian Hitchman, Theron ]., Rigidity theorems derstanding of "appropriate use" of density estimation and smoothing for large dynamical systems with hy­ graphing calculators in the context of splines. perbolic behavior. collegial inquiry. Xu, Ke (Bill), Efficient parameterization johnson, Amanda, Multiplier ideals of and estimation of spatia-temporal dy­ detrimental ideals. MINNESOTA namic models. jupiter, Daniel, Envelopes of holomorphy University of Missouri, and approximation theorems. University of Minnesota, Rolla (1l Klodginski, Elizabeth, Essential surfaces Twin Cities (10l in fibered 3-manifolds. BrOSTA TIS TICS MATHEMATICS AND STATISTICS Kravitz, Scott, The homology of a filtered Guo, Xu, On Kay and Little's approach Lathrom, Grant, Automorphism groups Boolean algebra. to logistic regression model and some of resolvable incidence structures. Lawes, Elliot, Motivic integration and the new results. regular Shalika germ. Short, Margaret, Topics in hierarchical Washington University (9) spatial models: Covariate-adjusted spa­ Papikian, Mihran, Optimal elliptic curves, MATHEMATICS discriminants, and the degree conjec­ tial and spatia-temporal CDF modelling. Apfel, Lynn, Localization properties and ture over function fields. Zhao, Yanli, Interim monitoring of ran­ domized clinical trials with multiple boundary behavior of the Bergman Slapar, Marko, Real surfaces in complex endpoints. kernel. surfaces. Draghici, Cristina, Polarization and re­ Storm, Peter, The barycenter method on MATHEMATICS arrangement inequalities for multiple singular spaces. Kim, Kyeong-Hun, On stochastic par­ integrals. Walker, Ronald, Concerning characteri­ tial differential equations with variable Liu, Ningping, Statistical properties of zations of boundaries of holomorphic coefficients in C1 domains. maximum likelihood estimators for i-chains within complex surfaces. Lee, ]ae-Hyouk, Geometries motivated complete and censored data from from normed algebras. mixed exponential and Weibull dis­ Wester/and, Craig, Stable splittings of configuration spaces of surfaces and Lee, Kijung, Lp theory of stochastic tributions. related mapping spaces. partial differential systems. Zhang, ]ing, Threefolds with vanishing Rademacher, ]ens, A mechanism for Hodge cohomology. Yang, Alexander, On combinatorics or periodic secondary wave bifurcation of degeneracy loci and H(G/ B) . pulses in reaction-diffusion systems. SYSTEMS SCIENCE AND MATHEMATICS Albright, Brian, An STATISTICS embedded optimiza­ STATISTICS tion-simulation approach to dynamic Choe, ]ee-Weon, Bayesian optimality cri­ Barnes, Katherine, Bayesian inference in pickup and delivery problems. teria for supersaturated designs. spatial clustering models of crime data. Celani, Fabio, Omega-limit sets of non­ Sung, Yun ]u, Likelihood inference for linear systems that are semiglobally Gopikrishnan, Ajita, Reliability inference mutation accumulation experiments. based on time-to-failure and degrada­ practically stabilizable. Zamba, Kakou (Gideon), Some issues in Lan, Chun Hua, Controllability of time tion data: Some models, methods and SPC: Change-point problems. efficiency comparisons. dependent quantum control systems. Kim, Dong-Yun, Sequential test and Liu, Ping, Appearance methods of solving change point problems with staggered MISSISSIPPI recognition and estimation problems in entry. robotics. Mississippi State Polpitiya, Ashoka, Mease, David, Contributions to engineer­ Geometry and control of human eye movements. ing statistics: X -testing for reliability University nl and optimal partitioning strategies. MATHEMATICS AND STATISTICS Shin, Yang-Yun, Inference and applica­ Liao, Wenyuan, Efficient higher order al­ MONTANA tions in hierarchical linear models with gorithms for solving reaction-diffusion missing data. equations. Montana State University (1) Wayne State University (4) University of Mississippi (1) MATHEMATICAL SCIENCES MATHEMATICS MATHEMATICS Griffiths, Roger, Return map characteri­ Crachiola, Anthony, On the AK invariant zation of singular solutions for a model Welch, Amy, Tychonoff's theorem and of bursting with two slow variables. of certain domains. the metric topology of path spaces. Naga, Ahmed, On recovery type a pos­ University of Montana (2) teriori error estimators in adaptive C0 Galerkin finite element methods. MISSOURI MATHEMATICAL SCIENCES Shvartsman, Ilya, Discrete approxima­ University of Missouri, Bedros, Varoujan, An exploratory study tions and minimax synthesis in dynamic Columbia (4) of students' understanding of indirect optimization. proof. Wang, Lianwen, Optimal control of hered­ MATHEMATICS Clouse, Chris, Greedoid invariant theory itary differential inclusions. Duda, ]akub, Aspects of delta-convexivity. and the greedoid Tutte polynomial.

FEBRUARY 2005 NOTICES OF THE AMS 273 Doctoral Degrees Conferred

NEBRASKA Gonzalez, Maria Del Mar, Singular sets of Kehowski, Walter, Hypernormal mani­ a class of fully nonlinear equations in folds. University of Nebraska, conformal geometry. Liang, Hwa Ching, Diagnostic methods Keevash, Peter, Lincoln (2) The role of approximate for accelerated failure time models. structure in extremal combinatorics. Malloy, Elizabeth, Diagnostics for the MATHEMATICS Ng, Ting Fai, Geometry of algebraic scale of functional predictors. Hinrichs, Paul, Consumer expenditure varieties. Martinez, Derek, Greenberg transforms estimation incorporating generalized Prasanna, Kartik, On a certain ratio of singular varieties and maps. variance functions in hierarchical Bayes of Petersson norms and level-lowering models. congruences. NEW YORK Lindblad, Steven, Inverse monoids pre­ Rodrigo, Jose Luis, On the evolution of sented by a single sparse relator. sharp fronts for the surface quasi­ geostrophic equation. City University of New Rajas-Leon, Antonio, General estimates York, Graduate Center (9) NEW HAMPSHIRE for exponential sums. MATHEMATICS Rutgers University, New Abbaspour, Hossein, On string topology Dartmouth College (2) of 3-manifold. Brunswick (12) MATHEMATICS Brock, Martin, Conjugate reducibility of MATHEMATICS families of block-diagonal matrices over Clark, Lisa, Classifying the type of group­ oid C*-algebras. Biezuner, Rodney Josue, Best constants, an extension field of a perfect field, and optimal Sobolev inequalities on Rie­ applications to matrix subalgebras and Dryden, Emily, Geometric and spectral mannian manifolds and applications. subgroups. properties of compact Riemann or­ ]ames, Taylor, Connections with Bohmian Khan, Bila/, The structure of automorphic bisurfaces. mechanics. conjugacy in the free group of rank two. Kruczek, Klay, Tic-tac-toe and tumble­ Kvaschuk, Alexei, One-variable equations NEW JERSEY weeds. in torsion-free hyperbolic groups. Li, Aobing, On some conformally invari­ Majewicz, Stephen, Nilpotent IQl [x)-power­ New Jersey Institute of ant fully nonlinear equations. ed groups and Z[x)-groups. Li, Xiaoyong, Pinned constrained Brown­ (3) Prado, Lucio, p-potential theory on Technology ian motion with application to bond graphs p-parabolicity and p-hyperboli­ MATHEMATICAL SCIENCES pricing. city. Mazza, Carlo, Schur functors and mo­ Serbin, Denis, lnfinite words and length Goul/et, Arnaud, Mixing enhancement by tives. dual speed rotating stirrer. functions. Radnell, David, Schiffer variation in Suzuki, Cristina, Rough isometries be­ Picarel/i, Michele, A Gibbs sampling ap­ Teichmuller space, determinant line tween non-compact Riemannian mani­ proach to maximum a posteriori time bundles and modular functors. delay and amplitude estimation. folds. Rosenthal, Maika, Extremal hypergraphs Wan, Aaron, The local theory of root Segin, Tetyana, Nonlinear long-wave in­ for certain forbidden traces. numbers. terfacial stability of two-layer gas-liquid Schutzer, Waldeck, On some combinato­ flow. rial aspects of representation theory. Clarkson University nl Taylor, Yuka, Quantum 6j symbols MATHEMATICS AND COMPUTER SCIENCE Princeton University (15) and a semiclassical invariant of three­ APPLIED AND COMPUTATIONAL manifolds. Morawska, Barbara, Goal-directed £- unification-completeness, decidability MATHEMATICS Young, Matthew, Random matrix theory and families of elliptic curves. and complexity. Brown, Eric, Neural oscillators and in­ Zhang, Lin, Vertex operator algebras and tegrators in the dynamics of decision Kazhdan-Lusztig's tensor category. Columbia University (13) tasks. BIOSTATISTICS Liu, Di, Topics in the analysis and computation of stochastic differential NEW MEXICO Xie, Hui, An index of sensitivity to nonig­ equations. New Mexico State norability: Extensions and applications. Rickard, Scott, Time-frequency and time­ Zawadzki, Rosita, A study of the perfor­ scale representations of doubly spread University (3) mance of the truncated Levin Robbins channels. MATHEMATICAL SCIENCES sequential elimination procedure for choosing the best of three binomial Rudin, Cynthia, Boosting, margin and Feng, Ding, Choquet weak convergence populations. dynamics. of capacity functionals and statistical Worden, Lee, Evolution, constraint, co­ inference with random sets. MATHEMATICS operation, and community structure in Mehta, Farag, Actions of the complex Cadman, Charles, Quantum cohomology simple models. additive group on affine spaces. of stacks and enumerative applications. Oh, Hyunju, The universal Vassiliev MATHEMATICS Casa/aina-Martin, Sebastian, Singularities invariant for the Lie superalgebra of the Prym theta divisor. osp(ll2). Araujo, Carolina, The variety of tangents Sadykov, Marat, Two results in the to rational curves. University of New arithmetic of Shimura curves. Berger, Eli, Topological methods in Sampsa, Samila, Models of decision mak­ matching theory. Mexico (5) ing in a social context. Coskunuzer, Baris, Minimal surfaces and MATHEMATICS AND STATISTICS Song, ]ian, The Szego kernel of an orb­ genuine lamination. Brock, Guy, Analysis of gene regula­ ifold circle bundle and its application. Eftekhary, Eaman, Holomorphic curves tory networks using fuzzy logic and Thillainatesan, Meera, A kernel for auto­ in topology and geometry. probabilistic models. morphic L-functions on GL(n,R).

274 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Doctoral Degrees Conferred

Weinkove, Benjamin, The ]-flow, the Courant Institute, New Bi, ]inbo, Support vector regression with Mabuchi energy, the Yang-Mills flow York University (22) applications in automated drug recov­ and multiplier ideal sheaves. ery. MATHEMATICAL SCIENCES Frank, Scott, Modeling nonlinear internal STATISTICS Atzberger, Paul, Stochastic modeling of wave effects on broadband shallow Feng, Xin, Functioning in computerized the kine sin motor protein. water acoustics. adaptive testing. Cherepinsky, Vera, On mathematical as­ Outing, Donald, Parabolic equation meth­ ods for range dependent layered elastic Huang, Zaiying, Bayesian computation pects of genomic analysis. media. for multilevel models: Some new meth­ de Aranjo, Thelma, Effects of upward ods with applications. propagating gravity waves or the mean Renzi, Daniel, Interior elastodynarnics inverse problems: Shear wave speed re­ Liu, Mangling, Semiparametric analysis state of the atmosphere. Demers, Mark, Markov extensions and covery in transient elastography using on longitudinal data in the presence of level set based inversion of arrival time. information censoring. natural conditionally invariant mea­ sures for dynamical systems with holes. Pasarica, Cristian, Topics in statistics and State University of New probability. Forger, Daniel, Deterministic and sto­ chastic mathematical modeling and York, Albany (3) computer simulation of the mammalian MATHEMATICS AND STATISTICS Cornell University (18) intracellular circadian clock. Featherstonhaugh, Stephen, Abelian Hopf Friz, Peter, Rough path theory and appli­ APPLIED MATHEMATICS Galois structures on Galois field exten­ cations to stochastic analysis. Casey, Richard, Periodic orbits in neural sions of prime power order. Goldfeld, Paulo, Balancing Neumann­ Kelley, Amy, Blaschke products, inner models: Sensitivity analysis and algo­ Neumann preconditions for the mixed rithms for parameter estimates. functions with finite spectrum and formulation of almost-incompressible operators similar to a contraction. Cetin, Umut, Default risk and liquidity linear elasticity. risk modeling. Olsen, Darlene, The spectrum of Zd- Herbert, Robert, Codimension two place­ actions in ergodic theory. Diaz, Aaron, Topics in hybrid systems. wise linear immersion of complex pro­ Mehta, Prashant, Nonbifurcating solu­ jection space. State University of New tions for parallel flows. Iwasawa, Kazuhiro, Fast relevant simula­ York, Binghamton (4) Patron, Maria-Cristina, Risk measures tion in finance. and optimal strategies for discrete Jiang, Huiqiang, Free boundary problems MATHEMATICAL SCIENCES hedging. with volume constraints: Zero set of Brown, Marlo, Detection of change-points Tomita, Tiberiu, Applications of sto­ Sobolev functions. in categorical data. chastic calculus and partial differential Judice, Pedro, Dynamic asset pricing via Donnelly, john, Properties of Richard equations in financial economics. conic duality. Thompson's group F related to amena­ Kim, Yongsam, The penalty immersed bility. BIOMETRICS boundary method and its application to Koban, Nicholas, Controlled topology in­ aerodynamics. Briggs, William Matthew, Assessing the variants of translation actions. value of yes/no forecasts. Lim, ]u Young, Pricing and hedging index Wang, Xueqin, The properties of the options. Theil-Sen estimator. Crainiceanu, Ciprian, Non parametric like­ Lou bet, Enrique, Genesis and extinction of lihood testing. solitons arising from individual flows State University of New El Sheneity, Sahar, Alternative methods of the Camassa-Holm hierarchy: The to the maximum likelihood in the rise of a novel Darboux-like transform. York, Buffalo (4) logistic discrimination model. Miller, Laura, A computational study of MATHEMATICS ]oo, Yongsung, Evaluation of model se­ flight in the smallest insects. Chae, Hyungjik, Some results concerning lection criteria in log spline models. Mogultay, Itir, Modeling the atmospheric polarized partition relations. Madsen, Lisa, Regression with spatially mixed layer. Chen, Qi, Integral TQFTs and periodic misaligned data. Perez, ]osi Antonio, Convergence of nu­ 3-manifolds. Zhang, Dabao, Bayesian inference for merical schemes in the total variation Chen, Shr-jing, On nonlinear stability of differential gene expression data. sense. spherically symmetric model ·of stellar Pignol, Ricardo, Energy transfer in sys­ dynamics under spherically symmetric MATHEMATICS tems with random forcing and nonlin­ perturbations. ear dissipation. Best, janet, The mathematics of ecological Lo, Min-lin, Bargmann transform and competition. Plaza-Villegas, Ramon, On the stability of windowed Fourier localization. shock profiles. Horak, Matthew, Mapping class sub­ Podesta, john, Some results concerning State University of New groups of outer automorphism groups. the MHD boundary conditions on the York, Stony Brook (15) Hsiao, Samuel, Quasisymmetric func­ base of the solar corona. tions and combinatorial enumerations Reznikoff, Maria, Rare events in finite APPLIED MATHEMATICS AND STATISTICS in spheres. and infinite dimensions. Baek, Songjoon, Variable selection for Marques, Fernando, Existence and com­ Slastikov, Valeriy, Topics in micromag­ heteroscedastic data. pactness theorems on conformal defor­ netics. George, Erwin, A numerical study of mation of metrics. Rayleigh-Taylor instability. Schuller, Rebecca, A theory of multitask Rensselaer Polytechnic Greenwald, Lorraine, Performance of learning for learning from disparate Institute (5) simulating annealing with generalized data sources. move generation. Walker, Shawn, Shift techniques and MATHEMATICAL SCIENCES Hsiang, Tien-Ruey, Geometric algorithms multicover inequalities on colored com­ Basescu, Vasile, An analytic center cutting for controlling and analyzing swarms plexes. plane method in conic programming. of robots and groups of aircraft.

FEBRUARY 2005 NOTICES OF THE AMS 275 Docto~IDegreesConfurred

]i, Fei, Linkage analysis of a disease Hale, Christopher, On calculations of STATISTICS related trait using a pleiotropic analysis. leaky modes in photonic crystals. Doi, Jimmy, Comparison of exact uncon­ Kang, Sun ]ung, Effects of errors in Karp, Robert, D-branes on Calabi-Yau ditional methods for the difference of specification of genotypes of single manifolds and II-stability in the derived two binomial proportions. nucleotide polymorphisms. category. Gauvin, jennifer, Stepwise hypothesis Oh, Cheongeun, Robust Bayesian variable Kesseler, Kevin, Analysis of feedback­ testing with applications in pharmaceu­ selection. mediated dynamics in two coupled tical responses. Panini, Radha, Option pricing with Merlin nephrons. transforms. Leon, Selene, Semiparametric efficient es­ Kozdron, Michael, Simple random walk timation of treatment effect in a pretest­ Sztainberg, Marcello, Algorithms for excursion measure in the plane. posttest study with missing data. swarm robotics. STATISTICS AND DECISION SCIENCES Mcintyre, Julie, Density deconvolution Wang, Xuena, Pattern detection and dis­ with replicate measurements and auxil­ crimination in MS based proteomic Molina, German, Bayesian stochastic iary data. analysis. computation, with application to model Weaver, Christina, Effects of errors in selection and inverse problems. Morris, Richard, Likelihood ratio tests specification of genotypes of single for association with multiple disease nucleotide polymorphism on the 2 x 3 North Carolina State susceptibility alleles genotyping errors or missing parental data. test of independence. University, Raleigh (31) Yoo, Yun ]oo, Power study of likelihood Mukhopadhyay, Pralay, Exact test and based linkage statistics. MATHEMATICS exact confidence intervals for the ratio of two binomial proportions. Al-Ashhab, Samer, The role of sh-Lie MATHEMATICS algebras in Lagrangian field theory. Scholl, Elizabeth, Molecular evolution and Behrstock, Jason, Asymptotic geometry horizontal gene transfer in meloido­ Attiogbe, Cyril, On characterizing nilpo­ gyne spp. of the mapping class group and Teich­ tent Lie algebras by their multipliers. muller space. Tang, Yongqiang, Dirichlet process mix­ Chen, Guo, Immersed interface method ture models for Markov processes. Crai£1, Gordon, Dehn filling and asymp­ for the biharmonic equation on irregu­ totically hyperbolic Einstein manifolds. lar domain and its applications. Thompson, Denis, Finding homologous genes with primers designed using Panafidin, Sergei, Nevanlinna theory and Daily, Marilyn, [-structures on spaces of Plucker identities. low dimension. evolutionary models. Dometrius, Christopher, Relationship be­ Wahed, Abdus, Efficient estimation of Syracuse University (4) the survival distribution and related t~~en symmetric and skew-symmetric MATHEMATICS b1lmear forms and involutions on quantities of treatment policies in two­ SL(N,K) and SO(N,K, b). stage randomization designs in clinical john, Thomas, Selection procedures for trails. lognormal populations. Drake, Kimberly, Analysis of numerical Wang, Dazhe, Frequentist and Bayesian Lee, Travis, An extension of the Thom­ methods for fault detection and model identification in linear systems with analysis of random coefficient autore­ Porteous formula to a certain class of gressive models. coherent sheaves. delays. Wu, Weiwei, Estimating value at risk Subramanian, Uma, Biting convergence Fowler, Kathleen, Nonsmooth nonlineari­ ties in applications from hydrology. and the expected shortfall for het­ of null-Lagrangians. eroscedastic financial log returns: A Zangor, Roxana, Numerical methods for Han, Chuan-Hsiang, Singular perturba­ two-stage method. smooth, detectable image perturba­ tions on non-smooth boundary prob­ tions. lems in finance. University of North Hicks, Gregory, Modeling and control of University of Rochester (4) a snake-like serial-link structure. Carolina, Chapel Hill (13) MATHEMATICS Kharebaua, Zviad, Singular cochains and BIOSTATISTICS rational homotopy type. Felea, Raluca, Composition of Fourier Condon, Sean, Lewis, Brian, Optimal control and shape Spatial analysis of birth­ integral operators with fold and blow design: Theory and applications. weight and infant mortality. down singularities. Massad, jordan, Macroscopic models for Hu, ]ianhua, Identifying differentially Mustafaev, Zokhrab, Some geometric in­ expressed genes, computing gene ex­ equalities in Minkowski spaces. shape memory alloy characterization and design. pression indexes and sample size in Voloshina, Maria, On the holomorph of a microarray experiments. discrete group. Nealis, ]ames, Model-based robust con­ trol designs for high performance mag­ Lee, ]i-Hyun, Practical issues arising Zhang, Yilian, The one dimensional in­ netostrictive transducers. in clustered data: Modified GEE and verse problem and new integrable dy­ goodness-of-fit test. namical systems. Seaton, Gerald, The lattice of equivalence <;lasses of closed sets and the Stone­ Leu, Szu-Yun, Non-homogeneous Poisson Cech compactification. process models for genetic crossover interference. NORTH CAROLINA Weiman, Robert, Granular flow models: Analysis and numerical simulations. Pan, William, Multilevel spatial and sta­ tistical analyses to examine the rela­ Duke University (8) Williams, Ellison Anne, A formula for tionship between population and envi­ n-row Macdonald polynomials. MATHEMATICS ronment: A case study of Ecuadorian Barnes, Andrew, Electromagnetic scat­ Williams, Michael, Nilpotent n-Lie alge­ Amazon. bras. tering by three-dimensional periodic Wang, Kai, Designs for two-dimensional structures. Williams, Vicky, Root multiplicities of the phase I trials in oncology. indefinite Kac-Moody algebras HCn(l). Benes, Christian, On some problems Wang, Xiaofei, Semiparametric methods Zager, Michael, Modeling the distribution concerning planar random walks. for ~iased sampling schemes in epi­ Greer, john, Fourth order diffusions for and metabolism of the phytoestrogen dermologic studies with auxiliary co­ image processing. genistein in rats. variates.

276 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Doctoral Degrees Conferred

Young, Mary, Generalized estimating Boros, Dan, On L (squared)-homology of University of Oklahoma (1l equations (GEE) with design-based cor­ low dimensional buildings. MATHEMATICS relation structures for cluster-unit tri­ Han, Zhongxian, Actuarial modeling of als. extremal events using transformed gen­ White, jonathan, Using technology to Zink, Richard, Correlated binary regres­ eralized extreme value distribution and facilitate visualization in multivariable sion using orthogonalized residuals. generalized Pareto distribution. calculus. Iancu, Aniela Karina, Numerical methods MATHEMATICS for pricing basket options. DeCoste, Rachelle, Density of closed Lladser, Manuel, Asymptotic enumera­ OREGON geodesics in a compact nilrnanifold tion via singularity analysis. with Chevalley rational structure. Malyushitsky, Sergey, On Sylow 2-sub­ Oregon State University (4) Lau, Stephen, Rapid evaluation of radia­ groups of finite simple groups of order MATHEMATICS tion boundary kernels for time-domain up to 210. Bell, Andrea, Hilbert modular surfaces wave propagation on blackholes. Mendris, Robert, The link of suspension singularities and Zariski's conjecture. and uniformizing groups of Klein in­ Stevens, Laura, KZ type equations, elliptic variants. hypergeometric functions and elliptic Ott, Michael, Symplectic convexity theo­ Selberg integrals. rems and applications to the structure Black, Wendy, Pseudo orbit shadowing. Vembar, Navin, Oriented matroid integer theory of semisimple Lie groups. Lin, Fusen, Numerical inversion of Laplace chains. Wang, Chian-jen, On the existence of transforms by the trapezoidal type cuspidal distinguished representations methods. of metaplectic groups. STATISTICS NORTH DAKOTA Zhou, Xiangqian, Some excluded minor theorems of binary matroids. Amer, Sa faa, Neural network imputation: North Dakota State A new fashion or a good tool. University nl STATISTICS Biswas, Swati, On incorporating hetero­ Portland State MATHEMATICS geneity in linkage analysis. University (1) Maney, jack, On the boundary map and Guha, Subharup, Benchmark estimation integral morphisms. for Markov chain Monte Carlo samples. MATHEMATICS AND STATISTICS Kelbick, Nicole, Detecting underlying Blair, Steve, Describing undergraduates' emotional sensitivity in bereaved chil­ reasoning within and across Euclidean, OHIO dren via a multivariate normal mixture taxicab, and spherical geometries. Bowling Green State distribution. Liu, Yu{eng, Multicategory psi-learning University of Oregon nl University (1) and support vector machine. MATHEMATICS MATHEMATICS AND STATISTICS Tang, Yuxiao, Inference on cross correla­ tion with repeated measures data. Geer, Nathan, Link invariants, quantized Sanqui, jose (Joel), Characterization and Wang, Qiang, Maximum likelihood es­ superalgebras and the Kontsevich inte­ statistical inference for the skew­ timation of phylogenetic trees with gral. normal distribution. evolutionary parameters.

Case Western Reserve Ohio University (3) PENNSYLVANIA . University (3l MATHEMATICS Carnegie Mellon STATISTICS Dinh, Hai, On the structure and equiva­ University (16) Charnigo, Richard, Testing homogene­ lence of codes over finite rings. ity in finite mixtures and semi-local Er, Noyan, Rings characterized by direct MATHEMATICAL SCIENCES paradigm for wavelet denoising. sums of CS modules. Bocea, Marian, A Young measure ap­ Ganocy, Steve, Estimation of problems Voisei, Mircea, First-order necessary opti­ proach to nonlinear membrane theory. from data with change points. mality conditions for nonlinear optimal Kolesnikov, Alexei, Generalized amalga­ Wang, Bin, Estimation problems from control. mation in simple theories and char­ biased sampling. acterization of dependence in non­ University of Cincinnati (2) elementary classes. Kent State University (4l MATHEMATICAL SCIENCES Komarek, Paul, Logistic regression for MATHEMATICAL SCIENCES Wang, Guojun, Some Bayesian methods data mining and high-dimensional clas­ in the estimation of parameters in sification. Ghaim, Berhane, On the geometry of Radu, Petronela, On sernilinear wave Banach space operators. the measurement error models and crossover trial. equations. Kim, Sun-mi, Orthogonal polynomials, Simic, Ksenija, Aspects of ergodic theory quadrature rules and linear algebra. Yu, Weiming, Identification of coefficients in reaction-diffusion equations. in subsystems of second-order arith­ Shuibi, Abdallah, Numerical methods for metic. large-scale ill-posed problems. Sirbu, Mihai, A two-person game for Sprague, Emily, Uniform integrability and OKLAHOMA pricing convertible bonds. related topics. Oklahoma State Trapp, Kathryn, A class of compatible discretizations with applications to div­ Ohio State University (16) University (1) curl systems. MATHEMATICS MATHEMATICS Xu, Mingxin, Minimizing shortfall risk us­ Argesanu, George, Risk analysis and Cox, jonathan, A presentation for the ing duality approach-an application to partial hedging in incomplete markets. hedging in incomplete markets. Chow ring A*(Mo,z(p 1, 2)).

FEBRUARY 2005 NOTICES OF THE AMS 277 Doctoral Degrees Conferred

STATISTICS McDermott, ]ames, Low-storage sequen­ University of tial methods for datarnining and the Behseta, Sam, Bayesian multiple curve Pittsburgh (10l fitting in the analysis of neuronal data. analysis of massive datasets. MATHEMATICS Chen, Fang, A two-stage method for Ray, Surajit, Distance-based model-selec­ approximate spatial inferences by com­ tion with application to the analysis of Curtu, Rodica, Waves and oscillations in bining independent site-specific analy­ gene expression data. model neuronal networks. sis. Tan, Hensiong, Variance estimation with Guo, Yixin, Existence and stability of Haviland, Amelia, Understanding gender astronomical measurement errors. standing pulses in neural networks. and racial wage gaps among the highly Wang, ]iping, NPMLE in estimating the Heitmann, Noel, Subgrid stabilization of educated. number of expressed genes using EST evolutionary diffusive transport prob­ fang, Woncheol, Nonparametric density data while accounting for measurement lems. estimation and clustering with applica­ error. Marsh, Andrew, Topology of function tion to cosmology. Wang, Lan, Testing in heteroscedastic spaces. Lee, Pak Kuen Philip, The generalized AN OVA with large number of levels and Sahin, Niyazi, Derivation, analysis and lambda distribution applied to spot in nonparametric ANCOVA. testing of new near wall models for exchange rates. large eddy simulation. Trottini, Mario, (2) Decision models for data Temple University Wisloski, Gregory, Some characterizations disclosure limitation. MATHEMATICS of generalized metric spaces using the Tzeng, ]ung-Ying, Identification of mu­ diagonal. tations affecting liability to complex Sun, Xinyu, Computer-assisted and com­ diseases by the analysis of haplotypes. puter-generated research on combin­ STATISTICS Zhang, Yangang, Hierarchical spatial atorial games and pattern-avoidance. Auh, Sungyoung, Isotonic logistic dis­ models and Monte Carlo analysis of Yayenie, Orner, Hyperbolic convexity of crimination. mine locations in robotic land-mine a standard fundamental domain of a search. subgroup of the Heeke discrete groups. Koyama, Tatsuki, A framework for design of two-state adaptive procedure. Drexel University (1) University of Li, Yulin, Aging properties of mixture distributions. MATHEMATICS Pennsylvania (14l Yothers, Gregory, Methodologies for iden­ Kheyfets, Boris, Some stochastic prop­ MATHEMATICS tifying subsets of the population where erties of random classical and Carlitz two treatments differ. compositions. Aker, Kursat, Higgs bundles on Del Pezza fibrations. Lehigh University (2) Butler, Frederick, Cycle-counting q-rook RHODE ISLAND MATHEMATICS theory and other generalizations of classical rook theory. Brown University (13) Potocka, Katarzyna, The number of sum­ Chadha, Rohit, mands in v 1 -periodic homotopy groups A formal analysis of APPLIED MATHEMATICS of SU(n). · exchange of digital signatures. Gheorghiciuc, Irina, The subword com­ Amarasingham, Asohan, Statistical meth­ Shimkus, Beth, Limit theory for function­ ods for the assessment of temporal als on random bipartite sets. plexity of finite and infinite binary words. structure in the activity of the nervous system. Pennsylvania State Khalid, Madeeha, K3 correspondences. Chen, Qianyong, Topics in spectral meth­ University (13l Mag/and, Jeremy, Discrete inverse scat­ ods. tering theory for NMR pulse design. MATHEMATICS Li, Fengyan, On locally divergence-free Parsley, R. jason, The Biot-Savart oper­ discontinuous Galer kin methods. Binns, Stephen, The Medvedev and Much­ ator and electrodynamics on bounded nik lattices of classes. Liu, Dong, Spectral element/force cou­ IT~ subdomains of the 3-sphere. pling method: Application to colloidal Chacon, Ben, Undecidability of the prob­ Shen, ]unhao, Free probability, free en­ devices and self-assembled structures lem of distinguishing k-theory classes tropy and generator problems for von in 3D domains. of the reduced group C*-algebra for a Neumann algebras. finitely presented group. Lucor, Didier, Generalized polynomial Song, Chunwei, Combinatorial theory chaos: Applications to random oscilla­ Dogru, Filiz, Polygonal outer billiards in of q,t-Schroder polynomials, parking tors and flow-structure interactions. the hyperbolic plane. functions and trees. Pai, Hui-Ming, A robust formulation of Talitskaya, Anna, Partially hyperbolic a multi-class queueing network control phenomena in dynamical systems with STATISTICS problem. discrete and continuous time. Levins, Mihails, Variance estimation for Wu, Wei, Statistical models of neural STATISTICS nonparametric regression and its appli­ coding in motor cortex. cations. Demirtas, Hakan, Multiple imputation for Xiu, Dongbin, Generalized (Wiener-Askey) nonignorable dropout using Bayesian Li, Xuefeng, Infinitely divisible time series polynomial chaos. pattern-mixture models. models. MATHEMATICS Elmore, Ryan, Semiparametric analysis Liu, Linxu, Semi-parametric and non­ of finite mixture models with repeated parametric models for survival data. Christoforou, Cleopatra, Hyperbolic. sys­ measures. Shen, Haipeng, Nonparametric regres­ tems of balance laws via vanishing Hare/, Ofer, Strategies for data analysis sion for problems involving lognormal viscosity. with two types of missing values. distributions. Horozov, Ivan, Euler characteristics of Liu, ]iawei, Robust fitting of multinomial Venkataramani, Chandramouliswar, Ran­ arithmetic groups. models based on assessment of model dom walk hypotheses and profitability Karageorgis, Paschalis, Nonlinear waves . building errors. of momentum based trading rules . with sign-changing potentials.

278 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Doctoral Degrees Conferred

Leonard, Kathryn, Measuring shape space: TENNESSEE Rice University (11) E-entropy, adaptive coding and two­ COMPUTATIONAL AND APPLIED dimensional shape. University of Memphis (4) MATHEMATICS Wang, Qingxue, Multiple polylogarithm MATHEMATICAL SCIENCES motives and moduli spaces Mo,n- Husband, Christopher, Stochastic opti­ Cutler, jonathan, Extremal and algebraic mization applications in molecular elec­ University of Rhode graph theory. tronics. Island (2) Hubenko, Alice, Cliques, strong packing Li, Ming, New algorithms of pathwidth and cycle covers. computation. MATHEMATICS Kombe, Ismail, Linear and nonlinear Red/, Timothy, A study of university Clark, Cathy Ann, Global behavior of parabolic partial differential equations timetabling that blends graph color­ nonlinear difference equations and sys­ with singular lower order term. ing with the satisfaction of various tems. Liang, Yulan, Gene expression temporal essential and preferential conditions. Travers, Brian, Generalized whist tourna­ patterns classification with hierarchical Wang, Zhen, A generalized trust region ments and generalized whist frames. Bayesian neural networks and time SQP algorithm for equality constrained lagged recurrent neural networks. optimization. SOUTH CAROLINA University of MATHEMATICS Tennessee (4) Gwosdz-Gee, Carol, Strong S -equivalence Clemson University (5) of ordered links. MATHEMATICS MATHEMATICAL SCIENCES Heap, Aaron, Bordism invariants of the Battle, Laurie, Eigenvalue dependence mapping class group. Farr, Jeffrey, Computing Grabner bases, on problem: Parameters for Stieltjes Huang, Zheng, Harmonic maps and the with applications to Pade approxima­ Sturm-Liouville problems. geometry of Teichmuller space. tion and algebraic coding theory. Khanal, Harihar, Computational models Leidy, Constance, Higher-order linking Gorka, Artur, The random multi-direc­ of diffusion of second messengers in forms. tional method of feasible directions. visual transduction. Ntasin, Louis, A posteriori error esti­ Salinas, Rene, Modeling the effects of STATISTICS mation and adaptive computation of alternative harvesting strategies on the Ghebremichael, Musie, Nonparametric es­ viscoelastic fluid flow. black bear population of the southern timation of bivariate mean residual life Rodrigues, Virginia, Multivariate polyno­ Appalachians. function. mials: Irreducibility and Grabner bases. Smith, Neal, Graph-theoretic properties Sung, Hsi-Guang, Gaussian mixture re­ Waters, Lawrence, A parallel implemen­ of the zero-divisor graph of a ring. gression and classification. tation of the Glowinski-Pironneau algo­ Swartz, Michael, Stochastic search gene rithm for the modified Stokes problem. Vanderbilt University (3) suggestion: Hierarchical Bayesian model Medical University of MATHEMATICS selection meets gene mapping. Alewine, john Alan, An inductive unit South Carolina (2) topology on the Denjoy space. Southern Methodist BIOMETRY AND EPIDEMIOLOGY jennings, Dana Lynn Gaston, Separating University (5) Khedouri, Christopher, Use of global tests cycles in triangulations of the double MATHEMATICS torus. for multiple outcomes with applications Li, Baoyan, A control volume function in psychiatry. Stephens, David Christopher, The nonori­ entable genus of the complete tripartite approximation method and reservoir Sadler, Zara, An approach to estimating simulation with flexible grids. relative goodness of fit with application graph. to the diagnostic interview schedule for STATISTICAL SCIENCE selected ethnic groups in the US. TEXAS Cohlmia, Krista, Filtering M-stationary University of South processes. Baylor University (6) Jiang, Huiping, Time-frequency analysis Carolina, Columbia (5) Q(lambda) stationary process. MATHEMATICS MATHEMATICS Shen, Shuyi, Minimum L2 estimation for Singh, Parmjeet, Existence of positive Poisson mixtures. Park, Kyungwon, Bivariate rational ap­ solutions to singular boundary value Spence, Jeffrey, A spatial analysis of proximation and anisotropic Franklin problems. SPECT brain imaging data: Optimal bases. predictions in regions of interest. Ryan, Pamela, Hardy-Sobolev spaces and STATISTICAL SCIENCE Banach algebras on the unit ball of c

FEBRUARY 2005 NOTICES OF THE AMS 279 Doctoral Degrees Conferred

Husain, Ali-Amir, On the cohomology of University of North UTAH operator algebras. Texas (4) Khalmanova, Dinara, Productivity index University of Utah (s) as an integral characteristic of diffusion MATHEMATICS MATHEMATICS processes. Bahreini, Manneh, Complemented sub­ Kim, Mijoung, The D-Neumann operator spaces of bounded linear operators. Guy, Robert, A continuum model of and the Kobayashi metric. platelet aggregation: Closure, computa­ Boykin, Charles, The study of translation tional methods and simulation. Le Gia, Quae, Approximation of lin­ equivalence on integer lattices. ear partial differential equations on Kohler, Brynja, T-lymphocyte population Ghenciu, Joana, Spaces of compact oper­ dynamics in health and auto immunity. spheres. ators. Lukic, Denis, Twisted Harish-Chandra STATISTICS Muller, Kimberly, Polish spaces and ana­ sheaves and Whittaker modules. lytic sets. Boucher, Thomas, V -uniform ergodicity Piepmeyer, Gregory, Constructing per­ of threshold autoregressive nonlinear University of Texas, fect complexes with given intersection time series. properties. Arlington (4) Guan, Yongtao, Nonparametric methods Robbins, Thomas, Seed dispersal and bi­ of assessing spatial isotropy. MATHEMATICS ological invasion: A mathematical anal­ Holan, Scott, ysis. Time series exponential Kadjo, Hilaire, Age structured population models: Theory and methods. model: Interaction between nutrients Utah State University (2) Lee, Kyeong Eun, Bayesian models for and phytoplankton. DNA microarray data analysis. Luo, Sheng, A multigrid method for 2-D MATHEMATICS AND STATISTICS Lee, Sang-]oon, Asymptotics and compu­ MGD flow control analysis. Biesecker, Matthew, Geometric studies in tations for approximation of method of Nguyen, Vinh, Regression model with hyperbolic systems in the plane. regularization estimators. explanatory variable subject to asym­ Zhu, Zewen, Optimal experimental de­ Park, Chun Gun, MCMC methods for metric measurement errors. signs with correlated observations. wavelet representations in single index Sohaee, Nassim, Upward embedding of models. digraphs on the surfaces. Yu, ]ihnhee, Approaches to the multivari­ VIRGINIA ate random variables associated with University of Texas, stochastic processes. College of William and Austin (7) Zhao, Caixia, One-sided cross-validation Mary (l) for a model motivated by variable star COMPUTATIONAL AND APPLIED MATHEMATICS, APPLIED SCIENCE data. MATHEMATICS Milligan, Thomas, On certain sets of Texas Tech University (6) Aizinger, Vadym, A discontinuous Galer­ matrices: Euclidean squared distance kin method for two and three-dimen­ matrices, ray-nonsingular matrices, and MATHEMATICS AND STATISTICS sional shallow-water equations. matrices generated by reflections. Emmert, Keith, Deterministic and sto­ Carnes, Brian Ross, Adaptive finite el­ chastic discrete-time epidemic models ements for nonlinear transport equa­ Old Dominion tions. with applications to amphibians. University (4) Lee, Eun-]oo, Estimating linear func­ Pardo, David, Integration of hp-adaptivity tionals of indirectly observed input with a two grid solver: Applications to MATHEMATICS AND STATISTICS electromagnetics. functions. Feldman, Gary, A forward-backward flu­ Lee, Seung-Hwan, Checking the censored Sun, Shuyu, Discontinuous Galer kin meth­ ence model for the low-energy neutron two-sample accelerated life model us­ od for reactive transport in porous Boltzmann equation. media. ing integrated cumulative hazard dif­ Novaprateep, Boriboon, Superconvergence ference. MATHEMATICS of iterated solutions for linear and Navaratna, Channa, Estimation of the nonlinear integral equations: Wavelet origin of contaminent particles using Goodman, Noah, Contact structures and applications. point measurements in a fluid flow. open books. Plungpongpun, Kusaya, Analysis of mul­ Omolo, Bernard, Aligned rank test for Pacetti, Ariel, A formula for the central tivariate data using Kotz type distribu­ repeated observation models with or­ value of certain Heeke L-functions. tion. thonormal design. Petsche, Clayton, The distribution of Shi, Genming, Estimation of parameters Perera, Pantaleon, Asymptotic feedback Galois orbits of low heights. in replicated time series regression controllability and topological structure models. of controllable linear switched systems. University of Texas, Dallas (3) University of Virginia (7) University of Houston (4) MATHEMATICS MATHEMATICAL SCIENCES MATHEMATICS Bhattacharya, Chirashree, Free groups Schmegner, Claudia, Decision theoretic Ahmed-Zaid, Abdelnour, Boundary stabi­ results for sequentially planned proce­ and their automorphisms. lization of wave equation type models: dures. Carley, Holly, The strong-coupling limit A numerical approach. for the ground state of a particle Seida, David Lee, Estimation of attitude harmonic oscillator interaction. Holmes, Roderick, Optimal frames. parameters from variation in image Kaneda, Masayoshi, Multipliers and alge­ overlap. Guadagni, Gianluca, Renormalization group for a lattice system. braizations of operator spaces. Wang, ]in, On nonparametric multivari­ Yi, Eunjeong, Nevanlinna theory and ate scale, kurtosis, and tailweight mea­ Meehan, Melissa, Detection of symplectic iteration of rational maps. sures. commutator subgroups.

280 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Doctoral Degrees Conferred

STATISTICS WASHINGTON Xu, Rui, On flows of graphs. Zhan, Mingquan, Eulerian subgraphs and Betcher, Joshua, Statistical inference un­ University of Harniltonicity of claw-free graphs. der order restrictions with applications. Washington (13) Buot, Max Louis, Applications of genetic algorithms in maximum likelihood esti­ APPLIED MATHEMATICS WISCONSIN mation. Hsu, Viktoria R. T., Ion transport through Tomita, Yuji, On properties of multi­ biological cell membranes: From electro­ Marquette University (1) variate mixture vector autoregressive diffusion to Hodgkin-Huxley via a quasi MATHEMATICS, STATISTICS AND models. steady-state approach. COMPUTER SCIENCE Virginia Commonwealth MATHEMATICS Oliveira, Luis, Varieties of pseudosemi­ Chen, ]ein-Shan, Merit functions and lattices. University (5) nonsmooth functions for the second­ Medical College of BIOSTATISTICS order cone complementarity problem. Hahn, Rebekah, K(l)-local Iwasawa the­ Wisconsin (1) Campbell, Leanne, Futility analysis with ory. BIOSTATISTICS covariables. Hladky, Robert, Boundary regularity of Eckel, jeanette, Statistical analyses of the Neumann problem for the Kahn Bajorunaite, Ruta, Comparison of fail­ time-course and dose-response mi­ Laplacian on the Heisenberg group. ure probabilities in the presence of croarray experiments. Kim, Panki, Potential theory for stable competing risks. Hamm, Adam, Analysis of an interaction processes. threshold in drug/chemical mixtures. Maxwell, David, Initial data for black University of Wisconsin, Massie, Tammy, Testing genetic hypoth­ holes and rough spacetimes. Madison (25) esis on bivariate dichotomous twin Ramaseshan, Karthik, Microlocal analysis MATHEMATICS data using repeated measures logistic of the Doppler transform on R 3. regression. van Opstal/, Michael, Some stable degen­ Chakrabarti, Manish, Representations of erations and applications to moduli. modular and quantum Weyl algebras Rutledge, Brandy, A comparison of twin and of generalized Heisenberg algebras. methods when the liability is non­ STATISTICS normal. Cho, Cheol-Hyun, Holomorphic discs, Anderson, Amy Dawn, The genetic struc­ spin structures and Floer cohomology of the Clifford torus. Virginia Polytechnic ture of related recombinant lines. Balabdaoui, Fadoua, Nonparametric esti­ de Sousa Dias Lopes, Samuel, On the Institute and State mation of a k-monotone density: A new structure and representation theory University no) asymptotic distribution theory. of the quantized enveloping algebra Drton, Mathias, Maximum likelihood es­ Uq(g)+, for g semisimple. MATHEMATICS timation in Gaussian AMP chain graph Lau, Michael, Fock representations and models and Gaussian ancestral graph central extensions. Buterakos, Lewis, The exit time distri­ models. Lee, Youngsuk, Anisotropic energy trans­ bution for small random perturbations fer in beta-plane and rotating flows. of dynamical systems with a repulsive Sieberts, Solveig Kara, Joint relationship type stationary point. inference from three or more individ­ Ondrus, Matthew, Whittaker modules, uals in the presence of genotyping central characters, and tensor products Camp, Brian, A class of immersed finite error. for quantum enveloping algebras. element spaces and their application to Sugar, Elizabeth Ann, Personal character­ forward and inverse interface problems. Thiem, F. Nathaniel, Unipotent Heeke al­ istics and covariate measurement error gebras: The structure, representations, Evans, Katie, Reduced order controllers in disease risk estimation. and combinatorics. for distributed parameter systems. Unlu, Ozgun, Constructions of free group Forcey, Stefan, Loop spaces and iterated Washington State actions on products of spheres. higher dimensional enrichment. University (3) Velikina, julia, Twisting transform and replicable functions. Garcia-Puente, Luis, Algebraic geometry MATHEMATICS of Bayesian networks. Edmeade, Dean Emmanuel, Nonlinear STATISTICS Gillespie, Jason, A combinatorial proof of stability analysis of hexagonal optical the positivity of Lusztig's q-analogue Ahn, Hongyup, Restricted likelihood ratio pattern formation in an atomic sodium tests for fixed effects in mixed effects of weight multiplicity for rank I Lie vapor ring cavity. algebras. models. Mapes, Eric, Analytic and numerical solu­ Cheng, Bin, Some hypothesis testing Nguyen, Hoan, Volterra systems with tions of framework models. realizable kernels. results for two-way linear models in Rajapakse, Indika, A mathematical model clinical trials. Rai, Tapan, Infinite Grabner bases and for neuronal groups. non-commutative polly cracker cryp­ Dahl, David, Conjugate Dirichlet pro­ cess mixture models: Efficient sam­ tosystems. WEST VIRGINIA pling, gene expression and clustering. Vugrin, Eric, On approximation and opti­ Debroy, Saikat, Computational methods mal control of non-normal distributed West Virginia for mixed-effects models. parameter systems. University (3) Gross, Kevin, The aphid, the wasp, and the matrix: Aspects of modeling host­ STATISTICS MATHEMATICS parasitoid and single-species dynamics. Kim, Keun Pya, Process monitoring with Wang, Yi, Fast wavelet collocation meth­ Hong, Quan, A pseudo empirical likeli­ multivariate data: Varying sample sizes ods for second kind integral equations hood approach to nonignorable nonre­ and linear profiles. on polygons. sponse.

FEBRUARY 2005 NOTICES OF THE AMS 281 Doctoral Degrees Conferred

]i, Yuan, On Bayesian modeling and design for microarray gene expression data. ]in, Chunfang, Contributions to the de­ sign and analysis of quantitative trait loci experiments. Lee, Yoonjung, Two essays on model­ ing financial markets as complex and interactive systems. Leng, Chenlei, Some problems in model selection. Li, Liang, Modeling the measurement error of apnea-hypopnea index. Li, Ruojia, Some new multivariate quality monitoring procedures. Ma, Shuangge, Penalized M-estimation for partly linear transformation models with current status data. Todern, David, Latent-structured regres­ sion modeling for longitudinal multi­ variate ordinal 1 count data. Yan, ]un, Functional regression models and temporal processes. Yuan, Ming, Automatic smoothing and Put Your Math variable selection via regularization. Intelligence to Work

When you join NSA, you join a highly talented group of Mathematicians who deduce structure where it is not apparent, find patterns in seemingly random sets, and create order out of chaos. They apply Number Theory, Group Theory, Finite Field Theory, Linear Algebra, PREPARING Probability Theory, Mathematical Statistics, MATHEMATICIANS TO Combinatorics, and more to a world of EDUCATE TEACHERS challenges. They exchange ideas and work PMET with some of the finest minds and most A growing set of national reports calls for better preparation of powerful computers in the country. And you the nation's mathematics teachers by mathematics faculty. can too, when you put your math intelligence The Mathematical Association of America has developed a multifaceted program , Preparing Mathematicians to Educate to work at NSA. Teachers (PMET) to help meet this need. During the spring and summer 2005, PMET will offer eight new workshops for NSA: Securing Tomorrow Today· college and university faculty who teach mathematics courses taken by prospective teachers. Each workshop will focus on preparing teachers for elementary, middle and/or secondary For more information and to apply online, school mathematics. Participants will examine how pre­ visit our Web site. service teachers learn mathematics; make sense of mathe­ matical ideas, and how they integrate their knowledge of mathematics into their thinking about teaching. Participants will also have opportunities to share ideas, discuss, and learn more about appropriate content and effective ways of helping pre-service teachers learn mathematics. They will explore specific topics including the use of technology and statistics education in school mathematics. Costs of lodging and food while at the workshops are covered by the program. Ques­ tions regarding the PMET workshops may be addressed to Ed Dubinsky at [email protected] Additional details, workshop descriptions and application www.NSA.gov materials are available at the PMET website

CLICK ON CAREERS http://www.maa.org/PMET. A PMET workshop is an opportunity to explore ways of U.S. citizenship is required for all applicants. NSA is an Equal Opportunity Employer and improving the mathematical background and pedagogi­ abides by applicable employment laws and regulations. cal practice of future teachers.

282 NOTICES OF THE AMS VOLUME 52, NUMBER 2 AMERICAN MATHEMATICAL SOCIETY

The selection committee for these prizes requests nominations for con­ sideration for the 2006 awards. Further information about the prizes can be found in the November 2003 Notices, pp. 1288-1302 (also avail­ able at http://www.ams.org/prizes-awards) .

... Three Leroy P. Steele Prizes are awarded each year in the following cat­ egories: (I) the Steele Prize for Lifetime Achievement: for the cumulative ~ influence of the total mathematical work of the recipient, high level of c research over a period of time, particular influence on the development of a field, and influence on mathematics through Ph.D. students; (2) the ·- Steele Prize for Mathematical Exposition: for a book or substantial sur­ E vey or expository-research paper; and (3) the Steele Prize for Seminal Contribution to Research: for a paper, whether recent or not, that has 0 proved to be of fundamental or lasting importance in its field, or a model of important research. In 2006 the prize for Seminal Contribution to Research will be awarded for a paper in Applied Mathematics.

Nominations with supporting information should be submitted to the Secretary, Robert J. Daverman, American Mathematical Society, 312D Ayres Hall, University ofTennessee, Knoxville, TN 37996-1330.1nclude a short description on the work that is the basis of the nomination, includ­ ing complete bibliographic citations. A curriculum vitae should be - included. The nominations will be forwarded by the Secretary to the -t\1 prize selection committee, which will, as in the past, make final decisions u on the awarding of prizes. Deadline for nominations is March 31, 2005. From the AMS Secretary

2004 Election Results

In the elections of 2004 the Society elected a vice president, Nominating Committee a trustee, five members at large of the Council, two mem­ Elected as new members of the Nominating Committee are bers of the Editorial Boards Committee, and three mem­ Phillip A. Griffith from the University of Illinois at Ur­ bers of the Nominating Committee. Terms for these posi­ bana-Champaign tions are three years beginning on 1 February 2005 and David Jerison from the Massachusetts Institute of Tech­ ending on 31 January 2008, except for the trustee, whose nology term is for five years ending on 31 January 2010. Members linda Keen from Lehman College and Graduate Center, elected to the Nominating Committee begin serving im­ City University of New York mediately, and their terms end on 31 December 2007. Suggestions for elections to be held in the fall of 2005 Vice President are solicited by the 2005 Nominating Committee. Positions to be filled in the 2005 election are: president elect, vice Elected as the new vice president is Halm Brezis president, trustee, and five members at large of the Council. from the Universite Paris VI and Institut Universitaire de The candidates for president elect will be James G. Glimm France. and Ronald ]. Stern. Suggestions concerning the other posts should be sent to the secretary. Trustee Suggestions for nominations for two positions on the Re-elected as trustee is Eric M. Friedlander from North­ Editorial Boards Committee and three positions on western University. the 2006 Nominating Committee can also be sent to the secretary: Members at Large ofthe Council Robert ]. Daverman, Secretary Elected as new members at large of the Council are American Mathematical Society Sara C. Billey from the University of Washington 312D Ayres Hall Carolyn S. Gordon from Dartmouth College University of Tennessee Knoxville, TN 37996-1330 Sheldon H. Katz from the University of Illinois at Ur­ [email protected] bana-Champaign The deadline for suggestions is 26 February 2005. Michael F. Singer from North Carolina State University Catherine H. Yan from Texas A&M University

Editorial Boards Committee Elected as new members of the Editorial Boards Commit­ tee are Margaret Cheney from Rensselaer Polytechnic Institute Abigail A. Thompson from the University of Califor­ nia at Davis

284 NOTICES OF THE AMS VOLUME 52, NUMBER 2 There will be a number of contested seats in the 2005 AMS Elections. SUGGESTIONS Your suggestions are wanted by: The Nominating Committee for vice president, trustee, and five members at large of the Council

and by

The President for three Nominating Committee members and two Editorial Boards Committee members.

In addition

The Editorial Boards Committee requests suggestions for appointments to various editorial boards of Society publications.

Send your suggestions for any of the above to:

Robert J. Daverman, Secretary American Mathematical Society 3120 Ayres Hall University of Tennessee Knoxville, TN 37996-1330 e-mail: secretary@ams. org

The deadline for suggestions is 26 February 2005. 2005 AMS El ction Nominations by Petition Vice President or Rules and Procedures Use separate copies of the form for each candidate for vice Member at Large . president, member at large, or member of the Nominating One position of vice president and member of the Coun­ and Editorial Boards Committees. cil ex officio for a term of,three years is to be filled in the election of 2005. The Council intends to nominate at least 1. To be considered, petitions must be addressed to Robert two candidates, among whom may be candidates nominated ]. Daverman, Secretary, American Mathematical Society, by petition as described in the rules and procedures. 312 D Ayres Hall, University of Tennessee, Knoxville, TN Five positions of member at large of the Council for a 37996-1330, and must arrive by 26 February 2005. term of three years are to be filled in the same election. 2. The name of the candidate must be given as it appears The Council intends to nominate at least ten candidates, in the Combined Membership List (www. ams. org/cml). among whom may be candidates nominated by petition in If the name does not appear in the list, as in the case of the manner described in the rules and procedures. a new member or by error, it must be as it appears in Petitions are presented to the Council, which, accord­ the mailing lists, for example on the mailing label of the ing to Section 2 of Article VII of the bylaws, makes the_ nom­ Notices. If the name does not identify the candidate inations. The Council of 23 January 1979 stated the mtent uniquely, append the member code, which may be ob­ of the Council of nominating all persons on whose behalf there were valid petitions. tained from the candidate's mailing label or by the can­ Prior to presentation to the Council, petitions in support didate contacting the AMS headquarters in Providence ([email protected]). of a candidate for the position of vice president or of mem­ ber at large of the Council must have at least fifty valid sig­ 3. The petition for a single candidate may consist of sev­ natures and must conform to several rules and opera­ eral sheets each bearing the statement of the petition, tional considerations, which are described below. including the name of the position, and signatures. The name of the candidate must be exactly the same on all sheets. Editorial Boards Committee 4. On the next page is a sample form for petitions. Copies Two places on the Editorial Boards Committee will be filled may be obtained from the secretary; however, petition­ by election. There will be four continuing members of the ers may make and use photocopies or reasonable fac- Editorial Boards Committee. similes. . The President will name at least four candidates for these 5. A signature is valid when it is clearly that of the mem­ two places, among whom may be candidates nominated by petition in the manner described in the rules and procedures. ber whose name and address is given in the left-hand The candidate's assent and petitions bearing at least 100 column. valid signatures are required for a name to be placed on 6. The signature may be in the style chosen by the signer. the ballot. In addition, several other rules and operational However, the printed name and address will be checked considerations, described below, should be followed. against the Combined Membership List and the mailing lists. No attempt will be made to match variants of names with the form of name in the CML. A name nei­ Nominating Committee ther in the CML nor on the mailing lists is not that of a Three places on the Nominating Committee will be filled member. (Example: The name Robert]. Daverman is that by election. There will be six continuing members of the of a member. The name R. Daverman appears not to Nominating Committee. be.) The President will name at least six candidates for these 7. When a petition meeting these various requirements ap­ three places, among whom may be candidates nominated pears, the secretary will ask the candidate to indicate by petition in the manner described in the rules and willingness to be included on the ballot. Petitioners can procedures. facilitate the procedure by accompanying the petitions The candidate's assent and petitions bearing at least 100 with a signed statement from the candidate giving valid signatures are required for a name to be placed on consent. the ballot. In addition, several other rules and operational considerations, described below, should be followed.

286 NOTICES OF THE AMS VOLUME 52, NUMBER 2 From the AMS Secretary Nom ination Petition fo r 2 00 5 Election

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

as a candidate for the position of (check one): D Vice President D Member at Large of the Council D Member of the Nominating Committee D Member of the Editorial Boards Committee of the American Mathematical Society for a term beginning 1 February, 2006.

Name and address (printed or typed)

Signature

Signature

Signature

Signature

Signature

Signature

fEBRUARY 2005 NOTICES OF THE AMS 287 Mathematics Calendar

The most comprehensive and up-to-date Mathematics Calendar information is available one-MATH at http:llwww. ams .orglmathcall.

February 2005 April 2005 '28-March 4 Conference on Arithmetic Geometry: Gainesville * 25-29 Analytical Methods in Number Theory, Probability Theory 2005, University of Florida, Gainesville, Florida. and Mathematical Statistics, Euler IMI, St. Petersburg, Russia. Topic: p-adic methods in arithmetic and algebraic geometry. Organizers: St. Petersburg Department of Steklov Institute of Organizers: Richard Crew, Kevin Keating, Norm Levin. Mathematics, Euler International Mathematical Institute. Topics: The conference is dedicated to the 90th anniversary of the Information: http: I lwww. math. ufl . edu;-crew I agconf . html. prominent Russian mathematician, Yuri V. Linnik (1915-1972). The conference will be devoted to recent achievements in branches of March 2005 mathematics close to Linnik's interests. Two parallel sections are '' 9-1 3 Minimal Surfaces, Sub-Elliptic POE's and Geometric Analy­ supposed: Number Theory; Probability Theory and Mathematical sis, Dartmouth College, Hanover, New Hampshire. Statistics. Workshop Topics: Minimal Surfaces, Sub-Elliptic PDE's and Geo­ Dead I ines: For submission is March 1, 2005. For abstract submission metric Analysis. is April15, 2005. Focus: On contemporary developments in the study of several Information: email: linnik90@imi. ras . ru; http: I lwww. pdmi. problems from analysis and geometry in the setting of Carnot­ ras.ruiEIMII2005ILinnik90I. Caratheodory metrics. Most of the invited lecturers will address a variety of interrelated topics, such as: "best-constant" type problems May 2005 concerning Sobolev and isoperimetric inequalities; the study of * 1 7-21 Lie algebras, Vertex operator algebras and their applica­ minimal and constant-curvature submanifolds; rectifiability and tions, North Carolina State University, Raleigh, North Carolina. geometric measure theory; quasiconformal maps and potential Main Topics: Lie algebras, Quantum groups and their repre­ theory; geometric flows and applications. sentations; Vertex operator algebras and their representations; Participants: Richard Beals (Yale University), Bill Beckner (Uni­ Applications to number theory, combinatorics, conformal field versity of Texas, Austin), Giovanna Citti (Universita' di Bologna, theory and statistical mechanics. Italy), Michael Cowling (University of New South Wales, Australia), Organizers: Kailash C. Misra, email: misra@math. ncsu. edu, Yi-Zhi Nicola Garofalo (Purdue University), Piotr Hajlasz (University of Huang, email: yzhuang©math. rutgers . edu. Pittsburgh), Ilkka Holopainen (University of Helsinki, Finland), Juan Deadline: For registration is April 20, 2005. Manfredi (University of Pittsburgh), Severine Rigot (Universite' de Information: http : I lwww. math. ncsu. edu;-misraiLieCon£2005. Paris-Sud XI Orsay, France). Information: http : I lwww. math. dartmouth. edur ccworkshopl '' 1 8-21 Combinatorial and additive number theory (CANT 2005): index.htm. A conference in celebration of Mel Nathanson's 60th birthday,

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

288 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Mathematics Calendar

CUNY Graduate Center, 365 Fifth Avenue, New York, New York. '' 6-8 Nonlinear Partial Differential Equations and Applications: Description: The conference will cover all areas of combinatorial Conference in honor of jim Serrin on the occasion of the awarding and additive number theory, and related parts of mathematics, of the title of Doctor Honoris Causa of Universite Fran~ois such as harmonic analysis, ergodic theory, and probability. There Rabelais, Faculty of Sciences-Universite, Fran<;ois Rabelais-Tours, will be invited lectures as well as sessions for contributed papers. France. To lecture at the conference, please submit a title and brief abstract Description: Besides the official ceremony of the delivery of the to the conference co-chair Xingde Jia at cant2005@hotmail. com or diploma, we intend to put into light the numerous contributions of j ia@txstate. edu by April 20, 2005. It is anticipated that some Professor Serrin and his collaborators in the domain of nonlinear travel support will be available. Younger mathematicians, and partial differential equations. We also strongly wish to associate especially graduate students, are encouraged to attend. younger brilliant mathematicians with this celebration. Information: Please send an email message to cant2005@hotmail. Invited speakers: D. Aronson (Univ. Minnesota), H. Berestycki com. Information is also available on the website http: I /www. (E.H.E.S.S., Paris), F. Bethuel (Univ. Paris 6), L. Boccardo (Univ. Roma theoryofnumbers.com. I), H. Brezis (Univ. Paris 6 & Rutgers), X. Cabre (I.C.R.E.A. & Univ. Poli. Catal.), ]. M. Coron (Univ. Paris 11), J. I. Diaz (Univ. Complutense, 27-30 Scattering theory and singular spaces, Northwestern Madrid), M. Escobedo (Univ. Bilbao), R. Finn (Univ. Stanford), Y. Y. University, Evanston, Illinois. Li (Univ. Rutgers), M. Marcus (Technion, Haifa), J. Mawhin (Univ. Organizers: Andras Vasy and Jared Wunsch. Louvain), F. Merle (Univ. Cergy-Pontoise), P. Mironescu (Univ. Lyon Information: http : I /www .math .northwestern. edurjwunsch/ l), L. A. Peletier (Univ. Leiden), P. Pucci (Univ. Perugia), D. Smets scattering. html. (Univ. Paris 6), Ph. Souplet (Univ. Arniens), ]. L. Vazquez (Univ. Aut6noma, Madrid). 31-June 4 2nd Conference on Analysis and Probability on Information: http: I /www. phys-uni v-tours . fr; email: serrin05@ Fractals, Cornell University, Ithaca, New York. lmpt. uni v-tours. fr, address: Conference]. Serrin 05, Laboratoire Description: Analysis and probability on fractals is an exciting new de Mathematiques et Physique Theorique, Faculte des Sciences, area of mathematical research that studies basic analytic operators Pare de Grandmont F. 37200 Tours, France. TeL (33) (0)2 47 36 69 and stochastic processes when the underlying space is fractal. 25 (secret.), (33) (0)2 47 36 70 68 (fax). Speakers: Martin Barlow (University of British Columbia), Zhen­ Qing Chen (University of Washington), Kenneth Falconer (University '' 6-11 14th Summer St. Petersburg Meeting in Mathematical of St. Andrews), Peter Grabner (Technical University of Graz), Ben Analysis, Euler IMI, St. Petersburg, Russia. Hambly (Oxford University), Masanori Hino (Kyoto University), Organizers: St. Petersburg Department of Steklov Institute of Jun Kigami (Kyoto University), Takashi Kumagai (Kyoto University), Mathematics; Euler International Mathematical Institute. Michel Lapidus (University of California, Riverside), Ka-Sing Lau (The Information: email: analysis@pdmi. ras . ru; http: I /www. pdmi. Chinese University of Hong Kong), Volker Metz (Bielefeld University), ras.ru/EIMI/2005/analysis14. Christophe Sabot (University of Paris), Robert Strichartz (Cornell University), Alexander Teplyaev (University of Connecticut), Martina ,., 7-1 2 25th Great Plains Operator Theory Symposium (GPOTS-05), Zaehle (University of Jena). University of Central Florida, Orlando, Florida. Applications: For financial support received by January 15, 2005, Description: GPOTS is one of the largest annual conferences in will receive preference. No registration fee. the area of operator theory/ operator algebras/applications. There Information: More information and an application form can be are generally more than ten main invited speakers whose lectures found at: http://www.math. cornell.edu/Colloquia/fractals . emphasize break-through areas and applications of interest to html or fractals05@math. cornell. edu. the participants. Many of the regular participants give shorter talks, including many graduate students currently working on their june 2005 doctorates. Support: Each year GPOTS receives funding from the National · 1-4 ACMS 15th Biennial Conference, Huntington College, Hunt­ Science Foundation specifically to provide partial support for young ington, Indiana. faculty, postdocs, graduate students, and other active researchers Description: The Association of Christians in the Mathematical who do not currently have a federal research grant. The same level Sciences will sponsor their 15th conference since 1977. of support from NSF for GPOTS-05 is expected. Featured speaker: Fernando Gouvea from Colby College. Information: email: gpots05@math. ucf. edu (for general inquiry) Conference Chair: W. Wetherbee, Dept. of Mathematics, Huntington or email: dhan@mail. ucf . edu (for conference program inquiry); College, Huntington, IN 46750; email: wwetherb@huntington. edu. http://gauss.math.ucf.edu/-gpots05. Information: General information is at http : I /www. acmsonline. org. Abstracts of proposed papers may be sent to the conference '' 8- 1 2 Computability in Europe 2005 (CiE 2005): New Computa­ chair. tional Paradigms, Amsterdam, The Netherlands. Description: CiE 2005 will have 3-hour tutorials on Quantum ' 2-1 0 Seventh International Conference on Geometry, Integrabil­ Computation (H. Buhrman) and Computability over the Reals (K. ity and Quantization with a special session on Multisymplectic Weihrauch) and invited talks by S. Abramsky, ].D. Hamkins, U. Geometry and Classical Field Theory, Sts. Constantine and Elena Kohlenbach,]. van Leeuwen, Y. Matiyasevich, Y.N. Moschovakis and resort (near Varna), Bulgaria. U. Schoening. There will be two-hour special sessions on Biological Goal: This seventh edition of the conference aims like the previous Computation, Complexity, Epistemology and Methodology of Com­ ones to bring together experts in the Classical and Modern Dif­ puting, Proofs and Computation, Real Computation, and Relative ferential Geometry, Complex Analysis, Mathematical Physics and Computation. related fields in order to assess recent developments in these areas Organizers: Barry Cooper, Benedikt Lowe, Leen Torenvliet, Peter and to stimulate research in intermediate topics. van Emde Boas. Organizers: Ivailo M. Mladenov (Sofia), Allen Hirshfeld (Dortmund) Program Committee: Klaus Ambos-Spies (Heidelberg), Albert At­ and Manuel de Leon (Madrid). serias (Barcelona), Barry Cooper (Leeds, co-chair), Sergei Goncharov Information: I. M. Mladenov, email: mladenov@obzor . bio21. bas. (Novosibirsk), Benedikt Loewe (Amsterdam, co-chair), Dag Normann bg; A. C. Hirshfeld, email: hirsh@physik. uni -dortmund. de; Manuel (Oslo), Helmut Schwichtenberg (Mnchen), Andrea Sorbi (Siena), Ivan de Leon, email: mdeleon@imaff. cfmac. csic. es. or visit the Con­ Soskov (Sofia), Leen Torenvliet (Amsterdam), John Tucker (Swansea), ference Web page: http: I /www. bio21. bas. bg/ conference/. Johan van Benthem (Amsterdam/ Stanford), Peter van Emde Boas fEBRUARY 2005 NOTICES OF THE AMS 289 Mathematics Calendar

(Amsterdam), Jiri Wiedermann (Praha). in these areas to discuss recent results and directions for future Sponsors: ASL, EATCS, NW. research. lnformation:http: I lwww. illc. uva.nliCiEICiE2005 .htmlorcon­ Organizers: Evarist Gine, Vladimir Koltchinskii, Wenbo Li, Joel tact one of the organizers. Zinn. Information: http : I lwww. math. udel . edu;-wlil conflhdp05l. '' 12-july 23 DIMACS Reconnect Conferences 2005: Reconnect­ ing Teaching Faculty to the Mathematical Sciences Research * 20-july 1 5 Clay Mathematics Institute Summer School: Ricci Enterprise, DIMACS, CoRE Building, 4th Floor, Rutgers, the State Flow, 3-Manifolds and Geometry, MSRI, Berkeley, California. University of New Jersey, 96 Frelinghuysen Road, Piscataway, New Organizers: Gang Tian, John Lott, John Morgan, Bennett Chow, Jersey. Tobias Colding, Jim Carlson, David Ellwood, and Hugo Rossi. Description: About the Reconnect Conferences: These conferences Program: Designed for graduate students and mathematicians expose faculty teaching undergraduates to the mathematical sci­ within five years of their Ph.D., the program is organized around ences research enterprise by introducing them to a current research Ricci Flow and the Geometrization of 3-manifolds, particularly, the topic relevant to the classroom through a series of lectures by a recent work of Grisha Perelman. Perelman's work builds on earlier leading expert and involving them in writing materials useful in work of Thurston and Hamilton in a deep and original way. Topics the classroom. covered will include an introduction to Geometrization, Ricci Flow These workshops offer the opportunity for junior faculty as well (both geometric and analytic aspects), Minimal Surfaces and various as mid-level and senior faculty to advance to research questions fundamental results in topology and differential geometry. We will in a new area of the mathematical sciences. Participants will also also have courses dedicated to Perelman's work on general Ricci acquire materials and gain ideas for seminar presentations and for Flow as well as some results and applications in 3-dimensions. The undergraduate research projects. school will consist of three weeks of foundational courses and one These conferences are also aimed at reconnecting faculty to the week of mini-courses focusing on more advanced topics. mathematical sciences enterprise by involving them in a leading Lecturers: Jeff Cheeger, Bennett Chow, Tobias Colding, Richard research center, which is a consortium of Princeton University, Hamilton, Bruce Kleiner, John Lott, John Morgan, Gang Tian, and Rutgers University, AT&T Labs, Bell Labs/Lucent Technologies, NEC others. Research and Telcordia Technologies. There will be opportunities Funding: Funding is available to graduate students and postdoctoral to follow up after the conference by getting connected to DIMACS fellows (within 5 years of their Ph.D.). Standard support amounts researchers and other DIMACS programs throughout the year. will include funds for local expenses and accommodation plus Conference Organizers: Rochelle Leibowitz, Wheaton College, economy travel. email: rochelle_leibowi tz@wheatonma. edu; Fred S. Roberts, Rut­ Deadline: February 28, 2005. gers University, email: roberts@dimacs . rutgers . edu. Information: http: I lwww. claymath. orgl summerschool or con­ Description: In Summer 2005, DIMACS will hold two Satellite tact email: summerschool@claymath. org; tel.: 617-995-2600. "Reconnect Conferences". 1st Satellite Program: Montclair State University. Topic: Mathemat­ * 2 5-July 1 The Twentieth IEEE Symposium on Logic In Computer ics of Elections and Decisions. Principal Speaker: Donald G. Saari, Science (LICS 200S): Call for Workshop Proposals, Chicago, University of California, email: dsaari@uci. edu. Guest Speaker: Illinois. Michael A. Jones, Montclair State University, email: j onesm@mail. Description: The organizers have made arrangements for pre­ montclair. edu. Dates: June 12-June 18, 2005. and post-LICS workshops to be run in conjunction with the main 2nd Satellite Program: Spelman College. Topic: The Mathematics of conference. Possible dates are June 25 (the day before LICS) and Medical Imaging. Principal Speakers: Lawrence Shepp, Rutgers Uni­ June 30 and July 1 (the two days after LICS). versity, email: shepp@stat . rutgers. edu. Martin Lindquist, Colum­ Researchers and practitioners are invited to submit proposals bia University, email: [email protected]. Dates: July 17-July for workshops on topics. relating logic- broadly construed-to 23, 2005. computer science or related fields. Typically, LICS workshops Information: http : I ldimacs. rutgers . edulreconnectl. Or, con­ feature a number of invited speakers and a smaller number of tact the Reconnect Program Coordinator, at email: reconnect@ contributed presentations. dimacs. rutgers. edu, phone: 732-445-4304. Proposals: Should include: A short scientific summary and justifi­ cation of the proposed topic. This should include a discussion of '' 1 7-23 (NEW DATE) Algebraic Geometry and Number Theory, the particular benefits of the topic to the LICS ·community. Euler IMI, St. Petersburg, Russia. A discussion of the proposed format and agenda and the proposed Organizers: St. Petersburg Department of Steklov Institute of Math­ duration, which may vary from half a day to two days,and preferred ematics, Euler International Mathematical Institute, St. Petersburg dates. State University. Procedures for selecting participants and papers. Information: email: sergei@SV1005. spb. edu; http : I lwww. pdmi. Expected number of participants. ras .ruiEIMII2005IAGI. Potential invited speakers. Plans for dissemination (for example, special issues of journals). '' 20-24 The Fourth International Conference on High Dimensional Please note that it is expected that LICS workshop organizers should Probability (HOP), St. John's College, Santa Fe, New Mexico. be present to run their workshops. It is also assumed that normally Description: The conferences on High Dimensional Probability workshop organizers (though not necessarily participants) will continue a long tradition of conferences that began in the mid register for the LICS conference. seventies under the title of "Probability in Banach Spaces". Re­ Deadline: Proposals are due November 15, 2004, and should be markable advances have led to the creation or introduction of submitted electronically to: Philip Scott Workshops Chair, LICS powerful tools, such as randomization, decoupling, moment and 2005; email: phil@site .uottawa.ca. exponential inequalities, chaining, isoperimetry, concentration of Selection Committee: Phokion Kolaitis (LICS General Chair), measures and deviation probabilities which apply to areas well Prakash Panangaden (LICS 2005 Program Committee Chair), Phil beyond those for which they were created. Gaussian processes Scott (LICS Workshop Chair) and Alan Jeffrey and RadhaJagadeesan techniques and methods from probability in Banach spaces have (LICS 2005 Conference co-chairs). The results will be announced made a substantial impact on broad areas such as statistics, learn­ by November 30th, 2004. ing theory, theoretical computer sciences, convex geometry and statistical physics. The conference will bring together researchers * 27-july 1 Nonlinear Modelling and Control, An International

290 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Mathematics Calendar

Seminar, Nayanova University, Samara, Russia. Organizers: D. Andrica,"Babes-Bolyai", Univ.-Cluj-Napoca, email: Purpose: The seminar's aim is the exchange of information about dandrica@math . ubbcluj . ro; R. Iordanescu, Institute of Mathemat­ recent trends inmathematicalmodeling and control theory and their ics of the Romanian Academy-Bucharest, email: Radu. Iordanescu@ applications to various problems in physics, chemistry, biology, imar . ro; I. Mos, Department of Colleges for Teachers of the Univ. medicine, economy, and industrial concerns. of the West from TimisoarainDeva, email: mos@isj .hd. edu.ro; M. Call for Papers: Original papers related to the aim of the seminar are Puta, Univ.of the West, Faculty of Mathematics, Timisoara, email: solicited. Potential speakers should submit an abstract before April putal1lmath. uvt . ro. 30. The cover page should contain title, affilation, and email address of each author. Electronic submissions in LATEX are encouraged. '' 12-19 Small Deviation Probabilities and Related Topics, Euler Sponsors: Samara Municipal Nayanova Univ., Samara State Univ., IMI, St. Petersburg, Russia. Samara Scientific Center of RAS, Russian Academy of Natural Organizers: St. Petersburg Department of Steklov Institute of Sciences, International Federation of Nonlinear Analysts, Univ. Mathematics, Euler International Mathematical Institute. College Cork (Ireland). Topics: The aim of the conference is to bring together outstanding Organizers: A. Pokrovskii (Cork, Ireland), V. Sobolev and E. So­ researchers working on small deviation probabilities and in related mov(Samara, Russia). fields of probability analysis, and applied mathematics such as Languages: English and Russian. stochastic processes, approximation theory, quantization, spectral Information: V. Sobolev (sable@ssu. samara. ru) or seminar coor­ theory of operators etc. dinator: He. Gorelova (gorhel@ssu. samara.ru), Nayanova Univ., Information: email: smalldev@euler. pdmi. ras. ru; email: www. Molodogvardeiskaya 196, Samara, 443001, Russia. pdmi.ras.ru/EIMI/2005/sd/. '' 16-20 International Conference of Numerical Analysis and July 2005 Applied Mathematics 2005 (ICNAAM 2005), Hotel Esperides, · 2 2-2 7 AMSI Workshop entitled "Noncom mutative Geometry and Rhodes, Greece. Index Theory", Australian National University, Canberra, Australia. Organizer: European Society of Computational Methods in Sciences Information: http: I /wwwmaths. anu. edu. au/ events/ngi t05/. and Engineering (ESCMCE). Deadlines: Important Dates: Early Registration ends (i.e. fees paid · 24-27 International Symposium in Symbolic and Algebraic and a bank Slip has arrived fax:(++ 30210 94 20 091, ++ 30 2710 Computation ISSAC'2005, Beijing, China. 237 397) to the Secretary of ICNAAM or a Visa-Master-American Invited Talks: Bruno Buchberger, RISC-Linz, Austria; Bruno Salvy, Express Card has been charged): April30, 2005. Normal Registration INRIA, France; Wen-Tsun Wu, Chinese Academy of Sciences, China. ends (i.e. fees paid and a Bank Slip has arrived fax: (++ 30210 Information: http: I /www .mmrc. iss. ac . cnrissac2005/; email: 94 20 091, ++ 30 2710 237 397) to the Secretary of ICNAAM or issac2005@mmrc . iss . ac.cn. a Visa-Master-American Express Card has been charged): May 31, 2005. Late Registration ends (i.e. fees paid and a bank Slip has · 25-30 First Announcement: International Conference on Dif­ arrived fax: (++ 30210 94 20 091, ++ 30 2710 237 397) to the ference Equations, Special Functions and Applications, Munich, Secretary of ICNAAM or a Visa-Master-American Express Card has Germany. been charged): June 30, 2005. Submission of Extended Abstract: Description: This is a joint meeting ofthree communities working in June 30, 2005 (final date). Notification of acceptance: July 10, the fields of difference equations, special functions and applications 2005. Submission of the source files of the camera ready extended (OPSFA, ISDE, and SIDE). abstracts to Wiley-VCH: July 20, 2005 (final date). Submission of Scientific Committee: Richard Askey (USA), Bernd Aulbach (Ger­ the full paper for consideration for publication in the journals: many), Christian Berg (Denmark), Alexander Bobenko (Germany), September 30, 2005-November 30, 2005. The deadline for proposal Saber Elaydi (USA), Basil Grammaticos (France), Jarmo Hietarinta submission is May 31, 2005. Send to email: icnaam@uop .gr. (Finland), Mourad Ismail (USA), Nalini Joshi (Australia), Gerry Ladas Important Information: Papers for Sessions, Workshops or Mini­ (USA), Rupert Lasser (Germany), Lance Littlejohn (USA), Vassilis symposia should be submitted directly to the Sessions, Workshops Papageorgiou (Greece), Allan Peterson (USA), George Sell (USA), or Minisymposia organizers who also defines the deadline. After Alexander Sharkovsky (Ukraine), Sergei Suslov (USA), Pavel Winter­ the selection, the Sessions, Workshops or Minisymposia organisers nitz (Canada). must send the final accepted papers to the Secretary of ICNAAM Organizing Committee: Bernd Aulbach (bernd .aulbach@math. 2005. uni -augsburg. de), Rupert Lasser (lasser@gsf. de), Frank Nijhoff ([email protected] . ac. uk), Andreas Ruffing (ruffing@ma . tum. November 2005 de). Information: More information about registration, housing, dead­ * 2 5-December 1 Reform, Revolution and Paradigm Shifts in lines, etc. will be available shortly on the website of the conference Mathematics Education, Johor Bharu, Southern Malaysia (very at:http://www-m6 .ma .tum.de/-ruffing/Conference2005/. close to Singapore). Organizer: Mathematics Education into the 21st Century Project. September 2005 Program: November 25th: Arrivals & Welcome Reception (7.00 on). Includes food and drink. November 26th: FirstWorkingDay. Includes '5-11 The Seventh International Workshop on Differential Ge­ Official Opening Ceremony, Open Forum of Ideas. November 2 7 or ometry and its Applications, Deva, Romania. 28: All-day Conference Excursion to Malacca. November 30th: Gala Program: 50 minute lectures and 25 minute talks. Poster commu­ Dinner. December 1st: Last working day, morning only, lunch and nications are also envisaged. farewells. Main Topics: Riemannian geometry and generalizations, nonas­ Working Sessions: Plenary Speechs, Paper Presentations, Working sociative algebra methods in (finite- and infinite-dimensional) dif­ Group Meetings. ferential geometry, complex and quaternionic geometry, foliation Workshops: Open Forum of Ideas, SuperCourse Meetings for theory, critical point theory and applications. General Information and for Writers. Foreign Invited Speakers (confirmed until the end of August Information: Alan Rogerson; email: arogerson@inetia. pl. 2004): W. Bertram (France), C.-H. Chu (England), J. Dorfmeister (Germany), L. Funar (France), W. Kaup (Germany), 0. Kowalski (Czech Republic), E. Macias-Virgos (Spain), S. Marchiafava (Italy), N. Teleman (Italy).

FEBRUARY 2005 NOTICES OF THE AMS 291 New Publications Offered by the AMS

rangular systems; Some remarks; Examples; The classification; Algebra and Algebraic Appendix A. Abelian quadrangular systems; Bibliography. Geometry Memoirs of the American Mathematical Society, Volume 173, Number 818 December 2004, 99 pages, Softcover, ISBN 0-8218-3608-0, LC Moduli Spaces of 2004057482, 2000 Mathematics Subject Classification: 51£12, ME¥,,9IRS 16W10, 20£42, Individual member $34, List $56, Institutional Amcri£nnMathematlcnLSncicty Polynomials in Two member $45, Order code MEM0/173/818

Moduli Spaces Variables of Polynomials Javier Fernandez de Analysis in Two Variables Bobadilla, Universiteit Utrecht, Javier Fernandez de Bobadilla Netherlands Contents: Introduction; Automor­ ME¥,.9IRS Necessary AmerlconMathematlcalSociety Amerlcan~!nthom a llc a iSoclely phisms of the affine plane; A partition Conditions in on ([[x,y]; The geometry of the parti- tion; The action of Aut( ([ 2 ) on Necessary Dynamic ([[x, y]; The moduli problem; The moduli spaces; Appendix A. Conditions Canonical orders; Bibliography. in Dynamic Optimization Optimization Francis Clarke, University of Memoirs of the American Mathematical Society, Volume 173, Francis Clarke Number 817 Lyon, Villeurbanne, France December 2004, 136 pages, Softcover, ISBN 0-8218-3593-9, LC Contents: Introduction; Boundary 2004057486, 2000 Mathematics Subject Classification: 14R05, Amcncnn Mathema tical Society trajectories; Differential inclusions; 14R10, 14H10; 14£07, 14H20, Individual member $36, List The calculus of variations; Optimal $60, Institutional member $48, Order code MEM0/173/817 control of vector fields; The Hamil­ tonian inclusion; Bibliography; Index. An Algebraic Memoirs of the American Mathematical Society, Volume 173, ME~9IRS Number 816 American Mathema tical Society Structure for December 2004, 113 pages, Softcover, ISBN 0-8218-3591-2, LC An Algebraic Moufang 2004057483, 2000 Mathematics Subject Classification: 49K15, Structure for 49K05, Individual member $34, List $57, Institutional Moufang Quadrangles member $46, Order code MEM0/173/816 Quadrangles Tom De Medts, Ghent Tom De Medts University, Belgium Contents: Introduction; Definition; AmNknn Mathematical Society Some identities; From quadrangular systems to Moufang quadrangles; From Moufang quadrangles to quad-

292 NOTICES OF THE AMS VOLUME 52, NUMBER 2 New Publications Offered by the AMS

February 2005, 235 pages, Softcover, ISBN 0-8218-3361-8, LC Differential Equations 2004046440, 2000 Mathematics Subject Classification: 53C44, 53C21, 35K55, 57MSO, 35K57, 53C42, 53C43, 58]05, 53C35, 58]35, All AMS members $55, List $69, Order code • .. ' Geometric Evolution CONM/367 ' Equations Geometric Evolution Shu-Cheng Chang, National Geometry and Topology Equations Tsing Hua University, Hsinchu, Shu-Cheng Chang Bennett Chow Taiwan, Bennett Chow, Sun-Chin Chu Chang-Shou lin University of California San Spectral Geometry of Editors Diego, La Jolla, and Sun-Chin Manifolds with (~',' Chu and Chang-Shou Lin, Spectral Geometry of Boundary and National Chung Cheng Manifolds with Boundary and Decomposition University, Chia-Yi, Taiwan, of Manifolds Decomposition of Editors Bernheim BooB-Bavnbek GerdGrubb Manifolds KfZYSZtof P. Wojciechowski The Workshop on Geometric Evolution Equations was a gath­ Editors Bernheim BooE-Bavnbek, ering of experts that produced this comprehensive collection Roskilde University, Denmark, of articles. Many of the papers relate to the Ricci flow and Gerd Grubb, University of Hamilton's program for understanding the geometry and topology of 3-manifolds. Copenhagen, Denmark, and Krzysztof P. Wojciechowski, The use of evolution equations in geometry can lead to remarkable results. Of particular interest is the potential solu­ Indiana University -Purdue tion of Thurston's Geometrization Conjecture and the University, Indianapolis, Editors Poincare Conjecture. Yet applying the method poses serious been brought technical problems. Contributors to this volume explain some In recent years, increasingly complex methods have of geometric and topological problems of these issues and demonstrate a noteworthy deftness in the into play in the treatment of handling of technical areas. for partial differential operators on manifolds. This collection papers, resulting from a Workshop on Spectral Geometry of Mani­ Various topics in geometric evolution equations and related folds with Boundary and Decomposition of Manifolds, provides a fields are presented. Among other topics covered are minimal broad picture of these methods with new results. surface equations, mean curvature flow, harmonic map flow, Calabi flow, Ricci flow (including a numerical study), Kahler-Ricci Subjects in the book cover a wide variety of topics, from flow, function theory on Kahler manifolds, flows of plane curves, recent advances in index theory and the more general theory with convexity estimates, and the Christoffel-Minkowski problem. of spectral invariants on closed manifolds and manifolds boundary, to applications of those invariants in geometry, The material is suitable for graduate students and researchers topology, and physics. interested in geometric analysis and connections to topology. Papers are grouped into four parts: Part I gives an overview of Related titles of interest include The Ricci Flow: An Introduction. the subject from various points of view. Part II deals with spec­ This item will also be of interest to those working in geometry tral invariants, such as traces, indices, and determinants. Part III and topology. is concerned with general geometric and topological questions. Part N deals specifically with problems on manifolds with Contents: S. Angenent and J. Hulshof, Singularities at t = oo in singularities. The book is suitable for graduate students and equivariant harmonic map flow; S.-C. Chang, Recent develop­ researchers interested in spectral problems in geometry. ments on the Calabi flow; A. Chau, Stability of the Kahler-Ricci flow at complete non-compact Kahler Einstein metrics; This item will also be of interest to those working in analysis. B. Chow, A survey of Hamilton's program for the Ricci flow on Contents: Part I. Basic material-Reviews: D. V. Vassilevich, 3-manifolds; S.-C. Chu, Basic properties of gradient Ricci soli­ Spectral problems from quantum field theory; G. Esposito, tons; D. Garfinkle and J. Isenberg, Numerical studies of the Euclidean quantum gravity in light of spectral geometry; behavior of Ricci flow; P. Guan and X.-N. Ma, Convex solutions G. Grubb, Analysis of invariants associated with spectral of fully nonlinear elliptic equations in classical differential boundary problems for elliptic operators; Part II. Spectral geometry; R. Gulliver, Density estimates for minimal surfaces invariants and asymptotic expansions: G. Grubb, A resolvent and surfaces flowing by mean curvature; D. Knopf, An intro­ approach to traces and zeta Laurent expansions; Y. Lee, duction to the Ricci flow neckpinch; L. Ni, Monotonicity and Asymptotic expansion of the zeta-determinant of an invertible Kahler-Ricci flow; M. Simon, Deforming Lipschitz metrics into Laplacian on a stretched manifold; J. Park and smooth metrics while keeping their curvature operator non­ K. P. Wojciechowski, Agranovich-Dynin formula for the zeta­ negative; L.-F. Tam, Liouville properties on Kahler manifolds; determinants of the Neumann and Dirichlet problems; Part III. D.-H. Tsai, Expanding embedded plane curves; M.·T. Wang, Geometric and topological problems: H. U. Boden, Remarks on a class of solutions to the minimal surface system. C. M. Herald, and P. Kirk, The Calderon projector for the odd Contemporary Mathematics, Volume 367 signature operator and spectral flow calculations in 3-dimen­ sional topology; E. Leichtnam and P. Piazza, Cut-and-paste on foliated bundles; M. Lesch, The uniqueness of the spectral flow on spaces of unbounded self-adjoint Fredholm operators;

FEBRUARY 2005 NOTICES OF THE AMS 293 New Publications Offered by the AMS

M. Marcolli and B.-L. Wang, Variants of equivariant Seiberg­ Katz's p-adic Hilbert modular forms; The operators 8'13,i; The Witten Floer homology; Part W. Manifolds with singularities: operator V; The operator U; Applications to filtrations of P. Loya, Dirac operators, boundary value problems, and the b­ modular forms; Theta cycles and parallel filtration (inert case); calculus; V. E. Nazaikinskii, G. Rozenblum, A. Yu. Savin, and Functorialities; Integrality and congruences for values of zeta B. Yu. Sternin, Guillemin transform and Toeplitz representa­ functions; Numerical examples; Comments regarding values of tions for operators on singular manifolds; V. Nistor, zeta functions; References. Pseudodifferential operators on non-compact manifolds and Memoirs of the American Mathematical Society, Volume 173, analysis on polyhedral domains. Number 819 Contemporary Mathematics, Volume 366 December 2004, 100 pages, Softcover, ISBN 0-8218-3609-9, LC February 2005, 328 pages, Softcover, ISBN 0-8218-3536-X, LC 2004057485, 2000 Mathematics Subject Classification: 11G18, 2004053991, 2000 Mathematics Subject Classification: 19K56, 14G35, 11F33, 11F41, Individual member $34, List $56, 35S15,46L80,47A53, 58]30, 58]32, 58]35, 58]42, 81T20, Institutional member $45, Order code MEM0/ 173/ 819 83C45, All AMS members $71, List $89, Order code CONM/366 Probability ~ Conformal and M.~.~~~.~~.~ Harmonic Measures Conformally Conformal and on Laminations Harmonic Measures Invariant Processes on Laminations Associated with Associated with in the Plane Rational Maps Rational Maps Gregory F. Lawler, Cornell Vadlm A. Kalmanovlch Mikhail Lyubich University, Ithaca, NY {) Vadim A. Kaimanovich, Universite Rennes, France, and Theoretical physicists have predicted Mikhail Lyubich, SUNY at that the scaling limits of many two­ Stony Brook, NY dimensional lattice models in statistical physics are in some sense Contents: Introduction; Affine and hyperbolic laminations; conformally invariant. This belief has Measures and currents on laminations; Laminations associated allowed physicists to predict many with rational maps; Measures on laminations associated with quantities for these critical systems. The nature of these rational maps; Appendix A. Laminations associated with scaling limits has recently been described precisely by using Kleinian groups; List of notations; Bibliography. one well-known tool, Brownian motion, and a new construc­ Memoirs of the American Mathematical Society, Volume 173, tion, the Schrarnm-Loewner evolution (SLE). Number 820 This book is an introduction to the conformally invariant December 2004, 119 pages, Softcover, ISBN 0-8218-3615-3, LC processes that appear as scaling limits. The following topics are 2004057484, 2000 Mathematics Subject Classification: 37F10, covered: stochastic integration; complex Brownian motion and 37F35, 57R30; 37D40, 37F30, 53C12, 57M50, 58]65, measures derived from Brownian motion; conformal mappings Individual member $35, List $58, Institutional member $46, and univalent functions; the Loewner differential equation and Order code MEM0/ 173/ 820 Loewner chains; the Schrarnm-Loewner evolution (SLE), which is a Loewner chain with a Brownian motion input; and applications to intersection exponents for Brownian motion. The prerequi­ sites are first-year graduate courses in real analysis, complex Number Theory analysis, and probability. The book is suitable for graduate students and research mathematicians interested in random processes and their applications in theoretical physics. Hilbert Modular MEJYI9IRS This item will also be of interest to those working in analysis --Amedcan Mothcmutkul S<>< 1cty Forms: mod p and and mathematical physics. Contents: Some discrete processes; Stochastic calculus; Hilbert Modular p-Adic Aspects Complex Brownian motion; Conformal mappings; Loewner Forms: modp F. Andreatta, University Degli differential equation; Brownian measures on paths; Schramm­ and p-Adic Aspects Studi, Padova, Italy, and E. Z. Loewner evolution; More results about SLE; Brownian F. Andreatta intersection exponent; Restriction measures; Hausdorff dimen­ E. Z. Goren Goren, McGill University, sion; Hypergeometric functions; Reflecting Brownian motion; Montreal, PQ, Canada Bibliography; Index; Index of symbols.

Amer~c•n Mothcmahcal Society Contents: Introduction; Notations; Mathematical Surveys and Monographs, Volume 114 Moduli spaces of abelian varieties with March 2005, approximately 242 pages, Hardcover, ISBN 0- real multiplication; Properties of (j; 8218-3677-3, 2000 Mathematics Subject Classification: 30C35, Hilbert modular forms; The q -expan­ 31A15, 60H30, 60]65, 81T40, 82B27, All AMS members $47, sion map; The partial Hasse invariants; Reduceness of the List $59, Order code SURV/114 partial Hasse invariants; A compactification of 9Jl(k, JlpN )Kum; Congruences mod pn and Serre's p-adic modular forms;

294 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Classified Advertisements Positions available, items for sale, services available, and more

WILLIAMS COLLEGE MASSACHUSETTS Department of Mathematics MICHIGAN WILLIAMS COLLEGE The Williams College Department of Math­ MICHIGAN STATE UNIVERSITY Department of Mathematics ematics and Statistics invites applications East Lansing, Ml48824 for one tenure-track position in statistics, proMSc Program in The Williams College Department of Math­ Industrial Mathematics ematics and Statistics invites applications beginning fall 2005, at the rank of assis­ for one tenure-track position in mathe­ tant professor (in an exceptional case, a Direct your students toward one of the matics, beginning fall2005, at the rank of more advanced appointment may be con­ professional M.Sc. programs. Industry assistant professor (in an exceptional case, sidered). We are seeking a highly quali­ needs business-savvy mathematicians. See a more advanced appointment may be con­ fied candidate who has demonstrated ex­ http://www.sciencemasters.com/. sidered). We are seeking a highly quali­ cellence in teaching and research, and who 000019 fied candidate who has demonstrated ex­ will have a Ph.D. by the time of appoint­ cellence in teaching and research, and who ment. will have a Ph.D. by the time of appoint­ Williams College is a private, residen­ ment. MISSISSIPPI tial, highly selective liberal arts college Williams College is a private, residen­ with an undergraduate enrollment of ap­ tial, highly selective liberal arts college UNIVERSITY OF MISSISSIPPI with an undergraduate enrollment of ap­ proximately 2,000 students. The teaching Department of Mathematics proximately 2,000 students. The teaching load is two courses per 12-week semester load is two courses per 12-week semester and a winter term course every other Jan­ The department of mathematics seeks to and a winter term course every other Jan­ uary. In addition to excellence in teaching, fill a tenure-track assistant professor po­ uary. In addition to excellence in teaching, an active and successful research program sition beginning August 2005. Ole Miss has 13,513 full time students on the Ox­ an active and successful research program is expected. is expected. ford Campus. The Department of Mathe­ To apply, please send a vita and have matics has 16 tenure-track faculty, 7 in­ To apply, please send a vita and have three letters of recommendation on teach­ structors, 51 undergraduate majors, 11 three letters of recommendation on teach­ ing and research sent to the Hiring Com­ M.S. students, and 20 Ph.D. students. All ing and research sent to the Hiring Com­ mittee, Department of Mathematics and candidates should have a Ph.D. (or equiv­ mittee, Department of Mathematics and Statistics, Williams College, Williamstown, alent) by August 2005 in mathematics, Statistics, Williams College, Williamstown, statistics or the mathematical sciences, MA 01267. Teaching and research state­ MA 01267. Teaching and research state­ ments are also welcome. Evaluations of and outstanding potential in both research ments are also welcome. Evaluations of and teaching. Candidates whose research applications will begin on or after No­ applications will begin on or after No­ vember 15 and will continue until the po­ interests coincide with those of existing vember 15 and will continue until the po­ faculty are sought in the areas of statistics sition is filled. Williams College is dedi­ sition is filled. Williams College is dedi­ and analysis. Applicants in statistics cated to providing a welcoming intellectual cated to providing a welcoming intellectual should have demonstrated research ex­ environment for all of its faculty, staff environment for all of its faculty, staff cellence in bioinformatics or semipara­ and students; as an EEO/ AA employer, and students; as an EEO/ AA employer, metric models or nonparametric methods. Williams especially encourages applica­ Williams especially encourages applica­ The successful applicant will teach 6 hours tions from women and minorities. For tions from women and minorities. For per semester and is also expected to con­ more information on the Department of more information on the Department of duct a vigorous research program. Mathematics and Statistics, visit http://www.williams.edu/Mathematics. Mathematics and Statistics, visit Applicants should complete the appli­ 000151 http://www.williams.edu/Mathematics. cation form, cover letter and curriculum 000152 vitae online at http: I /jobs. o l emi ss. edu.

Suggested uses for classified advertising are positions available, books or issue-February 25, 2005; june/ July 2005 issue-April 27, 2005; August lecture notes for sale, books being sought, exchange or rental of houses, 2005 issue-May 26, 2005; September 2005 issue-June 27, 2005. and typing services. U.S. laws prohibit discrimination in employment on the basis of color, The 2005 rate is $100 per inch or fraction thereof on a single column (one­ age, sex, race, religion, or national origin. "Positions Available" inch minimum), calculated from top of headline. Any fractional text of 1/ 2 advertisements from institutions outside the U.S. cannot be published inch or more will be charged at the next inch rate. No discounts for mul­ unless they are accompanied by a statement that the institution does not tiple ads or the same ad in consecutive issues. For an additional $10 discriminate on these grounds whether or not it is subject to U.S. laws. charge, announcements can be placed anonymously. Correspondence will Details and specific wording may be found on page 1373 (vol. 44). be forwarded. Situations wanted advertisements from involuntarily unemployed Advertisements in the "Positions Available" classified section will be set mathematicians are accepted under certain conditions for free publication. with a minimum one-line headline, consisting of the institution name Call toll-free 800-321-4AMS (321-4267) in the U.S . and Canada or above body copy, unless additional headline copy is specified by the ad­ 401-455-4084 worldwide for further information. vertiser. Headlines will be centered in boldface at no extra charge. Ads will Submission: Promotions Department, AMS, P.O. Box 6248, Providence, appear in the language in which they are submitted. Rhode Island 02940; or via fax: 401-331-3842; or send email to There are no member discounts for classified ads. Dictation over the [email protected]. AMS location for express delivery packages is telephone will not be accepted for classified ads. 201 Charles Street, Providence, Rhode Island 20904. Advertisers will be Upcoming deadlines for classified advertising are as follows: March 2005 billed upon publication. issue-December 29, 2004; April 2005 issue-January 28, 2005; May 2005

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A one-page statement on the applicant's are required. The review will begin No­ research interest, three letters of recom­ vember 2004, and continue until the po­ CANADA mendation about the applicant's research, sitions are filled. Submit a letter of inter­ and at least one letter of recommendation est, full curriculum vitae, transcripts, and UNIVERSITY OF ALBERTA about the applicant's teaching must be three letters of reference to: Mathematics Department of Mathematical and sent to: Education Search Committee, Department Statistical Sciences Tenure-track Department of Mathematics of Mathematics and Statistics, Sam Hous­ University Faculty Award Position Chairman of Tenure-Track Search ton State University, Box 2206, Huntsville, The Department of Mathematical and Sta­ Committee TX 77341-2206. 305 Hume Hall tistical Sciences is actively seeking to nom­ University, MS 38677 Sam Houston State University is an inate a candidate for an NSERC University EEO/ AAP employer. The letters of recommendation must be Faculty Award in the fall2005 competition. submitted directly by the referees. In­ 000031 The University Faculty Award was cre­ quiries about this position may be sent to ated by NSERC to encourage Canadian uni­ versities to appoint outstanding women mdepart@o l emi 55. edu. Screening of ap­ UNIVERSITY OF TEXAS AT EL PASO plications will begin on January 31, 2005, and aboriginal researchers to tenure-track Mathematical Sciences and will continue until the position is filled. positions in science and engineering. Fur­ The University of Mississippi is an Assistant/Associate Professor (Pure ther information on the program can be EEO/ AA/Title VI/Title IX/ Section Math) found be found at the following web page: 504/ADA/ ADEA employer. http://www.n5erc.ca/profes5ors_e. 000032 DESCRIPTION: The Department of Mathe­ asp?nav=profnav&lbi=c7/. matical Sciences seeks to hire a tenure­ The nominee will have an outstanding track assistant or associate professor in al­ record of research and publication. We are gebra, analysis, combinatorics, or topology. particularly interested in a field related to NEW YORK The successful candidate will show demon­ an area of existing or emerging strength strated research and teaching potential, in the department, although other areas ST.JOHN'S UNIVERSITY with preference given to those whose re­ will be considered too. Some areas of re­ Assistant Professor of Mathematics search may lead to collaboration with that search excellence, recently highlighted by of current faculty members. the University of Alberta Faculty of Science, Bringing knowledge to life. Working for a include: algebra, functional analysis, fluid better world. The University of Texas at El Paso has dynamics, statistics, mathematical biol­ St. John's University, founded by the an enrollment of almost 19,000 students, ogy and scientific computing. The candi­ Vincentian Fathers, one of the largest and is located in high, mountainous coun­ date will also have a strong commitment Catholic universities in the nation, cur­ try in the Chihuahuan Desert along the to and aptitude for teaching undergradu­ rently has one tenure-track position avail­ US-Mexico border. El Paso and its sister city ate students, and will be expected to su­ able in the Dept. of Mathematics & Com­ Ciudad Juarez have a combined population pervise graduate theses. puter Science of St. John's College. of about two million. The Department of This tenure-track appointment is sched­ The position is at the assistant profes­ Mathematical Sciences, one of the larger uled to begin on or near July 1, 2006. sor rank in mathematics on the Queens departments on campus, offers bachelor's Applications should be sent to the Chair campus for September 2005. Applicants and master's degrees in mathematics and at the address below. Applications should should possess a Ph.D. in mathematics statistics, as well as a Master of Arts in include a curriculum vitae and research and a commitment to both teaching and Teaching Mathematics degree. The Uni­ and teaching profiles, outlining experi­ research. versity has recently been awarded a pres­ ence and/or interests. Candidates should We offer competitive compensation, ex­ tigious NSF ADVANCE grant in the amount arrange for at least three confidential let­ cellent benefits and talented professional of 3.5 million dollars to fund 26 graduate ters of reference to be sent to the Chair at colleagues. To apply, please send letter of research assistants over 5 years to support the address below: application, curriculum vitae, three letters Anthony To-Ming Lau, Chair of reference, and graduate transcripts to: research teams with a female faculty lead investigator. Department of Mathematical and SEARCH COMMITTEE, Dept. of Mathemat­ Statistical Sciences ics & Computer Science SJH 334, St. John's QUALIFICATIONS REQUIRED: A doctor­ University of Alberta University, 8000 Utopia Pkwy, Queens, NY ate in mathematics is required. Edmonton, Alberta, Canada 11439; email: [email protected]. APPLICATION PROCEDURE: Send a let­ T6G 2G1 St. John's is an Equal Opportunity Em~ ter of interest, a complete curriculum vitae The closing date for applications is March ployer and encourages applications from and three letters of recommendation to the 1, 2005. Early applications are encouraged. women and minorities. Faculty Hiring Committee, Department of The University of Alberta hires on the 000033 Mathematical Sciences, UTEP, El Paso, TX basis of merit. We are committed to the 79968-0514. Consideration of applicants principle of equity in employment. We wel­ will begin immediately and continue until come diversity in the workplace and en­ TEXAS the position is filled or the search is aban­ courage applications from all qualified in­ doned. The University of Texas at El Paso dividuals, including aboriginal peoples, SAM HOUSTON STATE UNIVERSITY does not discriminate on the basis of race, persons with disabilities, and members of Mathematics Position in Mathematics color, national origin, sex, religion, age, visible minorities. According to NSERC reg­ Education disability, veteran's status or sexual ori­ ulations applicants must be Canadian cit­ entation in employment or in the provision izens or permanent residents of Canada. The Department of Mathematics and Sta­ of services. 00002 5 tistics is seeking to fill two or more assis­ 000034 tant/associate tenure-track positions in mathematics education. Candidates must have the equivalent of a master's degree in mathematics and hold a doctorate in mathematics education or equivalent. Teaching, service, and scholarly activities

296 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Meetings & Conferences oftheAMS

IMPORTANT INFORMATION REGARDING MEETINGS PROGRAMS: AMS Sectional Meeting programs do not appear in the print version of the Notices. However, comprehensive and continually updated meeting and program information with links to the abstract for each talk can be found on the AMS website. See http: I jwww. ams . org/meeti ngs/. Programs and abstracts will continue to be displayed on the AMS website in the Meetings and Conferences section until about three weeks after the meeting is over. Final programs for Sectional Meetings will be archived on the AMS website in an electronic issue of the Notices as noted below for each meeting.

James J. Zhang, University of Washington, Searching for Bowling Green, quantum projective spaces. Kentucky Special Sessions Advances in the Study of Wavelets and Multiwavelets (Code: Western Kentucky University SS SA), Douglas P. Hardin, Vanderbilt University, and March 18-19, 2005 Bruce Kessler, Western Kentucky University. Friday - Saturday Commutative Ring Theory (Code: SS llA), Michael C. Axtell, Wabash College, and Joe Alyn Stickles, Jr., Uni­ Meeting #1 004 versity of Evansville. Southeastern Section Dynamic Equations on Time Scales and Applications (Code: Associate secretary: Matthew Miller SS 3A), Ferhan M. Atici and Daniel C. Biles, Western Ken­ Announcement issue of Notices: January 2005 tucky University, and Billur Kaymakcalan, Georgia South­ Program first available on AMS website: February 3, 2005 ern University. Program issue of electronic Notices: March 2005 Geometric Topology and Group Theory (Code: SS 14A), Issue of Abstracts: Volume 26, Issue 2 Jens E. Harlander, Western Kentucky University. Deadlines Graph Theory (Code: SS 2A), Mustafa Atici, Western Ken­ For organizers: Expired tucky University. For consideration of contributed papers in Special Sessions: Hopf Algebras and Related Topics (Code: SS 1 OA), David E. Expired Radford, University of Illinois at Chicago, and Bettina For abstracts: January 25, 2005 Richmond, Western Kentucky University. The scientific information listed below may be dated. For Knot Theory and Its Applications (Code: SS 4A), Yuanan the latest information, see www. ams. o rg/amsmtgs/ Diao, University of North Carolina, Charlotte, and Claus section a 1 . html. Ernst, Western Kentucky University. L-Functions (Code: SS 9A), Heather Russell, Nilabh Sanat, Invited Addresses and Dominic Lanphier, Western Kentucky University. Bennett Chow, University of California San Diego, Title to Nonlinear Analysis and Applied Mathematics (Code: SS 13A), be announced. Robert J. McCann, University of Toronto, and Daniel P. Robert McCann, University of Toronto, Optimal convergence Spirn, University of Minnesota. rates for the fastest conservative nonlinear diffusions. Numerical Analysis, Approximation, and Computational M. Susan Montgomery, University of Southern California, Complexity: Interdisciplinary Aspects (Code: SS lA), David Some applications of group theory to classifying Hopf Benko, Western Kentucky University, and Steven B. algebras. Damelin, Georgia Southern University. fEBRUARY 2005 NOTICES OF THE AMS 297 Meetings & Conferences

Partial Differential Equations and Their Applications (Code: Asymptotic Behavior of Evolution Equations (Code: SS 4A), SS 12A), Zhongwei Shen and Changyou Wang, University Gaston M. N'Guerekata, Morgan State University, and of Kentucky. Nguyen Van Minh, James Madison University. Recent Advances in Noncommutative Algebra (Code: SS Designs, Codes, and Geometries (Code: SS SA), James A. 15A), Ellen E. Kirkman, Wake Forest University. Davis, University of Richmond, Keith E. Mellinger, Uni­ Representation Theory (Code: SS 6A), Markus Hunziker, versity of Mary Washington, and Qing Xiang, University of Delaware. University of Georgia. Frontiers on Complex Fluid Flows: Analytic and Semigroups of Operators and Applications (Code: SS 7A), Computational Methods (Code: SS 7A), L. Pamela Cook Khristo Boyadzhiev, Ohio Northern University, Lan and Louis F. Rossi, University of Delaware. Nguyen, Western Kentucky University, and Quoc-Phong Vu, Ohio University. Geometric Analysis (Code: SS 12A), Xiuxiong Chen, Uni­ versity of Wisconsin, Madison, Pengfei Guan, McMaster Topology, Convergence, and Order, in Honor of Darrell University, Zhiqin Lu, University of California Irvine, and Kent (Code: SS 8A), Gary Richardson, University of Cen­ Jeff A. Viaclovsky, Massachusetts Institute of Technology. tral Florida, and Thomas A. Richmond, Western Kentucky University. High Dimensional Probability (Code: SS 6A), Wenbo Li, University of Delaware, and joel Zinn, Texas A&M University. Homotopy Theory (in Honor ofDonald M. Davis's and Mar­ tin Bendersky's 60th Birthdays) (Code: SS lA), Kenneth G. Newark, Delaware Monks, University of Scranton, and W. Stephen Wilson, University of Delaware Johns Hopkins University. Integral and Operator Equations (Code: SS 13A), Charles W. April2-3, 2005 Groetsch, University of Cincinnati, and M. Zuhair Nashed, Saturday - Sunday University of Central Florida. Mathematical Biology (Code: SS 8A), David A. Edwards, Uni­ Meeting #1 005 versity of Delaware. Eastern Section Mathematical Methods for Efficient Simulation of Stochas­ Associate secretary: Lesley M. Sibner tic Nonlinear Optical Systems (Code: SS 15A), Richard 0. Announcement issue of Notices: February 2005 Moore, New Jersey Institute of Technology, and Tobin A. Program first available on AMS website: February 17, 2005 Driscoll, University of Delaware. Program issue of electronic Notices: April 2005 Issue of Abstracts: Volume 26, Issue 2 Mathematical Methods in Electromagnetic Wave Propaga­ tion (Code: SS 3A), Fioralba Cakoni and Peter B. Monk, Uni­ Deadlines versity of Delaware. For organizers: Expired Probabilistic Paradigms in Combinatorics (Code: SS 16A), For consideration of contributed papers in Special Sessions: Joshua N. Cooper, Courant Institute of Mathematics, NYU, Expired and Jozef Skokan, Universidade de Sao Paulo. For abstracts: February 8, 2005 Recent Progress in Thin Fluid Flows (Code: SS llA), Richard J. Braun, University of Delaware. The scientific information listed below may be dated. For Singular Analysis and Spectral Theory of Partial Differen­ the latest information, see www. ams. o rg/amsmtgs/ tial Equations (Code: SS 2A), juan B. Gil, Pennsylvania State secti anal . html. University, Altoona, and Gerardo A. Mendoza, Temple University. Invited Addresses Spectral and High-Order Discretization Methods for Partial Xiuxiong Chen, University of Wisconsin, Madison, Title to Differential Equations (Code: SS 14A), Tobin A. Driscoll, be announced. University of Delaware. Anna C. Gilbert, AT&T Labs-Research, Analysis, approxi­ Symmetry Methods for Partial Differential Equations (Code: mations, and algorithms. SS lOA), Philip Broadbridge, University of Delaware, and Alexander Lubotzky, Hebrew University of Jerusalem, Danny Arrigo, University of Central Arkansas. Counting primes, groups, and manifolds. Accommodations Lorenz Schwachhoefer, University of Dortmund, Special Participants should make their own arrangements directly symplectic connections. with a hotel of their choice as early as possible. Special rates Special Sessions have been negotiated with the hotels listed below. Rates quoted do not include sales tax of 8%. The AMS is not Arithmetic Groups and Related Topics (Code: SS 9A), Alexan­ responsible for rate changes or for the quality of the der Lubotzky, Hebrew University of Jerusalem, and accommodations. When making a reservation, participants Andrei Rapinchuk, University of Virginia. should state that they are with the American Mathemat-

298 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Meetings & Conferences ical Society (AMS) Meeting at the University of Delaware Registration and Meeting Information group. Cancellation and early checkout policies vary; be The meeting is on the main campus of the University of sure to check when you make your reservation. Delaware, Newark, Delaware. Sessions and Invited Ad­ Sleep Inn Hotel, 630 S. College Ave., Newark, DE 19713; dresses will take place in the Ewing, Kirkbride, Purnell, and phone: 302-453-1700, fax: 302-453-1710; $59/single or Smith Halls. double; free deluxe continental breakfast, free high-speed The registration desk will be in Purnell Hall and will be Internet, in-room minirefrigerator and coffeemaker; about open Saturday, April 2, 7:30 a.m. to 4:00 p.m., and Sun­ 1 mile to the meeting site (across from the stadium). Dead­ day, April 3, 8:00 a.m. to noon. Fees are $40 for AMS or line for reservations is March 11, 2005; cite group CMS members, $60 for nonmembers; and $5 for stu­ #100924. Be sure to check cancellation and early check­ dents/unemployed/emeritus, payable on site by cash, out policies. check, or credit card. Super 8 Motel, 268 East Main St., Newark, DE 19711; phone: 302-737-5050, fax: 302-737-4089; $48.88/single Social Event or double, free continental breakfast; about 1/2 mile to All participants are invited to a reception on Saturday the meeting site. This is a small hotel with a limited evening. The AMS thanks the Department of Mathematics number of rooms available. Deadline for reservations is and the university for their hospitality. March 1, 2005; cite group code CGCGAM. Be sure to check cancellation and early checkout policies. Travel and Campus Map Howard Johnson Inn & Suites, 1119 South College The University of Delaware is located in downtown Newark Ave., Newark, DE 19713; phone: 302-368-8521, fax: 302- and is approximately 3 5 miles from Philadelphia, 70 miles 368-9868; $56/single king bed, $59/two queen beds, from Baltimore, MD, and 105 miles from Washington, DC. $69/suite (two double beds plus separate parlor); free A campus map, parking map, a campus "walkabout" map, deluxe continental hot breakfast (eggs/waffles/fruit), and Newark area map can be found at http: I /www. ude l . in-room refrigerator/ microwave/coffeemaker; about edu/main/campuses/printmap.html. 1. 5 miles to the meeting site. Deadline for. reservations The closest airport is Philadelphia International Air­ is March 11, 2005; cite group #11-53. Be sure to check port (PHL) and is serviced by all major airlines. Delta Air cancellation and early checkout policies. Unes has been selected as the official airline for this meet­ Courtyard Newark, 400 Pencader Way, Newark, DE ing because of economical rates and convenient schedules. 19716; phone: 302-737-0900, fax: 302-737-0990; $109/sin­ The following specially negotiated rates are available for gle or double; restaurant open for breakfast and dinner, this meeting exclusively for mathematicians and their in-room coffeemaker and refrigerator, about 1/2 mile to families for the period March 30, 2005, through April 6, the meeting site. Deadline for reservations is March 3, 2005. Other restrictions/discounts may apply, and seats 2005. Be sure to check cancellation and early checkout are limited. penalties. Delta Air Lines is offering: • A 5% discount off Delta's published round-trip fares Food Service within the continental United States, excluding A, D, I, U Information will be available at the meeting. and T classes of service. • A 10% discount off Delta's domestic published unre­ Local Information stricted round-trip coach fares (Y06/YR06) rates. No ad­ The university's webpage is http: I jwww. ude l . edu; see vance reservations or ticketing is required. the "Travel" section below for map links to the campus and • An additional 5% bonus discount if you purchase surrounding area. your ticket 60 days or more prior to your departure through Meeting Network Reservations or your travel agent; online Other Activities not applicable. Book Sales: Examine the newest titles from the AMS! Many To take advantage of these discounts and make imme­ of the AMS books will be available at a special 50% discount diate reservations, visit http: I jwww. delta. com or call available only at the meeting. Complimentary coffee will Delta Meeting Network at 1-800-241-6760 between be served courtesy of AMS Membership Services. 8:00a.m. and 11:00 p.m. Eastern Standard Time, Monday AMS Editorial Activity: An acquisitions editor from through Sunday, referencing File Number 205779A. the AMS book program will be present to speak with Shuttle service between the Philadelphia International prospective authors. If you have a book project that you Airport and Newark, Delaware (to your hotel, campus, or would like to discuss with the AMS, please stop by the book other location and back), can be arranged through Delaware exhibit. Express Shuttle (phone 800-648-5466 or online at http://www.delexpress.com) for about $36 (plus tip) Parking each way for individuals. Parking will be available in the Trabant Parking garage at the corner of West Main and Elkton (next to the Trabant Getting to the University by Car University Center). The cost is $.55/hour with a maximum From the north: Take I95 South to Delaware Exit 1B, Route of $3/day. 896 North, which becomes South College Avenue at the

FEBRUARY 2005 NOTICES OF THE AMS 299 Meetings & Conferences intersection of Route 4. Continue on South College Avenue Invited Addresses (past Fred P. Rullo Stadium, the Bob Carpenter/Sports Nikolai Ivanov, Michigan State University, Title to be Convocation Center, Delaware Stadium, and the Delaware announced. Field House) until you come to Main Street. Turn left onto West Main Street; the Trabant Garage is on your left just Mattias Jonsson, University of Michigan, Title to be past Trabant University Center. announced. From the south: Take I95 North to Delaware Exit 1, Route Nicolas Monod, University of Chicago, Title to be 896 North, which becomes South College Avenue at the in­ announced. tersection of Route 4. Continue on South College Avenue Hee Oh, California Institute of Technology, Title to be (past Fred P. Rullo Stadium, the Bob Carpenter/Sports announced. Convocation Center, Delaware Stadium, and the Delaware Field House) until you come to Main Street. Turn left onto Special Sessions West Main Street; the Trabant Garage is on your left just past Trabant University Center. Classical and Differential Galois Theory (Code: SS 3A), From the west: Take the Pennsylvania Turnpike East to Lourdes juan and Arne Ledet, Texas Tech University, and Route 283 South. Continue on Route 283 South, which be­ Andy R. Magid, University of Oklahoma. comes Route 30 East outside of Lancaster, to Route 896 Differential Geometry and Its Applications (Code: SS 2A), South. As you reach campus and cross the railroad tracks, Josef F. Dorfmeister, Munich University of Technology, immediately turn left onto Delaware Avenue, right (at the Magdalena D. Toda, Texas Tech University, and Hongyou second traffic light) onto South College Avenue, then left Wu, Northern Illinois University. onto West Main Street. The Trabant Garage is on your left Discrete Groups, Homogeneous Spaces, Rigidity (Code: SS just past Trabant University Center. 15A), Alex Gorodnik, University of Michigan, Ann Arbor, Information for International Participants Hee Oh, California Institute of Technology, and Nicolas Monod, University of Chicago. International participants should view this important information about traveling to the United States: Extinction, Periodicity, and Chaos in Population and Epidemic http://www7.nationalacademies.org/visas/ Models (Code: SS lOA), Linda J. S. Allen, Texas Tech Uni­ Traveling_to_US.html. versity, Sophia Ruey-Jen Jang, University of Louisiana at Lafayette, and Lih-Ing W. Roeger, Texas Tech University. Weather Future Directions in Mathematical Systems and Control Weather conditions in Newark during early April are cool to Theory (Code: SS llA), David Gilliam and W. P. Dayawansa, moderate, with nighttime lows of about 40°F and daytime Texas Tech University. highs around 60°F. Graph Theory(Code: SS 12A), John C. George, Eastern New Mexico University, and Walter D. Wallis, Southern Illinois University at Carbondale. Lubbock, Texas Homological Algebra and Its Applications (Code: SS 4A), Alex Texas Tech University Martsinkovsky, Northeastern University, and Mara D. Neusel, Texas Tech University. ApriiS-1 0, 2005 Invariants of Links and 3-Manifolds (Code: SS 8A), Friday - Sunday Mieczyslaw Krzysztof Dabkowski, University of Texas at Dallas, Razvan Gelca, Texas Tech University, and Jozef Meeting #1 006 Henryk Przytycki, George Washington University. Central Section Associate secretary: Susan J. Friedlander Partial Differential Equation and Its Application in Biomed­ Announcement issue of Notices: February 2005 ical Study (Code: SS 16A), Jay R. Walton, Texas A&M Uni­ Program first available on AMS website: February 24, 2005 versity, and Padmanabhan Seshaiyer and Akif Ibragimov, Program issue of electronic Notices: April 2005 Texas Tech University. Issue of Abstracts: Volume 26, Issue 3 Real Algebraic Geometry (Code: SS 6A), Anatoly Korcha­ gin and David Weinberg, Texas Tech University. Deadlines Recent Advances in Complex Function Theory(Code: SS SA), For organizers: Expired Brock Williams, Roger W. Barnard, and Kent Pearce, Texas For consideration of contributed papers in Special Sessions: Tech University. Expired For abstracts: February 15, 2005 Statistical Image Processing and Analysis and Applications (Code: SS 13A), Victor Patrangenaru, Texas Tech University. The scientific information listed below may be dated. For Theory and Application of Stochastic Differential Equations the latest information, see www. ams. org/amsmtgs/ (Code: SS 9A), Edward]. Allen, Texas Tech University, and sectional . html. Armando Arciniega, University of Texas at San Antonio.

300 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Meetings & Conferences

Topology of Continua (Code: SS lA), Wayne Lewis, Texas AMS Editorial Activity: An acquisitions editor from Tech University. the AMS book program will be present to speak with Topology ofDynamical Systems (Code: SS 7A), Brian Raines, prospective authors. If you have a book project that you Baylor University. would like to discuss with the AMS, please stop by the book exhibit. Undergraduate and Graduate Student Research (Code: SS 14A), Ali Khoujmane, Edward W. Swim, Edward J. Allen, Parking and Padmanabhan Seshaiyer, Texas Tech University. Parking on campus is regulated during weekdays. Upon Poster Session entering campus inform the attendant at the entry station that you are here for the mathematics conference. You Poster session organized by Ali Khoujmane and Mara D. will be directed either to visitor parking or to metered Neusel, Texas Tech. parking. The Broadway entrance is the main entrance to Accommodations campus, with the Mathematics Building on the northwest side of the circle. On weekends parking is available in any Participants should make their own arrangements directly marked parking spot not indicated as reserved 24 hours. with the hotel of their choice and state that they will be attending the AMS meeting. The AMS is not responsible Registration and Meeting Information for rate changes or for the quality of the accommoda­ The registration desk will be open 8:00 a.m. to 4:00 p.m. tions. Rates quoted do not include sales tax. Hotels have on Friday, and 8:00 a.m. to noon on Saturday, in the Math­ varying cancellation or early checkout penalties; be sure ematics Building. to ask for details when making your reservation. Registration Fees: (payable on-site only) $40/AMS mem­ Four Points Sheraton, 505 Avenue Q, Lubbock, TX bers; $50/ nonmembers; $5/emeritus members, students, 79401; phone: 806-747-0171, fax: 806-747-9243. Group rate or unemployed mathematicians. Fees are payable by cash, of $58 per night plus 13% local tax. Doubles and kings re­ check, VISA, MasterCard, Discover, or American Express. served. Hotel provides complimentary 24-hour airport shuttle. Near Civic Center and Buddy Holly Walk of Fame. Social Event Approximately one mile east of campus. Deadline for The Department of Mathematics and Statistics will host a reservations is March 8. Limited shuttle service to and reception for all conference participants Friday evening, from the campus will be provided by the Department of April 8, 2005, at a time and location to be announced. Mathematics and Statistics. La Quinta Inn, Civic Center, 601 Avenue Q, Lubbock, TX Travel 79401; phone: 806-763-9441, fax: 806-747-9325. Group rate Lubbock (airport code LBB) is served by American, Conti­ of$ 56 per night plus 13% local tax. One block south of Four nental, and Southwest Airlines. (Though a fourth airline, Points. Deadline for reservations is March 31. Limited Delta, currently serves Lubbock, it will discontinue service shuttle service to and from the campus will be provided at the end of January 2005.) by the Department of Mathematics and Statistics. From the Lubbock Airport: Leaving the Lubbock airport, Hawthorn Suites, 2 515-19th Street, Lubbock, TX 7941 0; one will be heading south on M. L. King Boulevard. At the phone: 806-765-8900, fax: 806-765-5322. Group rate of $80 first intersection (a four-way stop with Budget Rent-A-Car per night plus 13% local tax for queen suite. Located across and the Airport Shelter Parking facility on the corners) turn the street (19th Street, six-lane U.S. 62/Texas 114) from right and proceed to Interstate 27. Turn left and enter southeast corner of campus. Deadline for reservations is Interstate 27 South. For the Four Points and La Quinta, take March 7. Exit 4, U.S. 82, and turn right on 4th street, then left on Ave. Q. The hotels will be in the second and third blocks Food Service on the left after turning onto Ave. Q. To reach campus, pro­ Information will be provided on site. ceed down Ave. Q to Broadway (which would otherwise be 12th Street in the numbering) and turn right. Broadway goes Local Information and Campus Map directly into the main entrance to campus. Please visit the web sites maintained by the Department of For the Hawthorn, take Exit 3, U.S. 62/Texas 114, and Mathematics and Statistics at http: I /www. math. ttu. turn right onto 19th Street. Proceed west on 19th Street edu/-wlewis/amscs/amscs.html and http://www. past the southern part of downtown. At University Avenue math. ttu. edu, the Texas Tech University website at turn left and then immediately right into the Hawthorn http: I /www. ttu . edu and for a campus map: http: I I parking lot. The Texas Tech University campus will be on www.ttu.edu/campusmap/. the other side of 19th Street. See the maps for more in­ formation. Other Activities From Interstate 27 South (from the direction of Amar­ AMS Book Sale: Examine the newest titles from the AMS! illo): Follow the directions from the airport from the point Complimentary coffee will be served, courtesy of AMS where one gets on Interstate 27 South. Membership Services. The AMS Book Sale will operate dur­ From U.S. 62/82/Texas 114 West (from the direction ing the same hours as registration. The location of the Book of Wichita Falls or Denton): U.S. 82 approaches Lubbock Sale will be announced at a later date. from Wichita Falls and Sherman. For the last 150 miles it

FEBRUARY 2005 NOTICES OF THE AMS 301 Meetings & Conferences coincides with Texas 114, which approaches Lubbock from just west of Denton. For the last 30 miles these coincide Santa Barbara, with U.S. 62, which approaches Lubbock from Childress. On the northeast edge of Lubbock, just after passing under California Loop 289, U.S. 621Texas 114 diverges to the right from U.S. 82. U.S. 82 becomes 4th Street, and the directions from the University of California Santa Barbara airport apply after crossing under Interstate 27, while U.S. Aprill6-l 7, 2005 621Texas 114 becomes 19th Street, and the directions Saturday - Sunday from the airport apply after crossing under Interstate 27. From U.S. 84 North (from the direction of Abilene or Meeting #1 007 Sweetwater): U.S. 84 North enters Lubbock at the south­ Western Section east corner of town. After entering town, proceed under Associate secretary: Michel L. Lapidus Loop 289 to Interstate 27. Turn right to enter Interstate Announcement issue of Notices: February 2005 27 North and proceed to Exit 3, U.S. 621Texas 114 (from Program first available on AMS website: March 3, 2005 this direction also labelled 19th Street). Take Exit 3 and Program issue of electronic Notices: April 2005 turn left for 19th Street heading west. From this point fol­ Issue of Abstracts: Volume 26, Issue 3 low the directions provided from the airport. From U.S. 84 South (from the direction of Clovis or Deadlines Santa Rosa, New Mexico): Follow U.S. 84 South under For organizers: Expired Loop 289. U.S. 84 South becomes Ave. Q just after a slight For consideration of contributed papers in Special Sessions: turn before 4th Street. The Four Points and La Quinta are Expired on the left side of Ave. Q in the second and third blocks For abstracts: February 22, 2005 after 4th Street. To reach campus, turn right on Broadway The scientific information listed below may be dated. For (which would otherwise be 12th Street in the numbering) the latest information, see www. ams. orglamsmtgsl and proceed directly to the main entrance to campus. (Al­ sectional.html. ternatively, to reach campus after coming into town, turn right onto University Avenue from U.S. 84 South before Invited Addresses reaching Ave. Q and proceed to Broadway, where a left turn Mei-Chu Chang, University of California Riverside, Set immediately takes you into the campus.) To reach the addition and set multiplication. Hawthorn Suites, from U.S. 84 South turn right onto Uni­ versity Avenue. Hawthorn Suites will be on the right just Mischa Kapovich, University of California Davis, Title to be announced. after passing campus and crossing 19th Street. Mihai Putinar, University of California Santa Barbara, Car Rental Positive polynomials, a hilbertian perspective. Avis is the official car rental company for the sectional James Sethian, University of California Berkeley, Advances meeting in Lubbock, Texas. All rates include unlimited in advancing interfaces: New techniques for propagating free mileage. Weekend daily rates are available from noon fronts in wave propagation and materials sciences. Thursday to Monday at 11:59 p.m. and start at $27 per day. Special Sessions Rates for this meeting are effective April1, 2005-April17, 2005. Should a lower qualifying rate become available at Algebraic Geometry and Combinatorics (Code: SS 14A), the time of booking, Avis is pleased to offer a 5% discount Alexander Yong and Allen Knutson, University of Cali­ off the lower qualifying rate or the meeting rate, whichever fornia Berkeley. is lower. Rates do not include any state or local surcharges, Arithmetic Geometry (Code: SS 13A), Adebisi Agboola, tax, optional coverages, or gas refueling charges. Renters University of California Santa Barbara, and Cristian must meet Avis's age, driver, and credit requirements. Dumitru Popescu, University of California San Diego. Reservations can be made by calling 1-800-3 31-1600 or Automorphisms of Surfaces (Code: SS 4A), Anthony online at http: I lwww. avis. com. Meeting Avis Discount Weaver, Bronx Community College of the City University Number Bl59266. of New York, and Peter Turbek, Purdue University Calumet. Complexity of Computation and Algorithms (Code: SS 1 OA), Weather Mark Burgin, University of California Los Angeles. Please visit http: I lwww. accuweather. comladcbi nl Curvature in Group Theory and Combinatorics (Code: SS pub l i ell oca l_index. asp?zi pcode=79401 for current 11A), Laura M. Anderson, State University of New York at and future weather conditions in Lubbock. Binghamton, Noel Patrick Brady, University of Oklahoma, Robin Forman, Rice University, and Jonathan P. McCam­ mond, University of California Santa Barbara.

302 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Meetings & Conferences

Dynamical Systems in Neuroscience (Code: SS 1A), Eugene M. desk. Food service will also be available in the University Izhikevich, The Neurosciences Institute. Center and the Arbor located on campus. Function Theory (Code: SS 12A), Mihai Putinar and Local Information and Campus Map Stephan R. Garcia, University of California Santa Barbara. Please visit the website maintained by the Department of Geometric Methods in Three Dimensions (Code: SS 6A), Mathematics at http: I jwww. math. ucsb. edu, campus Daryl Cooper, David Darren Long, and Martin G. Scharle­ map at http: I /www. aw. i d. ucsb. edu/ucsbmap. html, mann, University of California Santa Barbara. Santa Barbara Visitors Bureau site at http: I /www. Geometry and Physics (Code: SS SA), Xianzhe Dai, University santabarbaraca. com, or the site maintained by the city of California Santa Barbara, and Zhiqin Lu, University of of Santa Barbara at http: I /www. ci. santa-barbara. California Irvine. ca. us. History of Mathematics (Code: SS 2A), Shawnee L. Other Activities McMurran, California State University, San Bernardino, and james J. Tattersall, Providence College. AMS Book Sale: Examine the newest titles from the AMS! Complimentary coffee will be served, courtesy of AMS Noncommutative Geometry and Algebra (Code: SS SA), Membership Services. The AMS Book Sale will operate dur­ Kenneth R. Goodearl, University of California Santa Bar­ ing the same hours as registration. The location o.f the Book bara, J. T. Stafford, University of Michigan, and]. J. Zhang, Sale will be announced at a later date. University of Washington. AMS Editorial Activity: An acquisitions editor from Recent Advances in Combinatorial Number Theory (Code: the AMS book program will be present to speak with SS 3A), Mei-Chu Chang, University of California Riverside, prospective authors. If you have a book project that you and Van Ha Vu, University of California San Diego. would like to discuss with the AMS, please stop by the book Representation Theory of Algebras (in Honor of Claus exhibit. Michael Ringel) (Code: SS 7A), Alex Martsinkovsky, North­ eastern University, Dan Zacharia, Syracuse University, and Parking Birge K. Huisgen-Zimmermann, University of California After 5:00 p.m. on weekdays and virtually all day and Santa Barbara. evening on weekends, most campus lots are open to all parkers. There are a few exceptions to this, so be sure to Ricci Flow/Riemannian Geometry (Code: SS 9A), Guofang read lot signage or any special notations on parking stalls Wei and Rugang Ye, University of California Santa Barbara. in spaces that are marked "R" or "Service Vehicle" or the Accommodations like. There is no need to obtain a parking permit unless on campus during the work week (M-F 8-5). The kiosks at Participants should make their own arrangements directly the east and west gates are open on weekends and are a with the hotel of their choice and request the UCSB dis­ good check-in point for a campus map and further infor­ count. The AMS is not responsible for rate changes or for mation. Campus parking: http: I /www. tps. ucsb. the quality of the accommodations. Rates quoted do not edu/Paybyspace. html and http: I /wvwv. tps. ucsb. edu/ include sales tax of 10%. Hotels have varying cancella­ visitor. html. tion or early checkout penalties; be sure to ask for de­ tails when making your reservation. Registration and Meeting Information Best Western South Coast Inn, 5620 Calle Real, Goleta, The registration desk (location to be announced) will be CA 93117; 805-967-3200; $112 single/double. Free shut­ open 8:00 a.m. to 4:00 p.m. on Saturday and 8:00 a.m. to tle to/from the airport and UCSB between 7:30 a.m. and noon on Sunday. 10:30 p.m., complementary continental breakfast. Rooms Registration fees (payable on-site only) are $40/AMS have high-speed Internet connections. For further infor­ members; $50/nonmembers; $5/emeritus members, stu­ mation visit http: I /www. BWSCI . com. Deadline for reser­ dents, or unemployed mathematicians. Fees are payable vations is March 15. by cash, check, VISA, MasterCard, Discover, or American Motel 6, 5897 Calle Real, Goleta, CA; 805-964-6241; Express. rates start at $59/ single or double. Reservations are on a first-come-first-served basis. Travel Ramada Limited, 4770 Calle Real, Goleta, CA: 805-964- By Air: UCSB is served by the Santa Barbara Airport (SBA), 3 511; from $120/night. Complimentary transportation pro­ http: I /wvwv. fl ysba. com/?pageiD=42. Most people trav­ vided between airport and inn, complementary continental eling by air will initially land at Los Angeles International breakfast. Rooms have high-speed Internet connections. For Airport (LAX), approximately 2.5 hours driving time from further information visit http: I /wvwv. SBRAMADA. COM. Dead­ Santa Barbara. Options for travel to UCSB from LAX include line for reservations is March 1. the Santa Barbara Airbus or car rental. The Santa Barbara Airbus provides several daily trips from LAX to Santa Bar­ Food Service bara. For fare information phone 800-423-1618 (within the There are a number of restaurants adjacent to the campus. U.S./Canada) or 805-964-7759 (outside U.S./Canada) or A list of restaurants will be available at the registration visit http: I jwww. santabarbaraa i rbus. com. fEBRUARY 2005 NOTICES OF THE AMS 303 Meetings & Conferences

Delta Air lines has been selected as the official airline for this meeting. The following specially negotiated rates Mainz, Germany are available for this meeting exclusively for mathemati­ cians and their families for the period April 13, 2005, johannes Gutenberg University through April20, 2005. Other restrictions/discounts may June 16-19, 2005 apply and seats are limited. Thursday - Sunday Delta Air Lines is offering: • A 5% discount off Delta's published round-trip fares Meeting #1 008 within the continental United States, excluding A, D, I, U ]oint International Meeting with the Deutsche Mathematiker­ and T classes of service. Vereinigung (DMV) and the Oesterreichische Mathematis­ • A 10% discount off Delta's domestic published unre­ che Gesellschaft (OMG) stricted round-trip coach fares (Y06/YR06) rates. No ad­ Associate secretary: Susan]. Friedlander vance reservations or ticketing is required. Announcement issue of Notices: March 2005 • An additional 5% bonus discount if you purchase Program first available on AMS website: Not applicable your ticket 60 days or more prior to your departure through Program issue of electronic Notices: Not applicable Meeting Network Reservations or your travel agent; online Issue of Abstracts: Not applicable not applicable. Deadlines To take advantage of these discounts and make imme­ For organizers: Expired diate reservations, call Delta Meeting Network at 1-800-241- For consideration of contributed papers in Special Sessions: 6760 between 8:00a.m. and 11:00 p.m. Eastern Standard To be announced Time, Monday through Sunday, referencing File Number For abstracts: March 31, 2005 205779A. The scientific information listed below may be dated. For Car Rental the latest information, see www. ams. o rg/ amsmtgs/ Avis is the official car rental company for the sectional i nternmtgs. html. meeting in Santa Barbara, California. All rates include unlimited free mileage. Special rates for this meeting are Invited Addresses effective April9, 2005-April24, 2005, and begin at $26/day Helene Esnault, University of Essen, Deligne's Integrality for a subcompact car at the weekend rate (available from Theorem in unequal characteristic and rational points over noon Thursday through Monday at 11:59 p.m.). Should a finite fields. lower qualifying rate become available at the time of book­ Richard Hamilton, Columbia University, The Ricci flow. ing, Avis is pleased to offer a 5% discount off the lower Michael J. Hopkins, Massachusetts Institute of Technol­ qualifying rate or the meeting rate, whichever is lower. ogy, Title to be announced. Rates do not include any state or local surcharges, tax, optional coverages, or gas refueling charges. Renters must Christian Krattenthaler, University of Lyon-I, Exact and as­ ymptotic enumeration of vicious walkers with a wall inter­ meet Avis's age, driver, and credit requirements. Reser­ action. vations can be made by calling 1-800-331-1600 or online at http: I /www. avis. com. Meeting Avis Discount Num­ Frank Natterer, University of Muenster, Imaging and in­ ber Bl59266. verse problems for partial differential equations. Driving: UCSB is easily accessible from U.S. 101. From Horng-Tzer Yau, New York University and Stanford the south take the UCSB/Highway 217 exit. From the north University, Dynamics of Bose-Einstein condensate. take Storke Road/UCSB exit and drive south (toward the Special Sessions ocean) to the junction with El Colegio Road. Turn left onto El Colegio Road and proceed to the west gate kiosk. Affine Algebraic Geometry, Shreeram Abhyankar, Pur­ Other: Santa Barbara is also served by Amtrak train due University, Hubert Flenner, Fakultiit fiir Mathematik, service and Greyhound bus service. and Makar Limanov, Wayne State University. Algebraic Combinatorics, Patricia Hersh, University of Weather Michigan, Christian Krattenthaler, University of Lyon-I, and Located on the coast of California, Santa Barbara County's Volkmar Welker, Philipps University Marburg. climate is mild and sunny all year, with an average day­ Algebraic Cryptography, Dorian Goldfeld, Columbia time temperature between 60°F and 70°F (16oC and 21 OC). University, Martin Kreuzer and Gerhard Rosenberger, Santa Barbara attire is generally California casual. Universitat Dortmund, and Vladimir Shpilrain, City College of New York. Algebraic Cycles, Eric Friedlander and Marc Levine, North­ western University, and Fabien Morel, Universite Paris.

304 NOTICES OF TilE AMS VOLUME 52, NUMBER 2 Meetings & Conferences

Algebraic Geometry, Yuri Tschinkel, Georg-August­ Ordinary Differential, Difference, and Dynamic Equations, Universitat Gottingen, and Brendan E. Hassett, Rice Werner Balser, Universitat Ulm, Martin Bohner, University University. of Missouri-Rolla, and Donald Lutz, San Diego State Dirac Operators, Clifford Analysis and Applications, Klaus University. Giirlebeck, University of Weimar, Mircea Martin, Baker Uni­ Quantum Knot Invariants, Anna Beliakova, Universitat versity, John Ryan, University of Arkansas, and Michael Zurich, and Uwe Kaiser, Boise State University. Shapiro, IPN Mexico. Representations and Cohomology of Groups and Algebras, Discrete Geometry, Jacob Eli Goodman, The City College Dave Benson, University of Georgia, and Henning Krause, of New York (CUNY), Emo Welzl, Eidgen Technische Universitat Paderborn. Hochschule, and Gunter M. Ziegler, Technical University Set Theory, Joel Hamkins, City University New York, Peter of Berlin. Koepke, Universitat Bonn, and Benedikt Lowe, Univer­ Function Spaces and Their Operators, Ernst Albrecht, Uni­ siteit van Amsterdam. versitat des Saarlandes, Raymond Mortini, Universite de Spectral Analysis of Differential and Difference Operators, Metz, and William Ross, University of Richmond. Evgeni Korotyaev, Humboldt-University Berlin, Boris Functional Analytic and Complex Analytic Methods in Mityagin, The Ohio State University, and Gerald Teschl, Linear Partial Differential Equations, R. Meise, University University of Vienna. of Dusseldorf, B. A. Taylor, University of Michigan, and Stochastic Analysis on Metric Spaces, Laurent Saloff-Coste, Dietmar Vogt, University of Wuppertal. Cornell University, Karl-Theodor Sturm, University of Geometric Analysis, Victor Nistor, Pennsylvania State Uni­ Bonn, and Wolfgang Woess, Graz Technical University. versity, and Elamr Schrohe, Universitat Hannover. Topics in Applied Mathematics and Mechanics: Mathemat­ Geometric Topology and Group Theory, Cameron MeA ical Control Theory and Numerical Methods, Peter Benner, Gordon, University of Texas at Austin, Cynthia Hog­ Fakultat fUr Mathematik. Angeloni, Johann Wolfgang Goethe-Universitat, and Topics in Applied Mathematics and Mechanics: Mechanics, Wolfgang Metzler, University of Frankfurt. Friedrich Pfeiffer, Technical University of Munich. Group Theory, Luise-Charlotte Kappe, SUNY at Bingham­ Topics in Applied Mathematics and Mechanics: Multiscale ton, Robert Fitzgerald Morse, University of Evansville, Problems, Oscillations in PDEs, and Homogenization, Alexan­ and Gerhard Rosenberger, University of Dortmund. der Mielke, University of Hannover. Hilbert Functions and Syzygies, Uwe Nagel, University of Topics in Applied Mathematics and Mechanics: Numerical Kentucky, Irena Peeva, Cornell University, and Tim Romer, PDEs, Equations with Inherent Conditions, Rolf Jeltsch, Universitat Osnabruck. Eidgen Technische Hochschule, Maria Lukacova, Technical History of Mathematics: Mathematics and War, Thomas W. University of Brno, and Mac Hyman, Los Alamos National Archibald, Acadia University, John H. McCleary, Vassar Laboratory. College, Moritz Epple, University of Stuttgart, and Norbert Topics in Applied Mechanics: Algebraic Approaches to Schappacher, Technische Universitat Darmstadt. Preconditioning, Heike Fassbender, Technical University Homotopy Theory, Paul G. Goerss, Northwestern University, of Braunschweig, and Andreas Frommer, University of Hans-Werner Henn, Institut de Recherche Mathematique Wuppertal. Avancee, Strasbourg, and Stefan Schwede, Universitat Bonn. Topology of Manifolds, Matthias Kreck, University of Hopf Algebras and Quantum Groups, Susan Montgomery, Heidelberg, and Andrew Ranicki, University of Edinburgh. University of Southern California, and Hans-Jurgen Schneider, University of Munich. Annandale-on­ Mathematics Education, Gunter Torner, Universitat Duisburg-Essen, and Alan Schoenfeld, School of Education, Berkeley. Hudson, New York Modules and Comodules, Sergio L6pez-Permouth, Ohio Bard College University, and Robert Wisbauer, University of Dusseldorf. October 8-9, 2005 Multiplicative Arithmetic of Integral Domains and Monoids, Scott Chapman, Trinity University, San Antonio, Franz Saturday - Sunday Halter-Koch, University of Graz, and Ulrich Krause, Uni­ Meeting #1 009 versitat Bremen. Eastern Section Nonlinear Elliptic Boundary Value Problems, Thomas Associate secretary: Lesley M. Sibner Bartsch, Universitat Giessen, and Zhi-Qiang Wang, Utah Announcement issue of Notices: August 2005 State University. Program first available on AMS website: August 25, 2005 Nonlinear Waves, Herbert Koch, University of Dortmund, Program issue of electronic Notices: October 2005 and Daniel I. Tataru, University of California Berkeley. Issue of Abstracts: Volume 26, Issue 4

FEBRUARY 2005 NOTICES OF THE AMS 305 Meetings & Conferences

Deadlines For organizers: March 8, 2005 Johnson City, For consideration of contributed papers in Special Sessions: June 21, 2005 Tennessee For abstracts: August 16, 2005 East Tennessee State University The scientific information listed below may be dated. For October 1 5-16, 2005 the latest information, see www. ams. org/amsmtgs/ Saturday - Sunday sectional . html. Meeting #1 010 Invited Addresses Southeastern Section Associate secretary: Matthew Miller Persi Diaconis, Stanford University, Title to be announced Announcement issue of Notices: August 2005 (Erdos Memorial Lecture). Program first available on AMS website: September 1, 2005 Harold Rosenberg, University of Paris VII, Title to be Program issue of electronic Notices: October 2005 announced. Issue of Abstracts: Volume 26, Issue 4 Alice Silverberg, University of California Irvine, Title to be Deadlines announced. For organizers: March 15, 2005 Christopher Sogge, Johns Hopkins University, Title to be For consideration of contributed papers in Special Sessions: announced. June 28, 2005 For abstracts: August 23, 2005 Benny Sudakov, Princeton University, Title to be announced. The scientific information listed below may be dated. For the latest information, see www. ams. org/amsmtgs/ Special Sessions sectional . htm l. Geometric Group Theory( Code: SS 1A), Sean Cleary, The City Invited Addresses College of New York, and Melanie I. Stein, Trinity College. Alberto Bressan, Pennsylvania State University, Title to be Geometric Transversal Theory (Code: SS 3A), Richard announced. Pollack, Courant Institute, New York University, and Jacob Assaf Naor, Microsoft Research, Title to be announced. Eli Goodman, The City College of New York. Prasad V. Tetali, Georgia Institute of Technology, Title to Global Theory ofMinimal Surfaces (Code: SS 6A), David A. be announced. Hoffman, Mathematical Sciences Research Institute, and Rekha R. Thomas, University of Washington, Title to be Harold Rosenberg, University of Paris VII. announced. The History ofMathematics (Code: SS 2A), Patricia R. Allaire, Queensborough Community College, CUNY, Robert E. Bradley, Adelphi University, and Jeff Suzuki, Bard College. Lincoln, Nebraska Homological Aspects of Commutative Algebra (Code: SS 4A), University of Nebraska in Lincoln Alexandre Tchernev, University of Albany, SUNY, and janet Vassilev, University of Arkansas. October 21-23,2005 Special Functions and Orthogonal Polynomials: Theory and Friday - Sunday Applications (Code: SS 7A), Diego Dominici, State University Meeting #1 011 of New York at New Paltz. Central Section Theory ofInfinite-Dimensional Lie Algebras, Vertex Operator Associate secretary: Susan]. Friedlander Algebras, and Related Topics (Code: SS SA), Antun Milas, Announcement issue of Notices: August 2005 SUNY at Albany, Alex J. Feingold, Binghamton University, Program first available on AMS website: September 8, 2005 and Yi-Zhi Huang, Rutgers University. Program issue of electronic Notices: October 2005 Issue of Abstracts: Volume 26, Issue 4 Deadlines For organizers: March 22, 2005 For consideration of contributed papers in Special Sessions: July 5, 2005 For abstracts: August 30, 2005

306 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Meetings & Conferences

The scientific information listed below may be dated. For University of Oregon, and Vladimir Retakh, Rutgers the latest information, see www. ams. org/amsmtgs/ University. sectional . html. Regular Algebras and Noncommutative Projective Geometry Invited Addresses (Code: SS 2A), Brad Shelton, University of Oregon, Michaela Vancliff, University of Texas at Arlington, and James J. Howard Masur, University of Illinois at Chicago, Title to Zhang, University of Washington. be announced. Resolutions (Code: SS 1A), Christopher Alan Francisco, Uni­ Alejandro Uribe, University of Michigan, Title to be versity of Missouri, and Irena Peeva, Cornell University. announced. Judy Walker, University of Nebraska, Title to be announced. Jack Xin, University of Texas, Title to be announced. Taiwan Special Sessions December 14-18,2005 Wednesday - Sunday Algebraic Geometry (Code: SS 1A), Brian Harbourne, Uni­ versity of Nebraska-Lincoln, and Bangere P. Purnaprajna, Meeting #1 013 University of Kansas. First ]oint International Meeting between the AMS and the Recent Progress in Operator Algebras (Code: SS 2A), Allan P. Taiwanese Mathematical Society. Donsig and David R. Pitts, University of Nebraska. Associate secretary: John L. Bryant Announcement issue of Notices: May 2005 Program first available on AMS website: Not applicable Eugene, Oregon Program issue of electronic Notices: Not applicable Issue of Abstracts: Not applicable University of Oregon Deadlines November 12-13, 2005 For organizers: To be announced Saturday - Sunday For consideration of contributed papers in Special Sessions: Meeting #1 012 To be announced Western Section For abstracts: To be announced Associate secretary: Michel L. Lapidus Announcement issue of Notices: September 2005 Program first available on AMS website: September 29, San Antonio, Texas 2005 Program issue of electronic Notices: November 2005 Henry B. Gonzalez Convention Center Issue of Abstracts: Volume 26, Issue 4 January 12-1 5, 2006 Deadlines Thursday - Sunday For organizers: April12, 2005 Meeting #1 014 For consideration of contributed papers in Special Sessions: ]oint Mathematics Meetings, including the 112th Annual July 26, 2005 Meeting of the AMS, 89th Annual Meeting of the Mathe­ For abstracts: September 20, 2005 matical Association of America, annual meetings of the Association for Women in Mathematics (A WM) and the The scientific information listed below may be dated. For National Association of Mathematicians (NAM), the winter the latest information, see www. ams. o rg/ amsmtgs/ meeting of the Association for Symbolic Logic (ASL), with sectional . html. sessions contributed by the Society for Industrial and Invited Addresses Applied Mathematics (SIAM). Matthew Foreman, University of California Irvine, Title to Associate secretary: Matthew Miller be announced. Announcement issue of Notices: October 2005 Program first available onAMS website: November 1, 2005 Mark Haiman, University of California Berkeley, Title to be Program issue of electronic Notices: January 2006 announced. Issue of Abstracts: Volume 27, Issue 1 Wilhelm Schlag, California Institute of Technology, Title to be announced. Deadlines Hart H. Smith, University of Washington, Title to be For organizers: April12, 2005 announced. For consideration of contributed papers in Special Sessions: To be announced Special Sessions For abstracts: To be announced Noncommutative Algebra and Noncommutative Birational For summaries of papers to MAA organizers: To be Geometry (Code: SS 3A), Arkady Dmitrievich Berenstein, announced

FEBRUARY 2005 NOTICES OF THE AMS 307 Meetings & Conferences

Deadlines Miami, Florida For organizers: To be announced For consideration of contributed papers in Special Sessions: Florida International University To be announced Aprill-2, 2006 For abstracts: To be announced Saturday - Sunday The scientific information listed below may be dated. For Southeastern Section the latest information, see www. ams. org/amsmtgs/ Associate secretary: Matthew Miller sectional.html. Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Special Sessions Program issue of electronic Notices: To be announced History of Mathematics (Code: SS lA), Shawnee L. Issue of Abstracts: To be announced McMurran, California State University, San Bernardino, and James J. Tattersall, Providence College. Deadlines For organizers: September 1, 2005 For consideration of contributed papers in Special Sessions: To be announced Fayetteville, For abstracts: To be announced Arkansas Durham, University of Arkansas November 3-4, 2006 New Hampshire Friday - Saturday Southeastern Section University of New Hampshire Associate secretary: Matthew Miller Announcement issue of Notices: To be announced April22-23, 2006 Program first available on AMS website: To be announced Saturday - Sunday Program issue of electronic Notices: To be announced Eastern Section Issue of Abstracts: To be announced Associate secretary: Lesley M. Sibner Announcement issue of Notices: To be announced Deadlines Program first available on AMS website: To be announced For organizers: April 3, 2006 Program issue of electronic Notices: To be announced For consideration of contributed papers in Special Sessions: Issue of Abstracts: To be announced To be announced For abstracts: To be announced Deadlines For organizers: September 22, 2005 For consideration of contributed papers in Special Sessions: New Orleans, To be announced For abstracts: To be announced Louisiana New Orleans Marriott and Sheraton San Francisco, New Orleans Hotel January4-7, 2007 California Thursday - Sunday ]oint Mathematics Meetings, including the 113th Annual San Francisco State University Meeting of the AMS, 90th Annual Meeting of the Mathe­ April29-30, 2006 matical Association ofAmerica (MAA), annual meetings of the Association for Women in Mathematics (A HIM) and the Saturday - Sunday National Association of Mathematicians (NAM), and the Western Section winter meeting of the Association for Symbolic Logic (ASL), Associate secretary: Michel L. Lapidus with sessions contributed by the Society for Industrial and Announcement issue of Notices: To be announced Applied Mathematics (SIAM). Program first available on AMS website: To be announced Associate secretary: Susan ]. Friedlander Program issue of electronic Notices: To be announced Announcement issue of Notices: October 2006 Issue of Abstracts: To be announced Program first available on AMS website: To be announced

308 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Meetings & Conferences

Program issue of electronic Notices: January 2007 Issue of Abstracts: To be announced Washington, District Deadlines of Columbia For organizers: April 4, 2006 For consideration of contributed papers in Special Sessions: Marriott Wardman Park Hotel and Omni To be announced Shoreham Hotel For abstracts: To be announced January 7-10, 2009 For summaries of papers to MAA organizers: To be Wednesday - Saturday announced joint Mathematics Meetings, including the 115th Annual Meeting of the AMS, 92nd Annual Meeting of the Mathe­ matical Association of America (MAA), annual meetings of Oxford, Ohio the Association for Women in Mathematics (A l!VM) and the Miami University National Association of Mathematicians (NAM), and the winter meeting of the Association for Symbolic Logic (ASL). March 16-1 7, 2007 Associate secretary: Lesley M. Sibner Friday - Saturday Announcement issue of Notices: October 2008 Central Section Program first available on AMS website: November 1, 2008 Program issue of electronic Notices: January 2009 Associate secretary: Susan]. Friedlander Issue of Abstracts: Volume 30, Issue 1 Announcement issue of Notices: To be announced Program first available on AMS website: To be announced Deadlines Program issue of electronic Notices: To be announced For organizers: April 7, 2008 Issue of Abstracts: To be announced For consideration of contributed papers in Special Sessions: To be announced Deadlines For abstracts: To be announced For organizers: To be announced For summaries of papers to MAA organizers: To be For consideration of contributed papers in Special Sessions: announced To be announced For abstracts: To be announced San Francisco, San Diego, California California San Diego Convention Center Moscone Center West and the January 6-9, 2008 San Francisco Marriott Sunday - Wednesday January 6-9, 201 0 joint Mathematics Meetings, including the 114th Annual Wednesday - Saturday Meeting of the AMS, 91st Annual Meeting of the Mathe­ joint Mathematics Meetings, including the 116th Annual matical Association ofAmerica (MAA), annual meetings of Meeting of the AMS, 93rd Annual Meeting of the Mathe­ the Association for Women in Mathematics (A liVM) and the matical Association ofAmerica (MAA), annual meetings of National Association of Mathematicians (NAM), and the the Association for Women in Mathematics (A liVM) and the winter meeting of the Association for Symbolic Logic (ASL). National Association of Mathematicians (NAM), and the Associate secretary: Michel L. Lapidus winter meeting of the Association for Symbolic Logic (ASL). Announcement issue of Notices: October 2007 Associate secretary: Matthew Miller Program first available on AMS website: November 1, 2007 Announcement issue of Notices: October 2009 Program issue of electronic Notices: January 2008 Program first available on AMS website: November 1, 2 009 Program issue of electronic Notices: January 2010 Issue of Abstracts: Volume 29, Issue 1 Issue of Abstracts: Volume 31, Issue 1 Deadlines Deadlines For organizers: April 6, 2007 For organizers: April 5, 2009 For consideration of contributed papers in Special Sessions: For consideration of contributed papers in Special Sessions: To be announced To be announced For abstracts: To be announced For abstracts: To be announced For summaries of papers to MAA organizers: To be For summaries of papers to MAA organizers: To be announced announced fEBRUARY 2005 NOTICES OF THE AMS 309 Meetings & Conferences New Orleans, ECOLE PO LY TECH N IQUE FEDER ALE DE LAUSAN N E Louisiana New Orleans Marriott and Sheraton CENTREINTERFACULTAIRE New Orleans Hotel January 5-8,2011 BERNOULLI (CIB) Wednesday - Saturday ]oint Mathematics Meetings, including the 117th Annual Meeting of the AMS, 94th Annual Meeting of the Mathe­ matical Association of America, annual m eetings of the Association for Women in Mathematics (A HIM) and CALL FOR PROPOSALS the National Association of Mathematicians (NAM), and the winter meeting of the Association for Symbolic Logic (ASL). The Bernoulli Center (CIB), funded jointly by the Associate secretary: Susan ]. Friedlander Announcement issue of Notices: October 2010 Swiss National Science Foundation and the Swiss Program first available on AMS website: November 1, 2010 Federal Institute of Technology in Lausanne, has Program issue of electronic Notices: January 2011 started its activity in March 2002. Issue of Abstracts: Volume 32, Issue 1

Its mission is to support research in mathematics Deadlines and its applications, to organize and host thematic For organizers: April 2, 2010 programs, to provide a supportive and stimulating For consideration of contributed papers in Special Sessions: environment for researchers, and to launch and To be announced foster collaborations between mathematicians For abstracts: To be announced working in different areas as well as For summaries of papers to MAA organizers: To be announced mathematicians and other scientists.

The CIB launches a call for proposals of six one­ semester programs during the period July 1, 2006- June 30, 2009. A thematic program consists of a six months period (January 1 - June 30 or July 1 - December 31) of concentrated activity in a specific area of current research interest in the mathematical sciences. In exceptional cases, one year and three month programs will also be considered.

Those who are interested in organizing a program at the CIB should submit a two page letter of intent by Aprill, 2005. This letter should give the names of the organizers, of the potential visitors, and outline the program. For more details see http:/lbernoulli.epfl.ch/recruiting

Ecole Polytechnique Federale de Lausanne Centre Interfacu!taire Bernoulli SB CIB-GE AAC034 (Bat!ment AAC) Station 15 CH-1015 Lausanne

310 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Meetings and Conferences of the AMS

Associate Secretaries of the AMS Western Section: MichelL. Lapidus, Department of Math­ Eastern Section: Lesley M. Sibner, Department of Mathe­ ematics, University of California, Sproul Hall, Riverside, CA matics, Polytechnic University, Brooklyn, NY 11201-2990; 92521-0135; e-mail: l a pi dus@math. uc r. edu; telephone: 951- e-mail: lsi bne r@du ke. poly. edu; telephone: 718-260-3 505. 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: mill 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. 309 gives information on all AMS meetings and conferences approved by press time for this issue. Please refer to the page 2008 numbers cited in the table of contents on this page for more January 6-9 San Diego, California p. 309 detailed information on each event. Invited Speakers and Annual Meeting Special Sessions are listed as soon as they are approved by 2009 the cognizant program committee; the codes listed are needed January 7-10 Washington, DC p. 309 for electronic abstract submission. For some meetings the list Annual Meeting may be incomplete. Information in this issue may be dated. 2010 Up-to-date meeting and conference information can be January 6-9 San Franciso, California p. 309 found at www. ams. org/meeti ngs/. Annual Meeting 2011 ' Meetings: January 5-8 New Orleans, Louisiana p. 310 Annual Meeting 2005 Important Information regarding AMS Meetings March 18-19 Bowling Green, Kentucky p. 297 Potential organizers, speakers, and hosts should refer to April2-3 Newark, Delaware p.298 page 100 in the January 2005 issue of the Notices for general April8-10 Lubbock, Texas p. 300 information regarding participation in AMS meetings and April16-17 Santa Barbara, California p. 302 conferences. June 16-19 Mainz, Germany p. 304 Abstracts October 8-9 Annandale-on-Hudson, Speakers should submit abstracts on the easy-to-use interactive New York p. 305 Web form. No knowledge of LAI.£X is necessary to submit an October 15-16 Johnson City, Tennessee p. 306 electronic form, although those who use ktf.£X may submit October 21-23 Lincoln, Nebraska p. 306 abstracts with such coding, and all math displays and sirni­ November 12-13 Eugene, Oregon p. 307 larily coded material (such as accent marks in text) must December 14-18 Taiwan p. 307 be typeset in LAI.£X. Visit http: I jwww. ams. org/ cgi -bin/ abstracts/abstracts. pl, or send mail to abs-submi t@ 2006 ams. org, typing help as the subject line; descriptions and instructions on how to get the template of your choice will January 12-15 San Antonio, Texas p. 307 be e-mailed to you. Annual Meeting Questions about abstracts may be sent to abs-i nfo@ April1-2 Miami, Florida p. 308 ams. org. April 22-23 Durham, New Hampshire p. 308 Paper abstract forms may be sent to Meetings & Confer­ April29-30 San Francisco, California p. 308 ences Department, AMS, P.O. Box 6887, Providence, RI 02940. November 3-4 Fayetteville, Arkansas p. 308 There is a $20 processing fee for each paper abstract. There is no charge for electronic abstracts. Note that all abstract dead­ 2007 lines are strictly enforced. January 4-7 New Orleans, Louisiana p. 308 Close attention should be paid to specified deadlines in this issue. Unfortunately, late abstracts cannot be accommodated. Annual Meeting Conferences: (see http: I jwww . ams. o rg/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). Co-sponsored conference: June 2006: Fifth Conference on Poisson Geometry, Tokyo, Japan (watch http: I /tmugs. math. metro-u. ac. j p/general . html for future information).

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