2006 Steele Prizes

The 2006 Leroy P. Steele Prizes were awarded at Research (this year restricted to the field of applied the 112th Annual Meeting of the AMS in San An- ); and to FREDERICK W. GEHRING and tonio in January 2006. DENNIS P. SULLIVAN for Lifetime Achievement. The text The Steele Prizes were established in 1970 in that follows presents, for each awardee, the selection honor of George David Birkhoff, William Fogg Os- committee’s citation, a brief biographical sketch, and good, and William Caspar Graustein. Osgood was the awardee’s response upon receiving the prize. president of the AMS during 1905–1906, and Birk- hoff served in that capacity during 1925–1926. Mathematical Exposition: The prizes are endowed under the terms of a be- Lars V. Hörmander quest from Leroy P. Steele. Up to three prizes are Citation awarded each year in the following categories: (1) The four volumes of Lars Hörmander’s The Analysis Lifetime Achievement: for the cumulative influ- of Linear Partial Differential Operators are a com- ence of the total mathematical work of the recipi- pendium of practically all of the exciting develop- ent, high level of research over a period of time, ments that occurred in the theory of linear partial dif- particular influence on the development of a field, ferential equations and in the area of microlocal and influence on mathematics through Ph.D. stu- analysis in the period 1960–1985. dents; (2) Mathematical Exposition: for a book or Microlocal analysis emerged as a well-defined substantial survey or expository-research paper; (3) part of modern analysis with the development of Seminal Contribution to Research: for a paper, pseudodifferential operators in the early 1960s. This whether recent or not, that has proved to be of fun- made possible a “microlocal” way of thinking about damental or lasting importance in its field, or a the basic objects in linear partial differential equa- model of important research. Each Steele Prize car- tion theory: the fundamental solutions of these equa- ries a cash award of US$5,000. tions and the classes of generalized functions to The Steele Prizes are awarded by the AMS Coun- which the solutions of these equations belong. cil acting on the recommendation of a selection Thanks to microlocal techniques, one could analyze committee. For the 2006 prizes, the members of the singularities of these functions much more the selection committee were: Rodrigo Banuelos, precisely, and implement much more explicitly than Daniel S. Freed, John B. Garnett, Victor W. Guillemin, before, for many different varieties of differential Craig L. Huneke, Tsit-Yuen Lam (chair), Robert D. equations, the “semi-classical limit” of quantum MacPherson, Linda P. Rothschild, and David A. mechanics. Vogan. In these four volumes, Hörmander describes The list of previous recipients of the Steele Prizes these developments in a treatment that is seamless may be found in the November 2005 issue of the and self-contained. Moreover, the effort to make Notices, pages 1251–1255, or on the World Wide this treatment self-contained has inspired him to Web, http://www.ams.org/prizes-awards. recast, in much more simple and accessible form, The 2006 Steele Prizes were awarded to LARS V. the approach to much of this material as it origi- HÖRMANDER for Mathematical Exposition; to nally appeared in the literature. An example is the CLIFFORD S. GARDNER, JOHN M. GREENE, MARTIN D. KRUSKAL, theory of Fourier integral operators, which was in- and ROBERT M. MIURA for a Seminal Contribution to vented by him in two seminal papers in the early

464 NOTICES OF THE AMS VOLUME 53, NUMBER 4 1970s. (These get a completely new and much more Response elegant reworking in volume four.) In brief, these I am very happy and grateful four volumes are far more than a compendium of to receive this award for the random results. They are a profound and master- activity which has dominated ful “rethinking” of the whole subject of microlocal a great part of my professional analysis. life, and I wish to thank the Hörmander’s four volumes on partial differen- members of the Selection tial operators have influenced a whole generation Committee for their consid- of working in the broad area of mi- eration. crolocal analysis and its applications. In the history My expository writing of mathematics one is hard-pressed to find any started in the 1950s with mod- comparable “expository” work that covers so much est lecture notes just intended material, and with such depth and understanding, for the students in Stockholm of such a broad area of mathematics. I wanted to introduce to the the- Another of Hörmander’s masterpieces in expo- ory of partial differential equa- sition is his much shorter book, Complex Analysis tions. I toyed with the idea of in Several Variables, the first edition of which ap- expanding them to a book but peared in 1973. Like the four volumes cited above, this seemed unrealistic until in Lars V. Hörmander it is remarkable in the scope of what it covers. For 1960 I received a letter from instance the first chapter, only 22 pages long, is one one of the editors of the famous Springer “yellow of the best treatments of functions of one complex series” inviting me to write a book for it. This was an variable available anywhere in the literature. Now, enormous encouragement, and as a result I devoted more than 30 years later, this excellent book re- a great deal of the academic year 1960–1961 to this mains the gold standard in teaching a graduate project, including research on topics which had to be course in several complex variables at many uni- better understood to make a systematic exposition versities in the U.S. and abroad. This short text of possible. The manuscript of my first book Linear about 200 pages is a “must read” for anyone who Partial Differential Operators was finished in 1962, works or uses the modern theory of analysis of sev- and it appeared in 1963 in the yellow series. I was then eral complex variables. In particular, it contains the working to understand better the applications of the best treatment available for weighted L2 estimates theory of functions of several complex variables to for d-bar equations (originally invented by Hör- the theory of partial differential equations with con- mander), which continue to be used in other areas stant coefficients which I had not been able to cover of mathematics. in my book, and with the so-called ∂-Neumann prob- In conclusion, Lars Hörmander’s contribution to lem which through work of Morrey, Kohn, and oth- mathematical exposition is highly unusual and per- ers had just made it possible to conversely base the haps even unique in modern times. theory of functions of several complex variables on Biographical Sketch the theory of partial differential equations. When I Lars Hörmander was born on January 24, 1931, in lectured on these topics at Stanford in 1964 I wrote southern Sweden. He was an undergraduate and a detailed lecture notes. After some additions to round graduate student at the University of Lund, Sweden, them off they were published by van Nostrand in first with Marcel Riesz and then, after Riesz re- 1966 as An Introduction to Complex Analysis in Sev- tired, with Lars Gårding as advisor. After obtaining eral Variables, which is one of the books mentioned a Ph.D. in 1955 he spent a year in the U.S.—two quar- in the citation. Expanded editions were published ters at the University of Chicago and a semester at by North Holland in 1973 and 1990. what is now the Courant Institute at New York The rapid development of microlocal analysis in University—before returning as full professor to the the 1960s quickly made the book in the yellow se- University of Stockholm in 1957. During the acad- ries obsolete, but the pace was so fast that it seemed emic year 1960–1961 he was a member of the impossible to make it up to date. However, fifteen Institute for Advanced Study (IAS) in Princeton and years after it had been published I thought that it a visitor at Stanford University in the summers of was worth trying, and after the year 1977–1978 at 1960 and 1961, where he had a permanent ap- IAS and Stanford devoted to preparations, I could pointment in 1963–1964 before leaving both make preliminary plans for a replacement in three Stockholm and Stanford to become a professor volumes, again encouraged by Springer Verlag. and permanent member at the IAS. He left Princeton When the manuscript was finished in 1984 the in 1968 to return to Sweden as professor in Lund, third volume had grown so much that it had to be where he remained until retiring in 1996, apart divided in two, the last appeared in 1985. The title from about two more years in the U.S., mainly at IAS, The Analysis of Linear Partial Differential Opera- Stanford, the Courant Institute, and the University tors was chosen to indicate that the four volumes of California, San Diego. had developed from the 1963 book, which is why

APRIL 2006 NOTICES OF THE AMS 465 I have mentioned it here although it is not included National Laboratory, the Courant Institute, and the in the citation. After two decades they are of course Princeton Plasma Physics Laboratory. He was pro- no longer up to date but they can still serve as an fessor of mathematics at the University of Texas, introduction to many of the basic techniques in the Austin, from 1967 until his retirement in 1990. field. The first two volumes have been preserved Biographical Sketch: John M. Greene in the Springer Classics in Mathematics series, and John M. Greene received his B.S. degree in physics the last two should soon join them there. from the California Institute of Technology in 1950 In conclusion I would like to thank the many col- and his Ph.D. in theoretical particle physics from leagues and students whose encouraging interest the University of Rochester in 1956. He worked at has stimulated my expository writing. Without the Princeton Plasma Physics Laboratory (1956– such support and constructive criticism it would 1982) and at General Atomics from 1982 until his have been hard to persevere with that for so many retirement in 1995. He has been a Fellow of the years. American Physical Society and a member of the Seminal Contribution to Research: American Geophysical Union. Clifford S. Gardner, John M. Greene, In 1992 Greene was awarded the James Clerk Martin D. Kruskal, and Robert M. Miura Maxwell Prize from the Division of Plasma Physics of the American Physical Society. The citation reads: Citation “For outstanding contributions to the theory of The prize is awarded for their joint paper “Korteweg- magnetohydrodynamic equilibria and ideal and re- deVries equation and generalizations. VI. Methods sistive instabilities, for discovery of the inverse for exact solution”, Comm. Pure Appl. Math. 27 scattering transform leading to soliton solutions of (1974), 97–133. many nonlinear partial differential equations, and This is a fundamental paper in the theory of soli- for the invention of the residue method of deter- tons, inverse scattering transforms, and nonlinear mining the transition to global chaos.” completely integrable systems. Before it, there was Response: John M. Greene no general theory for the exact solution of any im- [This response is written by Alice Greene on behalf portant class of nonlinear differential equations. Ex- cept for a few special cases, only approximations to of John Greene.] John was always pleased with the solutions were possible. This paper, in the context of work on the Korteweg-de Vries equations. I recall the Korteweg-deVries equation, introduced the use his triumphal announcement, “It unfolded like a of scattering parameters of an associated linear prob- lily!” (After much intense work, I imagine.) He would lem to solve a nonlinear equation—effectively gen- be truly delighted with its recognition by the Amer- eralizing Fourier series and Fourier transforms to ican Mathematical Society. nonlinear equations. The idea was quickly extended Biographical Sketch: Martin D. Kruskal to other nonlinear evolution equations, triggering Martin D. Kruskal was born in New York City on important work in dynamical systems, inverse scat- September 28, 1925. He earned his B.S. from the tering, and symplectic geometry, to name a few. In University of Chicago in 1945 and his M.S. and applications of mathematics, solitons and their de- Ph.D. from New York University in 1948 and 1952, scendants (kinks, anti-kinks, in- respectively. He began his career as an instructor stantons, and breathers) have en- in the mathematics department at New York tered and changed such diverse University (1946–1951) and then moved to Princeton fields as nonlinear optics, plasma University as a Research Scientist in the Plasma physics, and ocean, atmospheric, Physics Laboratory (formerly Project Matterhorn), and planetary sciences. Nonlin- becoming Senior Research Associate in 1959. While earity has undergone a revolution: at Princeton, he was a lecturer in astronomy (1959– from a nuisance to be eliminated, 1961), Director of the Program in Applied (and to a new tool to be exploited. Computational) Mathematics (1968–1986), profes- Biographical Sketch: Clifford S. sor of astrophysical sciences (1961–1989), profes- Gardner sor of mathematics (1979–1989), and is professor Clifford S. Gardner was born in emeritus (1989– ). He is currently David Hilbert Fort Smith, Arkansas, in 1924. Professor of Mathematics at Rutgers University. He graduated from Phillips Kruskal has given innumerable invited lectures Academy in 1940 and received at conferences and institutions and has served on his A.B. from Harvard College many advisory committees and editorial boards. He in 1944 and his Ph.D. from New has traveled widely and has held various visiting and York University in 1952. He fellowship positions at the Max Planck Institut für worked in applied mathematics Physik und Astrophysik (Munich), the University of at various places including Grenoble (France), the Lebedev Institute (Moscow), the Clifford S. Gardner NASA Langley Field, Livermore Weizmann Institute of Science (Israel), Nagoya

466 NOTICES OF THE AMS VOLUME 53, NUMBER 4 John M. Greene Martin D. Kruskal Robert M. Miura University (Japan), Bharathidasan University (India), degrees in mechanical engineering from the Uni- Australian National University, the University of New versity of California at Berkeley in 1960 and 1962, South Wales (Australia), the University of Adelaide respectively, and his M.A. and Ph.D. in aerospace (Australia), Los Alamos National Laboratory, the and mechanical sciences from University of California at Santa Barbara, and the in 1964 and 1966, respectively. His doctoral re- University of Chicago. search was in the area of the kinetic theory of Kruskal has been the recipient of numerous gases. His first postdoctoral position in 1965–1967 honors and awards, including the National Medal was at the Princeton Plasma Physics Laboratory, of Science, the National Academy of Sciences Award part of Princeton University, where he started re- in Applied Mathematics and Numerical Analysis, the search on nonlinear wave propagation. There he von Neumann Prize of the Society for Industrial and worked closely with Martin Kruskal, Clifford Gard- Applied Mathematics, and the Potts Gold Medal of ner, and John Greene on the Korteweg-de Vries the Franklin Institute (Philadelphia). He has re- equation, a nonlinear dispersive partial differential ceived an honorary doctorate from Heriot-Watt equation exhibiting soliton solutions and having nu- University. He is a member of the National Acad- merous applications. This collaboration led to the emy of Sciences and the American Academy of inverse scattering method for exact solution of the Arts and Sciences, a foreign member of the Royal KdV equation and also to the proof of an infinite Society of London and the Russian Academy of number of conservation laws. His postdoctoral po- Natural Sciences, and an Honorary Fellow of the sition at the Courant Institute in 1967–1968 was Royal Society of Edinburgh. in the Magneto-Fluid Dynamics Division headed Response: Martin D. Kruskal by Harold Grad. It is usual for a prize recipient to thank the rele- Miura has taught at New York University (1968– vant society, the AMS in the present case, and the 1971), Vanderbilt University (1971–1975), and the committee members who made the selection, for University of British Columbia (1975–2001). In being selected—and I do certainly wish to express 1975, upon his arrival at the University of British those sentiments. However, I also wish warmly to Columbia, his research interests changed to math- thank my co-recipients, who played such a major ematical neuroscience, specifically excitable cells, role in our joint research, and from whom I learned and mathematical physiology more generally. Since so much in the process. 2001, he has been Professor of Mathematical Among the several functions that such prizes Sciences and of Biomedical Engineering at the New serve, a seldom mentioned one is to validate the Jersey Institute of Technology. He is currently act- decisions and efforts that the awardees invested ing chair of the Department of Mathematical Sci- in over, often, years of self-doubt and threatening ences. He is a fellow of the John Simon Guggenheim discouragement. Research success may indeed be Foundation (1980), the Royal Society of Canada its own reward, but it helps nevertheless to receive (1995), and the American Association for the Ad- the recognition of one’s peers. vancement of Science (2005). He has authored So, thanks to all of you! many research papers and served on several edi- Biographical Sketch: Robert M. Miura torial boards. Presently, he is co-editor-in-chief of Robert M. Miura was born on September 12, 1938, Analysis and Applications and is on the editorial in Selma, California. He received his B.S. and M.S. boards of the Canadian Applied Mathematics

APRIL 2006 NOTICES OF THE AMS 467 Quarterly and Integrative Neuroscience. He is a quasiconformality is an essential ingredient of the member of the American Mathematical Society, Mostow rigidity theorem and of recent work of the Society for Industrial and Applied Mathemat- Donaldson and Sullivan on gauge theory and four- ics, the Society for Mathematical Biology, the Cana- , and quasiconformality has inspired dian Mathematical Society, and the American As- much beautiful recent analysis on general metric sociation for the Advancement of Science. spaces by Heinonen, Koskela, and others. Response: Robert M. Miura Gehring’s mathematics is characterized by its I am particularly pleased, honored, and humbled elegance and simplicity and by its emphasis on to receive the 2006 Leroy P. Steele Prize along with deceptively elementary questions which later my colleagues, Clifford Gardner, John Greene, and become surprisingly significant. Martin Kruskal, and to be recognized for the work A person of incredible energy and enthusiasm, on the Korteweg-de Vries equation that we did Fred Gehring has trained twenty-nine Ph.D. stu- forty years ago. As a fresh postdoc, I was very for- dents, many of whom are now faculty members at tunate to have had the opportunity to work with research universities, and he has mentored more and to have been mentored by three generous and than forty postdoctoral fellows. The list of Gehring’s smart guys. The two years at the Princeton Plasma former postdocs at Michigan represents a large Physics Laboratory were the happiest and most ex- fraction of the present day leaders in complex citing years in my research career. Every day came analysis. with the time to think deeply about new ideas and Biographical Sketch to produce results. The soliton solutions of the KdV Frederick Gehring was born in Ann Arbor, Michi- equation, discovered by Kruskal and Zabusky, gan, and his association with the University of showed this equation is special. The initial-value Michigan goes back two generations to his grand- problem for the KdV equation is fascinating, and father, John Oren Reed, who was a member of the there are many special properties of the equations, physics faculty and Dean of the College of Litera- e.g., an infinity of conservation laws resulting in ture, Science and the Arts. Gehring joined the U.S. infinitely many conserved integrals of the motion. Navy in 1943 and subsequently earned two de- A major breakthrough was the development of a grees from Michigan—bachelor of science in math- method for exact solution of the initial-value prob- ematics and electrical engineering in 1946, and lem for the KdV equation on the infinite line, which master of science in mathematics in 1949. He re- we called the “inverse scattering method” since turned to teach mathematics at Michigan in 1955 it utilized the scattering problem for the time- after completing his Ph.D. at Cambridge and spend- independent Schrödinger equation. At the time, we ing three years as a Benjamin Peirce Instructor at thought this method was very special and only Harvard. He became a professor in 1962, was named could be applied to this equation. However, the to a collegiate chair in 1984, and became the T. H. Russians Zakharov and Shabat showed how to Hildebrandt Distinguished University Professor in generalize the method to systems of equations, and 1987, one of the university’s highest honors for fac- the rest is history. ulty. His long and distinguished history of service at Michigan includes three terms as chair of the de- Lifetime Achievement: partment of mathematics. Frederick W. Gehring Gehring has received numerous awards, in- Citation cluding the Distinguished Faculty Achievement For over fifty years F. W. Gehring has been a leading Award, the Sokol Faculty Award, the Humbolt figure in the theory of quasiconformal mappings. Award, and an Onsager Professorship. He was the The cornerstone of the two-dimensional theory is Henry Russel Lecturer for 1990. In 1989 he was his theorem that the geometric definition of quasi- elected to the National Academy of Sciences. He has conformality (infinitesimal discs are mapped to in- also received honorary degrees from the University finitesimal ellipses with eccentricity bounded) implies of Helsinki, the University of Jyväskylä, and the Nor- the more restrictive analytic definition. Gehring cre- wegian University of Science and Technology. ated the higher dimensional theory of quasiconfor- Gehring also has a long record of service to the mal maps, which is very different from the two- AMS. He has been a member of the Executive Com- dimensional case. His work on convergence theo- mittee (1973–1975, 1980–1982), a Member at Large rems, Hölder exponents, and the Lp integrability of of the Council (1980–1982), and a member of the Jacobians forms the foundation of the higher di- Board of Trustees (1983–1992; chair 1986, 1991). mensional theory. He has served on numerous committees, including Largely because of Gehring’s work, the theory of the Committee on Science Policy (1981–1983, 1985– quasiconformal mappings has influenced many 1987), the Committee on Governance (1993; chair), other parts of mathematics, including complex and the Editorial Committees for the Bulletin, Math- dynamics, function theory, partial differential ematical Reviews, Proceedings, and the Electronic equations, and . Higher dimensional Journal on Conformal Geometry and Dynamics.

468 NOTICES OF THE AMS VOLUME 53, NUMBER 4 Fulbright and Guggenheim Fellowships in 1958– manifolds. Later Sullivan de- 1960 allowed Gehring to study in Helsinki and Zürich, veloped and applied rational where he began to learn the theory of quasiconfor- to prob- mal mappings, a subject that became the focus of lems about closed geodesics, his life’s work. He was instrumental in developing the the automorphism group of theory, often in collaboration with Finnish colleagues, a finite complex, the topol- in bringing it into the mainstream of mathematical ogy of Kähler manifolds, and analysis, and in making contact with potential the- the classification of smooth ory, partial differential equations, geometric topol- manifolds. He has reinvented ogy, Riemannian geometry, and complex dynamics, himself several times, playing as well as classical function theory. In particular, he major or dominant roles in pioneered the important extension of the theory to dynamical systems, Kleinian n-dimensional space, emphasizing new tools such as groups, and low dimensional extremal length, and has brought quasiconformal topology. mappings into a broad study of discrete transfor- These brief remarks do mation groups. He has generously shared his passion not do justice to the scope of for mathematics and research by mentoring over Sullivan’s ideas and influ- seventy Ph.D. students and postdoctoral fellows dur- ence. Beyond the specific the- Frederick W. Gehring ing his career. ories he has developed and Response the problems he has Some of the earliest memories I had as a child were solved—and there are many music which my father played on a piano and or- significant ones not men- chestral pieces which he played on a large victrola. tioned here—his uniform vi- I was fascinated by what I heard and subsequently sion of mathematics perme- spent several years learning how to play the piano. ates his work and has Later as I was finishing high school in 1943 I inspired those around him. learned how to build radios and looked forward to For many years he was at the a career in physics. But world events intervened. I center of the mathematical joined the U.S. Navy V-12 program in June 1943 and conversation at IHÉS [Institut spent the next thirty-two months as a student in des Hautes Études Scien- the Department of Electrical Engineering at the tifiques]. Later he moved to University of Michigan. New York where his weekly This was a fascinating but somewhat frustrating seminar remains an impor- experience since I would have preferred to see more tant feature of mathemati- rigorous proofs for the things I had learned. Hence cal life in the City. after the war I changed my major and studied math- Biographical Sketch ematics at Michigan and then at Cambridge Univer- Dennis Sullivan was born sity in . February 12, 1941, in Port Dennis P. Sullivan I never regretted that decision, and I consider Huron, Michigan, but he grew the ensuing years of teaching and research as the up in Houston, Texas. He happiest possible. The opportunity to guide my graduated from in 1963 and went Ph.D. students and the postdoctoral fellows with to Princeton University; his Ph.D. thesis (1966) on whom I have worked was educational, rewarding, geometric topology was written under the direction and fulfilling. of William Browder. After graduation Indeed I would feel quite remiss in accepting this he held a NATO Fellowship at Warwick, where he award without acknowledging how much I owe to continued work in the general area of his thesis them. So now I thank you for this award which I ( for manifolds, 1967), and a Miller accept in their names also. Fellowship at Berkeley (work on the Adams con- jecture, K-theory, and étale homotopy). He spent Lifetime Achievement: Dennis P. Sullivan 1969 to 1973 as a Sloan Fellow of Mathematics at Citation the Massachusetts Institute of Technology, study- Dennis Sullivan has made fundamental contribu- ing localization in homotopy theory (in particular, tions to many branches of mathematics. Sullivan’s Galois symmetry), étale theory, and the construc- theory of localization and Galois symmetry, tion of minimal models for the rational homotopy propagated in his famous 1970 MIT [Massachusetts type of manifolds, using differential forms. Institute of Technology] notes, has been at the heart He shared the AMS Veblen Prize with Rob Kirby of many subsequent developments in homotopy the- in 1971. In 1973–1974, Sullivan visited the ory. Sullivan used it to solve the Adams Conjecture University of Paris-Orsay. He remained in France as and the Hauptvermutung for combinatorial professeur permanent at the Institut des Hautes

APRIL 2006 NOTICES OF THE AMS 469 Études Scientifiques, full-time until 1981, when he was named Einstein Professor at the City Univer- Photo Index to Pages 410–411 sity of New York, and half-time after that until 1996, when he joined the Mathematics Department and the Institute for Mathematical Sciences at 18 27 SUNY, Stony Brook. During his years in France, his 8 15 1 23 interests expanded first towards dynamical sys- 9 tems, including ergodic theory, foliations, Kleinian 2 19 28 groups, and renormalization, and then, motivated 16 3 10 24 originally by problems in conformal dynamics, to- wards Teichmüller theory (No Wandering Domains 20 29 11 Theorem, 1982). He was awarded the Prix Élie Car- 4 17 25 12 tan by the Académie des Sciences de Paris in 1981, 30 the in Science in 1994, the Ordem 21 5 Scientifico Nacional by the Brazilian Academy of 13 26 Sciences in 1998, and the United States National 6 22 Medal of Science in 2005. He was elected to the 7 14 United States National Academy of Sciences in 1983 and to the Brazilian National Academy of Sci- ences in 1984. He was awarded honorary degrees 1. Welcome to the Joint Mathematics Meetings, San by the University of Warwick in 1983 and the École Antonio, TX, Henry B. Gonzalez Convention Center. Normale Supérieure de Lyon in 2001. His most 2. MAA Booth, Exhibits area. recent work centers on quasiconformal analysis, 3. Moving about the Convention Center. holomorphic dynamics, and the relation between 4. Ribbon-cutting ceremony for the Exhibits area (left to , quantum theory, and fluid dy- right: James Tattersall (MAA), Martha Siegel (MAA), namics. Dennis Sullivan has three daughters, three John Ewing (AMS), James Arthur (AMS), Carl Cowen sons, and two grandchildren. (MAA), Robert Daverman (AMS), Tina Straley (MAA)). 5. Sharing ideas between sessions. Response 6. AMS Booth, Exhibits area. I am very honored and pleased to receive the Steele 7. Opening day of the Exhibits. Prize—with a small nuance that it is awarded for 8. Birkhoff Prize winner Cathleen S. Morawetz. work done up to now. I am still trying to understand 9. Steele Prize winner Dennis P. Sullivan. the correct algebraic structure of an algebraic model 10. Steele Prize winner Clifford S. Gardner with AMS for or spacetime. My thesis advisor’s orig- president James Arthur. inal emphasis on Poincaré duality is still the guide, 11. AMS Colloquium Lecturer Hendrik W. Lenstra Jr. but now expressed in new algebraic data related to 12. Audience in large lecture. the physicist’s correlations, or multilinear func- 13. Who Wants To Be a game contestant. tions on a space of states. I hope to apply this to 14. “Hands-on” at the Math in Art exhibit. write down finite dimensional computationally ef- 15. Interviewing in the Employment Center. fective algorithms in nonlinear problems like fluid 16. Math on the Web demonstration. dynamics with applications to problems like help- 17. Left to right, AMS executive director John Ewing, AMS ing out the 48 hour more precise advance predic- senior editor Ina Lindemann, former AMS president tion of the landfall of hurricanes like Katrina and David Eisenbud. Rita. 18. Mathematical artwork. 19. New Orleans (site of 2007 JMM) information booth. 20. Interviewing in the Employment Center. 21. Steele Prize winner Frederick W. Gehring and Mrs. Gehring. 22. JMM registration booth. 23. Who Wants To Be a Mathematician contestants during the game. 24. Chess between sessions. 25. Networking area. 26. “Glass Geometry” booth. 27. Email center. 28. Dusa McDuff, AMS Invited Address speaker. 29. Message Board. 30. Who Wants To Be a Mathematician winners Susan Zhang and David Neville with host Mike Breen.

470 NOTICES OF THE AMS VOLUME 53, NUMBER 4