DOCSLIB.ORG

Thomas H. Wolff (1954–2000) Lennart Carleson, Sun-Yung Alice Chang, Peter W

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Thomas H. Wolff (1954–2000) Lennart Carleson, Sun-Yung Alice Chang, Peter W fea-wolff.qxp 3/20/01 10:26 AM Page 482 Thomas H. Wolff (1954–2000) Lennart Carleson, Sun-Yung Alice Chang, Peter W. Jones, Markus Keel, Peter D. Lax, Nikolai Makarov, Donald Sarason, Wilhelm Schlag, and Barry Simon homas H. Wolff, a leading analyst and a win- Lennart Carleson ner of the Salem and Bôcher Prizes, was killed Tin an automobile accident on July 31, 2000, Harmonic analysis has a position in mathe- when he was forty-six years old. matics comparable to that of the theory of the Tom was raised in a mathematical environment. atom in physics. By understanding what goes on His uncle, Clifford Gardner, was a professor at at the micro level, we can understand large-scale NYU’s Courant Institute of Mathematics for many phenomena (even such as meteorology). By Fourier years, and Tom’s mother, Lucile, was a technical expansions we can analyze and understand global editor of volume 1 of the English translation of the functions, arithmetic problems, or differential celebrated book Methods of Mathematical Physics equations. As physics has a miracle method in by Courant and Hilbert. quantum mechanics, we use the theory of analytic Tom was an undergraduate at Harvard, where, functions, and of course, in a deeper sense, all he once told me, he regularly played poker with a this comes together as one piece. These methods fellow student named Bill Gates. After graduating are efficient when the number of variables n is from Harvard in 1975, Tom went to Berkeley, where either small or very large (where the theories be- he got his Ph.D. under Don Sarason in 1979. Tom come probability). In the intermediate range, say 10 <n<100, physicists and chemists have been then spent one year at the University of Washing- more successful than we mathematicians, and it ton and two at the University of Chicago before remains an important challenge for the future to coming to Caltech in the fall of 1982 as an assis- develop relevant harmonic analysis in this range. tant professor. The problems in harmonic analysis (of few vari- Tom spent most of the rest of his career at Cal- ables) today, after two hundred years of research, tech, although, for personal reasons, he resigned are very combinatorial and very complicated. Tom twice, spending two years (1986–88) at Courant and Wolff had a unique talent and a profound knowl- three (1992–95) at Berkeley. His promotion or edge in the area. The fundamental problems that appointment to a professorship at Caltech three he considered required long preparation, deep times is a record for our institution. concentration, and an ability to keep a very com- Tom is survived by his widow, Carol Shubin, a plicated set of arguments simultaneously active mathematics professor at California State Univer- and available in his mind. Two quotations come to sity, Northridge; two sons (aged three and five at mind. The first is Newton’s answer to how he his death); his parents; and two sisters. —Barry Simon Lennart Carleson is professor emeritus of mathematics at the Royal Institute of Technology, Stockholm, Sweden and Photographs included in this article are courtesy of Carol at the University of California, Los Angeles. His e-mail ad- Shubin. dress is [email protected]. 482 NOTICES OF THE AMS VOLUME 48, NUMBER 5 fea-wolff.qxp 3/20/01 10:26 AM Page 483 found the law of gravitation: “By constantly think- ing about it,” and the second is Tom’s remark Ph.D. Students of Tom Wolff when he was awarded the Bôcher Prize in 1999: “It’s never been easy for me.” Nobody else could have Ivo Klemes, Caltech, 1985 done what he did. Peter Holden, Caltech, 1987 Let me highlight some of Tom’s most striking Gregory Hungerford, Caltech, 1988 results, all coming from combinatorial harmonic Stewart Gleason, NYU, 1990 analysis. Tom’s thesis and early work were in the Dean Evasius, Caltech, 1992 direction of complex analysis. (His thesis is de- Wensheng Wang, Caltech, 1993 scribed below by D. Sarason.) While working on his Lawrence Kolasa, Caltech, 1994 thesis Tom found a new proof of the corona the- Wilhelm Schlag, Caltech, 1996 orem for H∞ of the unit disk. Here he managed to David Alvarez, UC Berkeley, 1997 summarize the combinatorics in a beautiful lemma Themistoklis Mitsis, Caltech, 1998 on bounded solutions, u of ∂u = f. As first pointed Oleg Kovrijkine, Caltech, 2000 out by Hörmander, one should first solve the rel- Burak Erdogan, Caltech, 2001 evant equations in a nonanalytic way and then modify the solution to make it analytic bounded, which leads to the above equation. To get the ω>0, but barely so. Consider, for example, = boundedness of the solutions, the old combina- complement of disjoint disks torics came back, and this is where Tom’s lemma works; see [4]. D : |z a|,a = + i , This lemma has had a large impact, although N N Tom never published it. He did not return much 0 < ||, ||N, to function algebras. I can mention a joint paper 1 with Alan Noell (1989) which gives an almost com- and choose so that ω(D)= 4N2 for all and plete description of sets E on |z| =1where an an- . The radii in the outer part of the square must alytic function f (z) in |z| < 1, satisfying be very small, but a proof is not easy and the |f (z) f (w)|C|z w| , |f (z)|1, f (0) = 0 , can precise size of is not known (to me). It was a be =1 (so-called peak sets). This is surprisingly tour de force when Tom and Peter Jones in 1988 hard! proved the statement about dim(E) 1 in full From function algebras Tom turned to potential generality [6], and Tom even proved (published theory, where his most important work in the 1980s in 1993 but from the same time) that E can be can be found. The first fundamental result [5] is chosen of -finite length.P In the above example, from 1983. L. I. Hedberg had proved that if is an Tom’s method proves that C, |a|1/2. Rn ∞ open set in , then C0 () is dense in all higher- There is a natural conjecture for the analogous m,p m order Sobolev spaces W0 () when p>2 n . problem in higher dimension n (Øksendal 1981) m The exceptions 1 <p 2 n had their origin in that E ∂ can be chosen of dimension n 1. In potential theory and more precisely in the miss- 1987 Tom produced a counterexample to this ing Kellogg lemma on the size of the set of thin conjecture for n =3. This was a sensation not boundary points outside that range. Tom closed only because of its complexity but also because it this gap by a clever construction. Today more simultaneously disproved two other conjectures. streamlined approaches exist. It was published only in 1991 [11]. Tom next turned to harmonic measure. Let The construction is based on the following be a domain in the plane containing ∞, and sup- lemma: For each unit vector e in R3 , there is a har- pose that we can solve the Dirichlet problem in monic function u in x3 > 0, vanishing at ∞, so for arbitrary continuous f on ∂. The value of the that Z solution at ∞ is given by integrating f against a (*) log |e + ∇u| dx1dx2 < 0. positive probability measure ω in the plane sup- R2 ported on ∂. This is called harmonic measure and is also the hitting probability on ∂ of a Brown- This fails in two dimensions by subharmonicity. ian particle in , starting at ∞. From this inter- This entropy-type of integral is relevant because pretation, it is natural to surmise that most mea- the counterexample domain is obtained in a sure lies in the exposed parts of ∂. The harmonic dynamic way by a snowflake construction where measure should therefore be 1-dimensional; more almost independent products of gradient vectors precisely: ∃?E of dimension 1 on ∂ with as above occur. (A result by Bourgain tells us that ω(E)=1. By using the Riemann map, N. G. dim(E) n n is possible, but the correct n is Makarov proved this in 1985 in a very precise not known.) Tom’s construction also solves (par- sense for simply connected domains. For general tially) a problem of Bers: There is u harmonic in 1+ domains it is much more complicated. The main x3 > 0, C up to x3 =0, such that u = |∇u| =0 difficulty comes from those parts of ∂ where on a set of positive measure on x3 =0. Here is MAY 2001 NOTICES OF THE AMS 483 fea-wolff.qxp 3/20/01 10:26 AM Page 484 Charles Fefferman’s solution of the “ball-multi- plier-problem” (1971). If ˆf (), ∈ Rd , d 2, is the Fourier transform of f ∈ Lp, p>1, is ˆf , restricted to ||1, the Fourier transform of some g ∈ Lp ? This is true for d =1(Hilbert transform) and for p =2 and all d, but Fefferman gave a counterex- ample for all other p and d. The obstruction comes from thin layers 1 ||1 which contain long ( 1/2) rectangles of width of all directions. In this way the counterexample comes from Besi- covitch’s 1928 construction (as a solution of a problem of Kakeya’s concerning “sets where you can turn a needle”) of a compact set in R2 of zero measure that contains a line segment of length 1 in every direction. (For this classical theory see [3].) It is rather easy to see that the Hausdorff di- mension of a Kakeya set is 2.
Load more

Recommended publications
  • Gromov Receives 2009 Abel Prize
    Gromov Receives 2009 Abel Prize . The Norwegian Academy of Science Medal (1997), and the Wolf Prize (1993). He is a and Letters has decided to award the foreign member of the U.S. National Academy of Abel Prize for 2009 to the Russian- Sciences and of the American Academy of Arts French mathematician Mikhail L. and Sciences, and a member of the Académie des Gromov for “his revolutionary con- Sciences of France. tributions to geometry”. The Abel Prize recognizes contributions of Citation http://www.abelprisen.no/en/ extraordinary depth and influence Geometry is one of the oldest fields of mathemat- to the mathematical sciences and ics; it has engaged the attention of great mathema- has been awarded annually since ticians through the centuries but has undergone Photo from from Photo 2003. It carries a cash award of revolutionary change during the last fifty years. Mikhail L. Gromov 6,000,000 Norwegian kroner (ap- Mikhail Gromov has led some of the most impor- proximately US$950,000). Gromov tant developments, producing profoundly original will receive the Abel Prize from His Majesty King general ideas, which have resulted in new perspec- Harald at an award ceremony in Oslo, Norway, on tives on geometry and other areas of mathematics. May 19, 2009. Riemannian geometry developed from the study Biographical Sketch of curved surfaces and their higher-dimensional analogues and has found applications, for in- Mikhail Leonidovich Gromov was born on Decem- stance, in the theory of general relativity. Gromov ber 23, 1943, in Boksitogorsk, USSR. He obtained played a decisive role in the creation of modern his master’s degree (1965) and his doctorate (1969) global Riemannian geometry.
    [Show full text]
  • Prvních Deset Abelových Cen Za Matematiku
    Prvních deset Abelových cen za matematiku The first ten Abel Prizes for mathematics [English summary] In: Michal Křížek (author); Lawrence Somer (author); Martin Markl (author); Oldřich Kowalski (author); Pavel Pudlák (author); Ivo Vrkoč (author); Hana Bílková (other): Prvních deset Abelových cen za matematiku. (English). Praha: Jednota českých matematiků a fyziků, 2013. pp. 87–88. Persistent URL: http://dml.cz/dmlcz/402234 Terms of use: © M. Křížek © L. Somer © M. Markl © O. Kowalski © P. Pudlák © I. Vrkoč Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz Summary The First Ten Abel Prizes for Mathematics Michal Křížek, Lawrence Somer, Martin Markl, Oldřich Kowalski, Pavel Pudlák, Ivo Vrkoč The Abel Prize for mathematics is an international prize presented by the King of Norway for outstanding results in mathematics. It is named after the Norwegian mathematician Niels Henrik Abel (1802–1829) who found that there is no explicit formula for the roots of a general polynomial of degree five. The financial support of the Abel Prize is comparable with the Nobel Prize, i.e., about one million American dollars. Niels Henrik Abel (1802–1829) M. Křížek a kol.: Prvních deset Abelových cen za matematiku, JČMF, Praha, 2013 87 Already in 1899, another famous Norwegian mathematician Sophus Lie proposed to establish an Abel Prize, when he learned that Alfred Nobel would not include a prize in mathematics among his five proposed Nobel Prizes.
    [Show full text]
  • Issue 73 ISSN 1027-488X
    NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Feature History Interview ERCOM Hedgehogs Richard von Mises Mikhail Gromov IHP p. 11 p. 31 p. 19 p. 35 September 2009 Issue 73 ISSN 1027-488X S E European M M Mathematical E S Society Geometric Mechanics and Symmetry Oxford University Press is pleased to From Finite to Infinite Dimensions announce that all EMS members can benefit from a 20% discount on a large range of our Darryl D. Holm, Tanya Schmah, and Cristina Stoica Mathematics books. A graduate level text based partly on For more information please visit: lectures in geometry, mechanics, and symmetry given at Imperial College www.oup.co.uk/sale/science/ems London, this book links traditional classical mechanics texts and advanced modern mathematical treatments of the FORTHCOMING subject. Differential Equations with Linear 2009 | 460 pp Algebra Paperback | 978-0-19-921291-0 | £29.50 Matthew R. Boelkins, Jack L Goldberg, Hardback | 978-0-19-921290-3 | £65.00 and Merle C. Potter Explores the interplaybetween linear FORTHCOMING algebra and differential equations by Thermoelasticity with Finite Wave examining fundamental problems in elementary differential equations. This Speeds text is accessible to students who have Józef Ignaczak and Martin completed multivariable calculus and is appropriate for Ostoja-Starzewski courses in mathematics and engineering that study Extensively covers the mathematics of systems of differential equations. two leading theories of hyperbolic October 2009 | 464 pp thermoelasticity: the Lord-Shulman Hardback | 978-0-19-538586-1 | £52.00 theory, and the Green-Lindsay theory. Oxford Mathematical Monographs Introduction to Metric and October 2009 | 432 pp Topological Spaces Hardback | 978-0-19-954164-5 | £70.00 Second Edition Wilson A.
    [Show full text]
  • The Abel Prize 2003-2007 the First Five Years
    springer.com Mathematics : History of Mathematics Holden, Helge, Piene, Ragni (Eds.) The Abel Prize 2003-2007 The First Five Years Presenting the winners of the Abel Prize, which is one of the premier international prizes in mathematics The book presents the winners of the first five Abel Prizes in mathematics: 2003 Jean-Pierre Serre; 2004 Sir Michael Atiyah and Isadore Singer; 2005 Peter D. Lax; 2006 Lennart Carleson; and 2007 S.R. Srinivasa Varadhan. Each laureate provides an autobiography or an interview, a curriculum vitae, and a complete bibliography. This is complemented by a scholarly description of their work written by leading experts in the field and by a brief history of the Abel Prize. Interviews with the laureates can be found at http://extras.springer.com . Order online at springer.com/booksellers Springer Nature Customer Service Center GmbH Springer Customer Service Tiergartenstrasse 15-17 2010, XI, 329 p. With DVD. 1st 69121 Heidelberg edition Germany T: +49 (0)6221 345-4301 [email protected] Printed book Hardcover Book with DVD Hardcover ISBN 978-3-642-01372-0 £ 76,50 | CHF 103,00 | 86,99 € | 95,69 € (A) | 93,08 € (D) Out of stock Discount group Science (SC) Product category Commemorative publication Series The Abel Prize Prices and other details are subject to change without notice. All errors and omissions excepted. Americas: Tax will be added where applicable. Canadian residents please add PST, QST or GST. Please add $5.00 for shipping one book and $ 1.00 for each additional book. Outside the US and Canada add $ 10.00 for first book, $5.00 for each additional book.
    [Show full text]
  • Sinai Awarded 2014 Abel Prize
    Sinai Awarded 2014 Abel Prize The Norwegian Academy of Sci- Sinai’s first remarkable contribution, inspired ence and Letters has awarded by Kolmogorov, was to develop an invariant of the Abel Prize for 2014 to dynamical systems. This invariant has become Yakov Sinai of Princeton Uni- known as the Kolmogorov-Sinai entropy, and it versity and the Landau Insti- has become a central notion for studying the com- tute for Theoretical Physics plexity of a system through a measure-theoretical of the Russian Academy of description of its trajectories. It has led to very Sciences “for his fundamen- important advances in the classification of dynami- tal contributions to dynamical cal systems. systems, ergodic theory, and Sinai has been at the forefront of ergodic theory. mathematical physics.” The He proved the first ergodicity theorems for scat- Photo courtesy of Princeton University Mathematics Department. Abel Prize recognizes contribu- tering billiards in the style of Boltzmann, work tions of extraordinary depth he continued with Bunimovich and Chernov. He Yakov Sinai and influence in the mathemat- constructed Markov partitions for systems defined ical sciences and has been awarded annually since by iterations of Anosov diffeomorphisms, which 2003. The prize carries a cash award of approxi- led to a series of outstanding works showing the mately US$1 million. Sinai received the Abel Prize power of symbolic dynamics to describe various at a ceremony in Oslo, Norway, on May 20, 2014. classes of mixing systems. With Ruelle and Bowen, Sinai discovered the Citation notion of SRB measures: a rather general and Ever since the time of Newton, differential equa- distinguished invariant measure for dissipative tions have been used by mathematicians, scientists, systems with chaotic behavior.
    [Show full text]
  • Tate Receives 2010 Abel Prize
    Tate Receives 2010 Abel Prize The Norwegian Academy of Science and Letters John Tate is a prime architect of this has awarded the Abel Prize for 2010 to John development. Torrence Tate, University of Texas at Austin, Tate’s 1950 thesis on Fourier analy- for “his vast and lasting impact on the theory of sis in number fields paved the way numbers.” The Abel Prize recognizes contributions for the modern theory of automor- of extraordinary depth and influence to the math- phic forms and their L-functions. ematical sciences and has been awarded annually He revolutionized global class field since 2003. It carries a cash award of 6,000,000 theory with Emil Artin, using novel Norwegian kroner (approximately US$1 million). techniques of group cohomology. John Tate received the Abel Prize from His Majesty With Jonathan Lubin, he recast local King Harald at an award ceremony in Oslo, Norway, class field theory by the ingenious on May 25, 2010. use of formal groups. Tate’s invention of rigid analytic spaces spawned the John Tate Biographical Sketch whole field of rigid analytic geometry. John Torrence Tate was born on March 13, 1925, He found a p-adic analogue of Hodge theory, now in Minneapolis, Minnesota. He received his B.A. in called Hodge-Tate theory, which has blossomed mathematics from Harvard University in 1946 and into another central technique of modern algebraic his Ph.D. in 1950 from Princeton University under number theory. the direction of Emil Artin. He was affiliated with A wealth of further essential mathematical ideas Princeton University from 1950 to 1953 and with and constructions were initiated by Tate, includ- Columbia University from 1953 to 1954.
    [Show full text]
  • The Abel Prize Laureate 2017
    The Abel Prize Laureate 2017 Yves Meyer École normale supérieure Paris-Saclay, France www.abelprize.no Yves Meyer receives the Abel Prize for 2017 “for his pivotal role in the development of the mathematical theory of wavelets.” Citation The Abel Committee The Norwegian Academy of Science and or “wavelets”, obtained by both dilating infinite sequence of nested subspaces Meyer’s expertise in the mathematics Letters has decided to award the Abel and translating a fixed function. of L2(R) that satisfy a few additional of the Calderón-Zygmund school that Prize for 2017 to In the spring of 1985, Yves Meyer invariance properties. This work paved opened the way for the development of recognised that a recovery formula the way for the construction by Ingrid wavelet theory, providing a remarkably Yves Meyer, École normale supérieure found by Morlet and Alex Grossmann Daubechies of orthonormal bases of fruitful link between a problem set Paris-Saclay, France was an identity previously discovered compactly supported wavelets. squarely in pure mathematics and a theory by Alberto Calderón. At that time, Yves In the following decades, wavelet with wide applicability in the real world. “for his pivotal role in the Meyer was already a leading figure analysis has been applied in a wide development of the mathematical in the Calderón-Zygmund theory of variety of arenas as diverse as applied theory of wavelets.” singular integral operators. Thus began and computational harmonic analysis, Meyer’s study of wavelets, which in less data compression, noise reduction, Fourier analysis provides a useful way than ten years would develop into a medical imaging, archiving, digital cinema, of decomposing a signal or function into coherent and widely applicable theory.
    [Show full text]
  • 2000 Annual Report
    2001 ANNUAL REPORT ALFRED P. SLOAN FOUNDATION 1 CONTENTS 2001 Grants and Activities Science and Technology 5 Fellowships 5 Sloan Research Fellowships 5 Direct Support of Research 9 Neuroscience 9 Computational Molecular Biology 9 Limits to Knowledge 10 Marine Science 11 Other Science and Science Policy 15 History of Science and Technology 16 Standard of Living and Economic Performance 17 Industries 17 Industry Centers 17 Human Resources/Jobs/Income 21 Globalization 21 Business Organizations 22 Economics Research and Other Work 24 Nonprofit Sectors 26 Universities 26 Assessment of Government Performance 26 Work, Workforce and Working Families 30 Centers on Working Families 30 Workplace Structure and Opportunity 31 Working Families and Everyday Life 34 Education and Careers in Science and Technology 36 Scientific and Technical Careers 36 Anytime, Anyplace Learning 36 Professional Master’s Degrees 42 Information about Careers 47 Entry and Retention 48 Science and Engineering Education 48 Education for Minorities and Women 49 Minorities 49 Women 53 Public Understanding of Science and Technology 55 Books 55 Sloan Technology Book Series 57 Radio 58 2 Public Television 59 Commercial Television and Films 60 Theater 61 General 63 Selected National Issues and The Civic Program 64 Selected National Issues 64 September 11 64 Bioterrorism 66 Energy 68 Federal Statistics 69 Public Policy Research 69 The Civic Program 71 Additional Grants 73 2001 Financial Report Financial Review 75 Auditors’ Report 76 Balance Sheets 77 Statements of Activities 78 Statements of Cash Flows 79 Notes to Financial Statements 80 Schedules of Management and Investment Expenses 83 3 2001 GRANTS AND ACTIVITIES 4 SCIENCE AND TECHNOLOGY FELLOWSHIPS Sloan Research Fellowships $4,160,000 The Sloan Research Fellowship Program aims to stimulate fundamental research by young scholars with outstanding promise to contribute significantly to the advancement of knowledge.
    [Show full text]
  • Fundamental Theorems in Mathematics
    SOME FUNDAMENTAL THEOREMS IN MATHEMATICS OLIVER KNILL Abstract. An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 243 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [6] without leading to panic. The order is not a ranking but ordered along a time-line when things were writ- ten down. Since [556] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context" we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The num- ber of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable" theorems with included proofs. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [193, 189, 29, 235, 254, 619, 412, 138], for history [217, 625, 376, 73, 46, 208, 379, 365, 690, 113, 618, 79, 259, 341], for popular, beautiful or elegant things [12, 529, 201, 182, 17, 672, 673, 44, 204, 190, 245, 446, 616, 303, 201, 2, 127, 146, 128, 502, 261, 172]. For comprehensive overviews in large parts of math- ematics, [74, 165, 166, 51, 593] or predictions on developments [47]. For reflections about mathematics in general [145, 455, 45, 306, 439, 99, 561]. Encyclopedic source examples are [188, 705, 670, 102, 192, 152, 221, 191, 111, 635].
    [Show full text]
  • The Legacy of Norbert Wiener: a Centennial Symposium
    http://dx.doi.org/10.1090/pspum/060 Selected Titles in This Series 60 David Jerison, I. M. Singer, and Daniel W. Stroock, Editors, The legacy of Norbert Wiener: A centennial symposium (Massachusetts Institute of Technology, Cambridge, October 1994) 59 William Arveson, Thomas Branson, and Irving Segal, Editors, Quantization, nonlinear partial differential equations, and operator algebra (Massachusetts Institute of Technology, Cambridge, June 1994) 58 Bill Jacob and Alex Rosenberg, Editors, K-theory and algebraic geometry: Connections with quadratic forms and division algebras (University of California, Santa Barbara, July 1992) 57 Michael C. Cranston and Mark A. Pinsky, Editors, Stochastic analysis (Cornell University, Ithaca, July 1993) 56 William J. Haboush and Brian J. Parshall, Editors, Algebraic groups and their generalizations (Pennsylvania State University, University Park, July 1991) 55 Uwe Jannsen, Steven L. Kleiman, and Jean-Pierre Serre, Editors, Motives (University of Washington, Seattle, July/August 1991) 54 Robert Greene and S. T. Yau, Editors, Differential geometry (University of California, Los Angeles, July 1990) 53 James A. Carlson, C. Herbert Clemens, and David R. Morrison, Editors, Complex geometry and Lie theory (Sundance, Utah, May 1989) 52 Eric Bedford, John P. D'Angelo, Robert E. Greene, and Steven G. Krantz, Editors, Several complex variables and complex geometry (University of California, Santa Cruz, July 1989) 51 William B. Arveson and Ronald G. Douglas, Editors, Operator theory/operator algebras and applications (University of New Hampshire, July 1988) 50 James Glimm, John Impagliazzo, and Isadore Singer, Editors, The legacy of John von Neumann (Hofstra University, Hempstead, New York, May/June 1988) 49 Robert C. Gunning and Leon Ehrenpreis, Editors, Theta functions - Bowdoin 1987 (Bowdoin College, Brunswick, Maine, July 1987) 48 R.
    [Show full text]
  • Council Congratulates Exxon Education Foundation
    from.qxp 4/27/98 3:17 PM Page 1315 From the AMS ics. The Exxon Education Foundation funds programs in mathematics education, elementary and secondary school improvement, undergraduate general education, and un- dergraduate developmental education. —Timothy Goggins, AMS Development Officer AMS Task Force Receives Two Grants The AMS recently received two new grants in support of its Task Force on Excellence in Mathematical Scholarship. The Task Force is carrying out a program of focus groups, site visits, and information gathering aimed at developing (left to right) Edward Ahnert, president of the Exxon ways for mathematical sciences departments in doctoral Education Foundation, AMS President Cathleen institutions to work more effectively. With an initial grant Morawetz, and Robert Witte, senior program officer for of $50,000 from the Exxon Education Foundation, the Task Exxon. Force began its work by organizing a number of focus groups. The AMS has now received a second grant of Council Congratulates Exxon $50,000 from the Exxon Education Foundation, as well as a grant of $165,000 from the National Science Foundation. Education Foundation For further information about the work of the Task Force, see “Building Excellence in Doctoral Mathematics De- At the Summer Mathfest in Burlington in August, the AMS partments”, Notices, November/December 1995, pages Council passed a resolution congratulating the Exxon Ed- 1170–1171. ucation Foundation on its fortieth anniversary. AMS Pres- ident Cathleen Morawetz presented the resolution during —Timothy Goggins, AMS Development Officer the awards banquet to Edward Ahnert, president of the Exxon Education Foundation, and to Robert Witte, senior program officer with Exxon.
    [Show full text]
  • Who Is Lennart Carleson?
    The Abel Prize for 2006 has been awarded Lennart Carleson, The Royal Institute of Technology, Stockholm, Sweden Professor Lennart Carleson will accept the Abel Prize for 2006 from His Majesty King Harald in a ceremony at the University of Oslo Aula, at 2:00 p.m. on Tuesday, 23 May 2006. In this background paper, we shall give a description of Carleson and his work. This description includes precise discussions of his most important results and attempts at popular presentations of those same results. In addition, we present the committee's reasons for choosing the winner and Carleson's personal curriculum vitae. This paper has been written by the Abel Prize's mathematics spokesman, Arne B. Sletsjøe, and is based on the Abel Committee's deliberations and prior discussion, relevant technical literature and discussions with members of the Abel Committee. All of this material is available for use by the media, either directly or in an adapted version. Oslo, Norway, 23 March 2006 Contents Introduction .................................................................................................................... 2 Who is Lennart Carleson? ............................................................................................... 3 Why has he been awarded the Abel Prize for 2006? ........................................................ 4 Popular presentations of Carleson's results ...................................................................... 6 Convergence of Fourier series....................................................................................
    [Show full text]