2003 Steele Prizes The 2003 Leroy P. Steele Prizes were awarded at the to VICTOR GUILLEMIN for Lifetime Achievement. The 109th Annual Meeting of the AMS in Baltimore in text that follows presents, for each awardee, the January 2003. selection committee’s citation, a brief biographical The Steele Prizes were established in 1970 in honor sketch, and the awardee’s response upon receiving of George David Birkhoff, William Fogg Osgood, and the prize. William Caspar Graustein. Osgood was president of the AMS during 1905–06, and Birkhoff served in that Mathematical Exposition: John B. Garnett capacity during 1925–26. The prizes are endowed Citation under the terms of a bequest from Leroy P. Steele. Up An important development in harmonic analysis to three prizes are awarded each year in the follow- was the discovery, by C. Fefferman and E. Stein, in ing categories: (1) Mathematical Exposition: for a the early seventies, that the space of functions of book or substantial survey or expository-research bounded mean oscillation (BMO) can be realized paper; (2) Seminal Contribution to Research (limited as the limit of the Hardy spaces Hp as p tends to for 2003 to the field of logic): for a paper, whether infinity. A crucial link in their proof is the use of recent or not, that has proved to be of fundamental “Carleson measure”—a quadratic norm condition or lasting importance in its field or a model of im- introduced by Carleson in his famous proof of the portant research; and (3) Lifetime Achievement: for “Corona” problem in complex analysis. In his book the cumulative influence of the total mathematical Bounded Analytic Functions (Pure and Applied work of the recipient, high level of research over a Mathematics, 96, Academic Press, Inc. [Harcourt period of time, particular influence on the develop- Brace Jovanovich, Publishers], New York-London, ment of a field, and influence on mathematics 1981, xvi + 467 pp.), Garnett brings together these through Ph.D. students. Each Steele Prize carries a far-reaching ideas by adopting the techniques of cash award of $5,000. singular integrals of the Calderón-Zygmund school The Steele Prizes are awarded by the AMS Council and combining them with techniques in complex acting on the recommendation of a selection com- analysis. The book, which covers a wide range of mittee. For the 2003 prizes, the members of the se- beautiful topics in analysis, is extremely well lection committee were: M. S. Baouendi, Andreas R. organized and well written, with elegant, detailed Blass, Sun-Yung Alice Chang, Michael G. Crandall, proofs. Constantine M. Dafermos, Daniel J. Kleitman, Barry The book has educated a whole generation of Simon, Lou P. van den Dries, and Herbert S. Wilf mathematicians with backgrounds in complex (chair). analysis and function algebras. It has had a great The list of previous recipients of the Steele Prize impact on the early careers of many leading ana- may be found in the November 2001 issue of the lysts and has been widely adopted as a textbook Notices, pages 1216–20, or on the World Wide Web, for graduate courses and learning seminars in both http://www.ams.org/prizes-awards. the U.S. and abroad. The 2003 Steele Prizes were awarded to JOHN B. Biographical Sketch GARNETT for Mathematical Exposition, to RONALD John B. Garnett was born in Seattle in 1940. He JENSEN and to MICHAEL D. MORLEY for a Seminal Con- received a B.A. degree from the University of Notre tribution to Research, and to RONALD GRAHAM and Dame in 1962 and a Ph.D. degree in mathematics 462 NOTICES OF THE AMS VOLUME 50, NUMBER 4 John B. Garnett Ronald Jensen Michael D. Morley D. Marshall, and the late from the University of Washington in 1966. His T. Wolff, whose exciting new thesis advisor at Washington was Irving Glicksberg. results at the time were some In 1968, following a two-year appointment as of the book’s highlights. C.L.E. Moore Instructor at the Massachusetts Encouragement is critical Institute of Technology, Garnett became assistant to the younger mathematician, professor at the University of California, Los and from that time I owe much Angeles, where he has worked ever since. At UCLA, to my mentors I. Glicksberg, Garnett was promoted to tenure in 1970 and to K. Hoffman, and L. Carleson, professor in 1974. In 1989 he received the UCLA and to my contemporaries Distinguished Teaching Award primarily for his T. W. Gamelin, P. Koosis, and work with Ph.D. students, and from 1995 to 1997 N. Varopoulos. I also want to he served as department chairman. thank the young mathemati- Garnett’s research focuses on complex analysis cians who over the years have and harmonic analysis. He has held visiting posi- told me that they learned from tions at Institut Mittag-Leffler; Université de Paris-Sud; the book. Eidgenössische Technische Hochschule, Zurich; Yale University; Institut des Hautes Études Scientifiques; Seminal Contribution to and Centre de Recerca Matemática, Barcelona. He Research: Ronald Jensen gave invited lectures to the AMS in 1979 and to the Citation Ronald Graham International Congress of Mathematicians in 1986. Ronald Jensen’s paper “The Response fine structure of the con- I am honored to receive the Steele Prize for the book structible hierarchy” (Annals Bounded Analytic Functions. It is especially satis- of Mathematical Logic 4 (1972) fying because the prize had previously been 229–308) has been of seminal awarded for some of the classic books in analysis importance for two different by L. Ahlfors, Y. Katznelson, W. Rudin, and E. M. directions of research in con- Stein, from which I first learned much mathemat- temporary set theory: the ics and to which I still return frequently. inner model program and the I wrote Bounded Analytic Functions around 1980 use of combinatorial princi- to explain an intricate subject that was rapidly ples of the sort that Jensen growing in surprising ways, to teach students tech- established for the con- niques in their simplest cases, and to argue that the structible universe. subject, which had become an offshoot of abstract The inner model program, mathematics, was better understood using the con- one of the most active parts of crete methods of harmonic analysis and geometric set theory nowadays, has as its function theory. I want to thank several mathe- goals the understanding of very maticians: L. Carleson, C. Fefferman, K. Hoffman, large cardinals and their use to and D. Sarason, whose ideas prompted the devel- measure the consistency opment of the subject; and S.-Y. A. Chang, P. Jones, strength of assertions about Victor Guillemin APRIL 2003 NOTICES OF THE AMS 463 much smaller sets. A central ingredient of this pro- together with a group of other young mathemati- gram is to build, for a given large cardinal axiom, a cians such as Bob Solovay, Tony Martin, and Jack model of set theory that either is just barely large Silver, all of whom influenced my work. It was enough to contain that type of cardinal or is just an exciting time. Much of the work centered on barely too small to contain it. The fine structure tech- independence proofs using Cohen’s method, but the niques introduced in Jensen’s paper are the foun- research on the consequences of strong existence dation of the more recent work of Mitchell, Steel, axioms, such as large cardinals and determinacy, Jensen himself, and others constructing such mod- was also beginning. The theory of inner models—in els. The paradigm, initiated by Jensen, for relating particular Gödel’s model L—was comparatively large cardinals to combinatorial properties of smaller underdeveloped. After discovering that the axiom sets is first to show that the desired properties hold V = L settles Souslin’s problem, I began developing in these inner models and then to show that, if they a body of methods, now known as “fine structure failed to hold in the universe of all sets, then that theory”, for investigating the structure L. Much of this universe and the inner model would differ so strongly work was done in 1969–71 at Rockefeller University that a large cardinal that is barely missing from and the University of Oslo. The above-mentioned the inner model would be present in the universe. paper was subsequently written at Berkeley. In the The paper cited here contains the first steps in this ensuing years it became apparent that these meth- direction, establishing for the first time combinato- ods were also applicable to larger inner models in rial properties of an inner model, in this case Gödel’s which strong existence axioms are realized. The most constructible sets, that go far beyond Gödel’s proof important breakthrough in this direction was made of the generalized continuum hypothesis in this by John Steel. He and Hugh Woodin have applied the model. methods widely. This work is being extended by a very The second direction initiated by Jensen’s paper capable group of younger mathematicians, such involves applying these combinatorial principles to as Itay Neeman, Ernest Schimmerling, and Martin problems arising in other parts of mathematics. The Zeman. I feel privileged to have worked in such principle , which Jensen proved to hold in the gifted company. constructible universe, has been particularly useful in such applications. A good example is Shelah’s Seminal Contribution to Research: Michael D. solution of the Whitehead problem in abelian group Morley theory; half of the solution was to show that a posi- Citation tive answer to the problem follows from . By now, Michael Morley’s paper “Categoricity in power” has become part of the standard tool kit of several (Transactions of the AMS 114 (1965) 514–538) set branches of mathematics, ranging from general in motion an extensive development of pure model topology to module theory.