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2011 Steele Prizes 2011 Steele Prizes The 2011 AMS Leroy P. Steele Prizes were pre- such as the Kuznetsov formula and the spectral sented at the 117th Annual Meeting of the AMS theory of Kloosterman sums, are covered for the in New Orleans in January 2011. The Steele Prizes first time in this book. It closes with a discussion of were awarded to Henryk Iwaniec for Mathemati- current research on the size of eigenfunctions on cal Exposition, to Ingrid Daubechies for a Seminal hyperbolic manifolds. By making these tools from John W. Milnor Contribution to Research, and to automorphic forms widely accessible, this book for Lifetime Achievement. has had a tremendous influence on the practice Mathematical Exposition: Henryk Iwaniec of analytic number theory. Topics in Classical Automorphic Forms develops Citation many standard topics in the theory of modular Henryk Iwaniec is awarded the Leroy P. Steele Prize forms in a nontraditional way. Iwaniec’s aim was for Mathematical Exposition for his long record of “to venture into areas where different ideas and excellent exposition, methods mix and interact”. One standout part is both in books and in the treatment of the theory of representation of classroom notes. He is quadratic forms and estimating sizes of Fourier honored particularly coefficients of cusp forms. The breakthrough in for the books Intro- the late 1980s in understanding representations duction to the Spectral by ternary quadratic forms originated with the Theory of Automor- seminal work of Iwaniec, which is described beau- phic Forms (Revista tifully here. Matemática Iberoamer- icana, Madrid, 1995) Biographical Sketch and Topics in Classical Henryk Iwaniec graduated in 1971 from Warsaw Automorphic Forms University, got his Ph.D. the next year, and became (Graduate Studies professor at the Institute of Mathematics of the in Mathematics, 17, Polish Academy of Sciences before leaving for the Henryk Iwaniec American Mathemati- United States in 1983. After taking several visiting cal Society, Providence, positions in the United States (including a long- RI, 1997). These books give beautiful treatments of the theory of automorphic forms from the author’s term appointment at the Institute for Advanced perspective of analytic number theory. They have Study), in January 1987 he was offered a chair as become classics in the field and are now a funda- New Jersey State Professor at Rutgers, the position mental resource for students. The two books are he enjoys to this day. complementary, with the first presenting the non- Iwaniec’s main interest is analytic number holomorphic theory of Maass forms for GL(2) and theory and automorphic forms. Prime numbers are the latter focusing on holomorphic modular forms. his passion. His accomplishments were acknowl- Introduction to the Spectral Theory of Automor- edged by numerous invitations to give talks at phic Forms begins with the basics of hyperbolic conferences, including the International Congress geometry and takes readers to the frontiers of of Mathematicians. Iwaniec is a member of the Pol- research in analytic number theory. Many topics, ish Academy of Sciences, the American Academy APRIL 2011 NOTICES OF THE AMS 593 of Arts and Sciences, the National Academy of oscillation, making Sciences, and the Polska Akademia Umiejetnosci. them flexible enough Among several prizes Iwaniec has received are to be used in a variety the Jurzykowski Foundation Award, the Sierpinski of situations. As such, Medal, the Ostrowski Prize, and the Cole Prize in these wavelets (now Number Theory. known as Daubechies Iwaniec teaches graduate students and collabo- wavelets) became ex- rates with researchers from various countries. In tremely popular in 2005 he was honored with the Doctorate Honoris practical signal pro- Causa of Bordeaux University. In 2006 the town cessing (for instance, council of his native city made Iwaniec an Honor- they are used in the ary Citizen of Elblag, a distinction he cherishes JPEG 2000 image com- very proudly. pression scheme). Even nowadays they are still Response Ingrid Daubechies the default, general- I thank the American Mathematical Society and the purpose wavelet family Committee of the Steele Prize for this award. I am of choice to implement in any signal processing very honored and happy. This is a very meaningful algorithm (although for specialized applications, recognition for me because the citation is telling sometimes a more tailored wavelet can be slightly not only about my fascination with the subjects superior). but also about my attention to educating new gen- At the time of this paper, wavelet theory was al- erations of researchers. Modern analytic number ready a booming field, with hundreds of papers de- theory takes ideas from the theory of automorphic voted to wavelet construction, efficient algorithms, forms and gives back new enhanced methods and and so forth. At present the field is more mature results. While more arithmetical aspects of auto- and settled, an effect to which Daubechies’s paper morphic forms are covered relatively well in the significantly contributed by largely “solving” the literature, there is still not a sufficient exposition problem of the best wavelets to use in general of analytic aspects. Hopefully more books will be (and also by giving order to the chaotic explosion written by other specialists that will address simi- of literature). lar topics from many different directions. These In his MathSciNet review of the paper, Hans two books selected by the Committee for the award Feichtinger wrote, “Even before its publication, came out of my teaching graduate courses and giv- the paper had a remarkable impact within applied ing presentations in workshops, so inevitably they analysis, and great interest in wavelet theory has contain some of my favorite ways of handling the been shown from many sides. By the summer of problems. I am glad that my choices and writing 1989 there was already a software package avail- style are well received. If indeed these works do able, running on PCs, which is based on the con- have “influence on the practice of analytic number struction described in this note. This sheds some theory”, I will be most happy. light on the speed with which new mathematical algorithms are brought to work these days and can Seminal Contribution to Research: Ingrid serve to underline the importance of mathematical Daubechies research to applied fields.” Citation The Leroy P. Steele Prize for Seminal Contribu- Biographical Sketch tion to Research is awarded to Ingrid Daubechies Ingrid Daubechies received both her bachelor’s for her paper “Orthonormal bases of compactly and Ph.D. degrees (in 1975 and 1980, respectively) supported wavelets” (Comm. Pure Appl. Math. 41 from the Free University in Brussels, Belgium. She (1988), no. 7, 909–996). In this paper Daubechies held a research position at the Free University until constructs the very first examples of families of 1987. From 1987 to 1994 she was a member of the wavelets (rescalings of a single “mother wavelet”) technical staff at AT&T Bell Laboratories, during that are simultaneously smooth, orthonormal, and which time she took leaves to spend six months compactly supported; earlier examples of wavelets (in 1990) at the University of Michigan and two had two out of three of these properties, but not years (1991–93) at Rutgers University. She is now all three at once. The orthonormality makes them at the Mathematics Department and the Program good as a basis to decompose arbitrary signals; in Applied and Computational Mathematics at the smoothness removes edge artifacts and makes Princeton University. wavelet series converge rapidly; and the compact Her research interests focus on the mathemati- support makes them viable for use in actual prac- cal aspects of time-frequency analysis, in particular tical applications. The wavelets also came with wavelets as well as applications. In 1998 she was a parameter that traded off their smoothness elected to the National Academy of Sciences and for the width of their support and amount of became a fellow of the Institute of Electrical and 594 NOTICES OF THE AMS VOLUME 58, NUMBER 4 Electronics Engineers. The American Mathemati- picture of the relation between the topological, cal Society awarded her a Leroy P. Steele Prize combinatorial, and smooth worlds developed by for Mathematical Exposition in 1994 for her book Milnor. Jointly with M. Kervaire, Milnor proved Ten Lectures on Wavelets, as well as the 1997 Ruth the first results showing that the topology of Lyttle Satter Prize. From 1992 to 1997 she was a 4-dimensional manifolds is exceptional by reveal- fellow of the John D. and Catherine T. MacArthur ing obstructions to the realization of 2-dimen- Foundation. sional spherical homology classes by smooth She is a member of the American Academy of embedded 2-spheres. This is one of the founding Arts and Sciences, the American Mathematical results of 4-dimensional topology. Society, the Mathematical Association of America, In this way Milnor opened several fields: singu- the Society for Industrial and Applied Mathematics, larity theory, algebraic K-theory, and the theory and the Institute of Electrical and Electronics Engi- of quadratic forms. Although he did not invent neers. In addition, Daubechies was elected in 2010 these subjects, his work gave them completely new to serve as the next president of the International points of view. For instance, his work on isolated Mathematical Union. singularities of complex hypersurfaces presented a great new topological framework for studying Response singularities and, at the same time, provided a I am delighted and very grateful to receive this rich new source of examples of manifolds with award, especially for this paper. In my work, I try different extra structures. The concepts of Milnor to distill, from extensive contacts with scientists fibers and Milnor number are today among the and engineers, challenging mathematical problems most important notions in the study of complex that nevertheless are still connected to the original singularities.
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