2014年度邵逸夫数学科学奖颁予 George Lusztig

George Lusztig, 1946 年于罗马尼亚蒂米甚瓦拉出生, 现为美国麻省理工学院Abdun-Nur 数学讲座教授. 1968年于罗马尼亚布加勒斯特大学毕业, 1971年于美国普林斯顿大学取得硕士和博士学位. 1971年至1977年于英国华威大学任教, 1974年成为教授. 自1978年起, 他一直在麻省理工学院兼职教授. 2005年获罗马尼亚科学院数学研究所授予荣誉院士. 他是英国皇家学会, 美国人文与科学学院及美国国家科学院院士.

The Shaw Prize in Mathematical Sciences is awarded to George Lusztig

for his fundamental contributions to algebra, algebraic geometry, and representation theory, and for weaving these subjects together to solve old problems and reveal beautiful new connections.

Lusztig received the 1985 AMS Cole Prize in Algebra “for his fundamental work on the representation theory of finite groups of Lie type”, particularly for his contributions to the classification of the irreducible representations in characteristic zero of the groups of rational points of reductive groups over finite fields. He was also awarded the 2008 AMS Steele Prize for Lifetime Achievement. The citation for the Steele Prize noted that Lusztig’s work “has entirely reshaped representation theory and in the process changed much of mathematics.”

Yakov G. Sinai, Princeton University and the Landau Institute for Theoretical Physics, Russian Academy of Sciences, is being awarded the 2014 Abel Prize “for his fundamental contributions to dynamical systems, ergodic theory, and mathematical physics.” Sinai received the AMS Steele Prize for Lifetime Achievement in 2013 and is a Fellow of the AMS.

The Abel Prize Committee cites Sinai’s discovery of surprising connections between order and chaos and his development of the use of probability and measure theory in the study of dynamical systems. The citation continues: “His achievements include seminal works in ergodic theory, which studies the tendency of a system to explore all of its available states according to certain time statistics; and statistical mechanics, which explores the behavior of systems composed of a very large number of particles, such as molecules in a gas… Sinai has trained and influenced a generation of leading specialists in his research fields.” Among his other awards are the Wolf Prize in Mathematics (1997), the Nemmers Prize in Mathematics (2002), the Henri Poincaré Prize from the International Association of Mathematical Physics (2009), and the Dobrushin International Prize from the Institute of Information Transmission of the Russian Academy of Sciences (2009).

On behalf of the American Mathematical Society, it is a great pleasure to congratulate Yakov Sinai of Princeton University and the Landau Institute, recipient of the 2014 Abel Prize. Sinai’s work has changed our understanding of change; his influence can be seen from number theory to physics. Congratulations!
David Vogan, AMS President

The Abel Prize is awarded by the Norwegian Academy of Science and Letters and recognizes contributions of extraordinary depth and influence to the mathematical sciences. Awarded annually since 2003, the prize carries a cash award of NOK 6,000,000 (approximately one million US). Sinai will receive the prize at an award ceremony in Oslo on May 20. Read more about Yakov Sinai, his achievements, and the Abel Prize.

Yitang Zhang wins the 2014 Rolf Schock Prize in Mathematics, for his spectacular breakthrough concerning the possibility of an infinite number of twin primes. The Royal Swedish Academy of Sciences decided the laureate.

Springer 刚刚推出了 2010 年出版的 “The Abel Prize 2003–2007” 的续集 “The Abel Prize 2008–2012“.

The Abel Prize 2008-2012

Covering the years 2008-2012, this book profiles the life and work of recent winners of the Abel Prize: John G. Thompson and Jacques Tits, 2008; Mikhail Gromov, 2009; John T. Tate Jr., 2010; John W. Milnor, 2011; Endre Szemerédi, 2012.

The profiles feature autobiographical information as well as a description of each mathematician’s work. In addition, each profile contains a complete bibliography, a curriculum vitae, as well as photos — old and new. As an added feature, interviews with the Laureates can be streamed from the Abel Prize web site.

The book also presents a  history of the Abel Prize written by the historian Kim Helsvig, and includes a facsimile of a letter from Niels Henrik Abel, which is transcribed, translated into English, and placed into historical perspective by Christian Skau.

The 2014 Wolf Prize in Mathematics is awarded to Peter Sarnak, for his deep contributions in analysis, number theory, geometry, and combinatorics.

Peter Sarnak is on the permanent faculty at the School of Mathematics of the Institute for Advanced Study, Princeton, NJ, USA.

Peter Clive Sarnak (born December 18, 1953) graduated University of the Witwatersrand (B.Sc. 1975) and Stanford University (Ph.D. 1980), under the direction of Paul Cohen.

Prof. Sarnak is a mathematician of an extremely broad spectrum with a far-reaching vision. He has impacted the development of several mathematical fields, often by uncovering deep and unsuspected connections. In analysis, he investigated eigenfunctions of quantum mechanical Hamiltonians which correspond to chaotic classical dynamical systems in a series of fundamental papers. He formulated and supported the “Quantum Unique Ergodicity Conjecture” asserting that all eigenfunctions of the Laplacian on negatively curved manifolds are uniformly distributed in phase space. Sarnak’s introduction of tools from number theory into this domain allowed him to obtain results which had seemed out of reach and paved the way for much further progress, in particular the recent works of E. Lindenstrauss and N. Anantharaman. In his work on L-functions (jointly with Z. Rudnick) the relationship of contemporary research on automorphic forms to random matrix theory and the Riemann hypothesis is brought to a new level by the computation of higher correlation functions of the Riemann zeros. This is a major step forward in the exploration of the link between random matrix theory and the statistical properties of zeros of the Riemann zeta function going back to H. Montgomery and A. Odlyzko. In 1999 it culminates in the fundamental work, jointly with N. Katz, on the statistical properties of low-lying zeros of families of L-functions. Sarnak’s work (with A. Lubotzky and R. Philips) on Ramanujan graphs had a huge impact on combinatorics and computer science. Here again he used deep results in number theory to make surprising and important advances in another discipline.

By his insights and his readiness to share ideas he has inspired the work of students and fellow researchers in many areas of mathematics.

Professor Gerd Faltings, winner of the prize in science, is the Director at the Max-Planck Institute for Mathematics in Bonn. He has made groundbreaking contributions to algebraic geometry and number theory. His work combines ingenuity, vision and technical power. He has introduced stunning new tools and techniques which are now constantly used in modern mathematics.

Faltings’ deep insights into the p-adic cohomology of algebraic varieties have been crucial to modern developments in number theory. His work on moduli spaces of abelian varieties has had great influence on arithmetic algebraic geometry. He has introduced new geometric ideas and techniques in the theory of Diophantine approximation, leading to his proof of Lang’s conjecture on rational points of abelian varieties and to a far-reaching generalization of the subspace theorem. Professor Faltings has also made important contributions to the theory of vector bundles on algebraic curves with his proof of the Verlinde formula.

The Ostrowski Prize for the year 2013 is confered to Yitang Zhang

张益唐从 2014 年开始以访问学者身份加入普林斯顿高等研究院. 他没有任何来自教学或者科研经费的压力, 可以专心的做理论研究.

Ostrowski 基金的目的是为了促进数学科学. The Foundation A. M. Ostrowski for an international prize in higher mathematics was created by Alexander Markovich Ostrowski (1893-1986) who  from 1928 to 1958 was professor of mathematics at the University of Basel.

The 2014 Frank Nelson Cole Prize in Number Theory is awarded to Yitang Zhang(张益唐), Daniel Goldston, Janos Pintz and Y. Yildirim.

2005 年, Goldston, Pintz and Yildirim(GPY) 使用常规手段–Selberg Sieve 与 Bombieri-Vinogradov theorem–结合一些新的想法, 证明了:

$|p-q|\lt\epsilon\log p.$

Cole Prize 分代数和数论两项, 目前都是每三年发一次, 代数奖在数论奖的后一年颁发. 这两个奖的奖金都是 \$5000, 获奖者必须是美国数学会的成员或者论文发表在获得承认的北美期刊. 数论奖 1997 年的获得者是 Andrew J. Wiles.