Jan 222014
 

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

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.

Jan 182014
 

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.

Jan 152014
 

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.

Dec 052013
 

据 Ostrowski 基金会网站 Ostrowski Foundation, 2013 年的 Ostrowski 奖授予张益唐:

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.

自1989 年开始, Ostrowski 基金会每两年发一次奖, 奖金 \(100,000\) Swiss francs(瑞士法郎), 奖励 for recent outstanding achievements in pure mathematics and in the foundations of numerical mathematics.  该奖 1997 年的获得者是 Andrew J. Wiles; 2001 年由  Henryk Iwaniec, Peter Sarnak, Richard L. Taylor 三人分享荣誉; 2005年的奖励授予 Ben Green 和 Terence Tao.

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.

Oct 122013
 

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

这是对他们在质数间隙取得的突破的肯定.

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:

对任意 \(\epsilon\gt0\), 存在无穷多对不等的质数 \(p,q\), 使得

\[|p-q|\lt\epsilon\log p.\]

值得注意的是, Goldston 和 Yildirim 稍早的一些关于这个思想的工作, 在 Green 和 Tao 证明他们令人吃惊的定理–Green-Tao theorem–发挥了作用.

张益唐修订了 Bombieri–Vinogradov theorem, 也改动了 Goldston, Pintz , Yildirim 的筛法, 使用了一些数论的深刻定理, 诸如 Weil 的关于曲线的黎曼假设, Deligne 的关于簇的黎曼假设的工作.

张的论文 “Bounded gaps between primes” 将在 Annals Volume 179, no. 3(2014) 刊登.

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.

May 292013
 

The Shaw Prize in Mathematical Sciences 2013 is awarded to David L Donoho for his profound contributions to modern mathematical statistics and in particular the development of optimal algorithms for statistical estimation in the presence of noise and of efficient techniques for sparse representation and recovery in large data-sets.

The Shaw Prize in Mathematical Sciences for 2013 is awarded to David L Donoho, Anne T and Robert M Bass Professor of the Humanities and Sciences, and Professor of Statistics at Stanford University, USA for his profound contributions to modern mathematical statistics and in particular the development of optimal algorithms for statistical estimation in the presence of noise and of efficient techniques for sparse representation and recovery in large data-sets.

The dramatic developments in technology in the last half century present fundamental new challenges in theoretical and applied mathematical statistics. David Donoho has played a major role in developing new mathematical and statistical tools to deal with such problems ranging from large data-sets in high dimensions to contamination with noise. His work provides fast, efficient and often optimal algorithms which are founded on rigorous mathematical analysis.

Key themes introduced in his works, and which today are standard features of the theory, include the exploitation of sparseness of representation of complex objects, related adaptive nonlinear thresholding techniques and the deep relation between sparseness and certain penalty functions that are being minimized (specifically \(L^1\) norms).

Many of these emerge from his development of algorithms for statistical estimators in the presence of noise. These are remarkable in that they overcome the difficulties associated with noise, with very little loss of efficiency or reliability. Along the way, he demonstrated the power of the mathematical theory of wavelets in dealing with such problems in statistics. The Donoho–Johnstone soft-thresholding algorithm has been widely used in statistical and signal processing applications.

During the last 15 years Donoho has developed a theory of sparse and multi-scale representations of signals and data-sets using nonlinear \(L^1\) optimization methods. These combine very well with techniques of unstructured and redundant dictionaries of functions and provide a fundamental approach to lower the dimensionality of complex problems. Along with Candes and Tao, he made fundamental contributions to the development of “compressed sensing”. In terms of sparseness and recovery, this method which “compresses while sensing the data”, using dramatically fewer data points while retaining the ability to recover the correct signal, yields strikingly efficient and even optimal algorithms for compressing and decompressing complex signals (e.g. images). This area remains a very active area of research especially in view of its wide applications.

David L Donoho was born in 1957 in Los Angeles, USA and is currently Anne T and Robert M Bass Professor of the Humanities and Sciences, and Professor of Statistics at Stanford University, USA. He graduated from Princeton University in 1978 and received his PhD from Harvard University in 1983. From 1984 to 1990, he was on the faculty of the University of California, Berkeley before moving to Stanford. He is a fellow of the American Academy of Arts and Sciences, a SIAM Fellow, a foreign associate of the French Academy of Sciences, and a member of the US National Academy of Sciences.

Mar 262013
 

今年的 Abel Prize 授予 Pierre Deligne.  Timothy Gowers, 1998 年的 Field Medal 得主, 写了一篇文章来介绍 Pierre Deligne 的工作. 这已经是 Timothy Gowers 连续第三次做这件事情了: 他 2012年介绍了 Endre Szemerédi 的工作, 2011年为 John Milnor 写了长文.

有一个数学家用 sowa 这个 ID 在 T. Gowers 的博客, 宣布今年的 Abel Prize 得主是 Pierre Deligne 的文章, 质疑 Abel Prize:

  1. 应该解释为什么选择 T. Gowers 连续三年来写得奖人工作介绍. T. Gowers 的数学知识是否可以承担这项光荣的职责?
  2. (有人向 sowa 透漏)Norwegian Academy 希望把奖授予那些会接受奖项, 会亲临现场并与国王交谈的候选人. 于是有些数学家就被排除了, 比如 H. Cartan, A. Grothendick. H. Cartan 因为年事太高, 不能亲临领奖(当然, H. Cartan 现在已经过世); A. Grothendick 肯定也不会亲临, 甚至会拒绝这个奖.
  3. 去年应该把奖颁给 W. Thurston. W. Thurston 是历史上最好的数学家之一. 去年, 他的病已经很严重了. 把 Abel Prize 授予他, “to do something good for a dying person”.
  4. 没有授奖给 H. Cartan, I.M. Gelfand 和  W. Thurston 这样伟大的数学家是不可原谅的.
  5. 2012 年的得主 Endre Szemerédi 是否能与 Milnor和 Deligne 相提并论?
  6. 组合数学的重要性是否与代数几何一样?

这个论战正在进行.  参与讨论的人包括 T. Gowers 和 Terry Tao.