Conference: Contemporary Combinatorics

该奖项将为在孟菲斯举行的当代组合学会议提供支持。在过去的一二十年里，组合学不断发展壮大。它一直有丰富的问题和猜想，但是，直到几年前，很少有工具来攻击许多重要的猜想。这种情况得到迅速改善，在很大程度上是由于概率论、遍历理论、傅立叶分析和代数等方法的涌入；特别是，组合学和概率论之间的相互作用使两个群体都受益匪浅。2004年的重大数学事件是由Ben Green和Terry Tao证明的关于素数的等差数列的深刻结果。他们巧妙的证明运用了纯组合学、遍历论、数论和概率方法。他们的证明的一个令人惊讶的方面是，它不需要像预期的那样密度小得多的Szemeredi定理：它足以将原来的定理转移到一个新的环境中。这一伟大成就的方法很可能会在未来很长一段时间内产生影响。这次会议的主要发言人是陶泰利。还有其他几位激动人心的演讲者。中南部没有多少高水平的数学会议。在孟菲斯举行的2006年当代组合学会议将产生相当大的影响。大部分NSF拨款将用于帮助研究生和高级数学家参加会议，从而从与演讲者的个人接触中受益。

This award will provide support for a conference in Contemporary Combinatorics, in Memphis. In the past decade or two, combinatorics has gone from strength to strength. It has always been rich in problems and conjectures but, until a few years ago, there had been rather few tools to attack many important conjectures. That this situation has been improving rapidly is due, to a large extent, to the influx of methods from probability theory, ergodic theory, Fourier analysis, and algebra; in particular, the interaction between combinatorics and probability theory has greatly benefited both communities.The major mathematical event of 2004 was the deep result proved by Ben Green and Terry Tao about arithmetic progressions in primes. Their ingenious proof makes use of pure combinatorics, ergodic theory, number theory, and probabilistic methods. A surprising aspect of their proof is that it does not need Szemeredi's theorem with a much smaller density, as had been expected: it suffices to transfer the original theorem to a new setting. It is likely that the methods of this great achievement will have implications for quite a while to come. The main speaker at the conference is Terry Tao. There will be several other exciting speakers. There are not many high-level mathematics conferences in the Mid-South. The Contemporary Combinatorics 2006 meeting in Memphis will have considerable impact. Most of the NSF grant would be used to help graduate students and senior mathematicians attend the meeting and so benefit from the personal contact with the speakers.