Conference: Contemporary Combinatorics

该奖项将为在孟菲斯举行的当代组合数学会议提供支持。在过去的一二十年里，组合数学已经越来越强大。它总是充满了问题和挑战，但直到几年前，还很少有工具来攻击许多重要的挑战。这种情况已经迅速改善，在很大程度上是由于大量涌入的方法，从概率论，遍历理论，傅立叶分析，代数，特别是组合学和概率论之间的相互作用，极大地受益于两个社区。2004年的主要数学事件是深的结果证明了本绿色和特里陶关于算术级数的素数。他们巧妙的证明利用了纯组合学、遍历理论、数论和概率方法。他们的证明令人惊讶的一点是，它不需要像预期的那样，在密度小得多的情况下使用Szemeredi定理：它足以将原始定理转移到一个新的设置。这一伟大成就的方法很可能会在未来相当长的一段时间内产生影响。 大会的主要发言人是陶喆。还会有其他一些令人兴奋的演讲者。 在中南地区没有太多高水平的数学会议。2006年在孟菲斯举行的当代组合学会议将产生相当大的影响。 美国国家科学基金会的大部分赠款将用于帮助研究生和高级数学家参加会议，因此受益于与演讲者的个人接触。

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.