Lie Groups, Representations and Discrete Mathematics

李群、表示和离散数学会议摘要2006年2月6日至10日该会议是新泽西普林斯顿高等研究院为期一年的李群、表示和离散数学项目的一部分。 在过去的二十年里，数论中的问题和结果之间存在着一些深刻而令人惊讶的联系，特别是自守形式，以及离散数学和计算机科学中看似无关的问题。 这些发展导致了拉马努金图和复形的构建，并解决了几个长期存在的问题。 这些问题中有许多与扩张器的概念有关。 这是组合数学和计算机科学中的一个基本概念，它在李群的表示论和离散子群理论中找到了自己的道路。 最近，它也发现了它在三维双曲几何中的用途。会议的目标是汇集来自这些完全不同的数学和计算机科学领域的专家，介绍他们的工作，并加强这些科学家之间的潜在合作，他们通常不见面或参加相同的会议。

Abstract for Lie Groups, Representations and Discrete Mathematics ConferenceFebruary 6-10, 2006The conference is part of a year-long program at the Institute for Advanced Study in Princeton, New Jersey on Lie Groups, Representations and Discrete Mathematics. The last two decades show some deep and surprising connections between questions and results in number theory in general, automorphic forms in particular and seemingly unrelated problems in discrete mathematics and computer science. These developments led to the constructions of Ramanujan graphs and complexes and to the solution of several long-standing problems. Many of these questions are related to the notion of expanders. This is a basic concept in combinatorics and computer science which found its way to the representation theory and the theory of discrete subgroups of Lie groups. Recently, it also found its use in 3-dimensional hyperbolic geometry.The goal of the conference is to bring together experts from these quite different areas of mathematics and computer science to present their work and to strengthen the potential cooperation between these scientists who usually do not meet or attend the same conferences.