Special Meeting: Collaborative Research: Affine Hecke algebras, the Langlands Program, Conformal Field Theory and Matrix Models

仿射Hecke代数、朗兰兹计划、共形场理论和矩阵模型会议将把一群不同的著名数学家、物理学家和年轻的研究人员聚集在一起，讨论这些领域的惊人最新发展，并允许其中一个领域的专家了解其他领域的专家。会议将由三部分组成：1)仿射Hecke代数(1周)2)朗兰兹程序(1周)3)共形场理论和矩阵模型(2周)这些领域之间存在着大量而深刻的联系，其中一些联系是最近才发现的。探索这些联系是这次会议的主要目标之一。会议将讨论的一些问题包括：仿射和双仿射Hecke代数的表示；割圆Hecke代数；Macdonald理论；几何表示理论；双圈群的表示；临界水平上的仿射李代数的表示；p-Add群的表示；几何朗兰兹猜想及其与弦理论的联系；Seiberg-Witten理论；ADS-CFT对应；矩阵模型与弦理论之间的关系。朗兰兹程序是R.朗兰兹于1967年在《致A·韦尔的信》中提出的，它是一个将表示论与数论紧密联系起来的意义深远的程序。这对于理解被称为自同构形式的中心数论对象是至关重要的。仿射Hecke代数是一种代数结构，在朗兰兹程序中起着至关重要的作用。共形场理论是量子粒子行为的物理模型，这在数学上特别容易处理，因为存在大量的对称性，称为共形对称性。这样的理论(在两个时空维度上)对于阐述弦理论的基础也是重要的。矩阵模型本质上是概率论的一个分支，研究随机矩阵的性质。然而，最近事实证明，它们在弦理论中有着深刻的应用。在过去10年中，在所有四个领域都取得了重大进展，而且很明显，它们是密切相关的。这次会议旨在帮助专家和年轻研究人员(包括许多妇女和少数族裔)探索这种进步和联系。

The conference ``Affine Hecke algebras, Langlands program, conformal field theory, and matrix models'' will bring together a diverse group of leading mathematicians and physicists and young researchers, to discuss striking recentdevelopments in these fields, and allow experts in one of them tolearn about the others. The conference will consist of three parts: 1) Affine Hecke algebras (1 week) 2) Langlands program (1 week)3) conformal field theory and matrix models (2 weeks).There are numerous and deep connections between these areas, some of whichwere found quite recently. To explore these connections is one ofthe main goals of the conference. Some of the topics to bediscussed in the conference are: representations of affine and double affine Hecke algebras; cyclotomic Hecke algebras; Macdonald theory; geometric representation theory; representations of double loop groups; representations of affine Lie algebras at the critical level; representations of p-adic groups; geometric Langlands conjecturesand their connections to string theory; Seiberg-Witten theory; AdS-CFTcorrespondence; relations between matrix models and string theory. The Langlands program, formulated by R. Langlands in 1967 in hisletter to A. Weil, is a far-reaching program deeply connectingrepresentation theory and number theory. It is crucial forunderstanding central number-theoretic objects called automorphicforms. Affine Hecke algebras are algebraic structures which playa crucial role in the Langlands program. Conformal field theoriesare physical models for the behavior of quantum particles, which are especially tractable mathematically, because of presence of a large amount of symmetry, called conformal symmetry. Such theories (in two spacetime dimensions) are also importantin formulating the basics of string theory. Matrix models is essentially a branch of probability theory, dealing withproperties of random matrices. However, it recently turned out that they have deep applications to string theory. In the last 10 years, there has been significant progress in allfour areas, and it became clear that they are intimatelyrelated. The conference is designed to help experts and youngresearchers (including many women and minorities) to explorethis progress and connections.