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

“仿射赫克代数、朗兰兹程序、共形场论和矩阵模型”会议将汇集不同的领先数学家、物理学家和年轻研究人员，讨论这些领域的最新发展，并允许其中一个领域的专家了解其他领域。会议将包括三个部分：1)仿射Hecke代数（1周）2)Langlands程序（1周）3)共形场论和矩阵模型（2周）。这些区域之间有许多深刻的联系，其中一些是最近才发现的。探讨这些联系是本次会议的主要目标之一。会议将讨论的一些主题是：仿射和双仿射赫克代数的表示；切环Hecke代数；麦克唐纳理论;几何表征理论；双环群的表示；仿射李代数在临界水平上的表示；p进群的表示；几何朗兰兹猜想及其与弦理论的联系；Seiberg-Witten理论;AdS-CFTcorrespondence;矩阵模型与弦理论之间的关系。朗兰兹纲领是由朗兰兹于1967年在给韦尔的信中提出的，它是一个意义深远的纲领，将表示论和数论紧密地联系在一起。这对于理解称为自同构形式的中心数论对象是至关重要的。仿射赫克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。共形场论是量子粒子行为的物理模型，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）对于形成弦理论的基础也很重要。矩阵模型本质上是概率论的一个分支，处理随机矩阵的性质。然而，最近发现它们在弦理论中有着深远的应用。在过去的10年里，这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。该会议旨在帮助专家和年轻研究人员（包括许多妇女和少数民族）探索这一进展和联系。

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.