Conference: The Interplay of Algebra and Geometry

首席研究员：Etingof，Pavel I.建议编号：DMS-0935974机构：麻省理工学院标题：会议：代数和几何的相互作用为期一周的会议名为“代数和几何的相互作用”，旨在介绍表示理论中的一些最重要和最新的发展。它将于2009年6月14日至20日，在Corrado de Concini诞辰60周年之际，在意大利Cortona的Palazzone举行，这是比萨Scuola Norale Superiore的一个会议地点。演讲者将是在李群、表示理论和相关领域工作的杰出数学家，重点是代数和几何方法在表示理论中的相互作用。会议的主要议题是：有限和无限维李群和李代数，李代数和代数的表示理论，不变理论，对称和奇妙簇及其紧化，量子群和量子仿射代数，超平面和子空间排列及其紧化。表示论是研究线性空间中对称性的数学领域。它在量子物理和化学中有着重要的应用。例如，它允许人们将空间的旋转对称性纳入对原子的研究，最终成为化学元素周期表结构的基础。此外，表象理论是对基本粒子进行分类的主要工具之一，也是弦理论的基本工具，弦理论旨在从量子力学的角度解释引力。此外，表象理论在统计物理和量子计算机理论中也有应用。近年来，由于借鉴了几何学的深层思想，表象理论取得了很大的进展。另一方面，表象理论可能为几何中的经典问题带来新的曙光。会议将突出这一相互作用，并将回顾这一领域的一些主要成就。

ABSTRACTPrincipal Investigator: Etingof, Pavel I. Proposal Number: DMS - 0935974 Institution: Massachusetts Institute of Technology Title: Conference: The Interplay of Algebra and GeometryThe one-week conference entitled "The Interplay of Algebra and Geometry" intends to present some of the most important and recent developments in representation theory. It will take place in Cortona (Italy), at the Palazzone, a conference location belonging to the Scuola Normale Superiore of Pisa, between June 14 and 20, 2009, on the occasion of Corrado De Concini's 60th birthday. The speakers will be distinguished mathematicians working in the areas of Lie groups, representation theory and related fields with an emphasis on the interplay of algebraic and geometric methods in representation theory. The main topics of the conference are: finite and infinite dimensional Lie groups and Lie algebras, representation theory of Lie algebras and algebraic groups, invariant theory, symmetric and wonderful varieties and their compactifications, quantum groups and quantum affine algebras, hyperplane and subspace arrangements and their compactifications.Representation theory is an area of mathematics that studies symmetry in linear spaces. It has important applications to quantum physics and chemistry. For instance, it allows one to incorporate the rotational symmetry of the space into the study of atoms, ultimately underlying the structure of the Periodic Table of chemical elements. Also, representation theory is one of the main tools in classifying elementary particles, and is a fundamental instrument of string theory, which aims to explain gravity quantum-mechanically. In addition, representation theory has applications to statistical physics, and to the theory of quantum computers. Recently, a great progress in representation theory was made thanks to applying deep ideas from geometry. In the other direction, representation theory may shed a new light on classical problems in geometry. The conference will highlight this interplay and will review some of the main achievements in this field.