Geometry and Representation Theory: A Conference in Honor of George Lusztig

这笔赠款为一次会议提供了资金，该会议强调了几何表示理论领域的最新发展和公开问题。会议将于2006年5月30日至6月3日在马萨诸塞州剑桥市的麻省理工学院举行。这次会议将汇集该领域的领先学者，描述他们的最新研究，并向乔治·卢兹蒂格致敬，他提出(并仍在介绍)许多构成几何表示理论的思想。预计将涵盖的主题包括箭图变种及其在表示理论中的作用；局部域和正特征域上的群的表示；量子群；以及特征标。表示理论可以被认为是线性代数的自然扩展。代数对象的表示是对代数对象的属性进行编码的矩阵(可能是无限维的)的集合。几何表象理论是指利用几何学的技巧来构造表象的程序。这些构造的优点在于，通常很容易证明表示的性质，否则不会很明显；例如，表示具有良好的基，或者某些矩阵元素变成正整数。George Lusztig是几何表示理论的领先研究人员，所支持的会议将汇集该领域许多最杰出的学者来纪念他。这笔助学金将帮助资助研究生和新近获得博士学位的学生，以便他们能够参加这次令人兴奋的会议。

The grant provides funding for a conference highlighting recent developments and open problems in the field of geometric representation theory. The conference is to be held May 30 through June 3, 2006, at the Massachusetts Institute of Technology in Cambridge, Massachusetts. The conference will bring together leading scholars in the field to describe their latest research and to honor George Lusztig, who introduced (and is still introducing) many of the ideas that underlie geometric representation theory. Among the topics expected to be covered are quiver varieties and their role in representation theory; representations of groups over local fields and fields of positive characteristics; quantum groups; and character sheaves.Representation theory can be thought of as a natural extension of linear algebra. A representation of an algebraic object is a collection of matrices (possibly infinite dimensional) which encode properties of the algebraic object. Geometric representation theory refers to the program of using techniques from geometry to construct representations. The advantage of these constructions is that it is often easy to prove a property of the representation that would not be apparent otherwise; for example, that the representation has a nice basis or that certain matrix elements turn out to be positive integers. George Lusztig is a leading researcher in geometric representation theory, and the conference being supported will bring together many of the most distinguished scholars in the field to honor him. The grant will help to support graduate students and recent doctorates in order that they may attend this exciting conference.