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

几何与表示论：纪念乔治·卢斯蒂格的会议

• 批准号: 0606631
• 负责人: Pavel Etingof
• 金额: $ 2.5万
• 依托单位: Massachusetts Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-07-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0606631&HistoricalAwards=false
• 关键词: Geometry; Representation; Theory; Conference; Honor

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.

该赠款为一次会议提供资金，该会议强调几何表示理论领域的最新发展和开放问题。 该会议将于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。会议将汇集该领域的顶尖学者，介绍他们的最新研究，并向乔治·卢斯蒂格（George Lusztig）致敬，他介绍了（并且仍在介绍）几何表示理论的许多思想。 预计涵盖的主题包括箭袋品种及其在表征理论中的作用； 群体在当地领域和具有积极特征的领域的代表性；量子群；表示论可以被认为是线性代数的自然延伸。 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）的集合。 几何表示理论是指使用几何技术来构造表示的程序。 这些构造的优点是，通常很容易证明表示的属性，否则该属性将不明显；例如，表示有一个很好的基础，或者某些矩阵元素结果是正整数。 乔治·卢斯蒂格（George Lusztig）是几何表示理论领域的一位领先研究者，所支持的会议将汇集该领域许多最杰出的学者来向他致敬。 这笔赠款将有助于支持研究生和最近的博士学位，以便他们能够参加这次激动人心的会议。