EMSW21-RTG: Research Training Group in Interactions of Representation Theory, Geometry and Combinatorics

EMSW21-RTG：表示论、几何和组合学相互作用研究培训小组

• 批准号: 0943745
• 负责人: Mark Haiman
• 金额: $ 120.01万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-10-01 至 2016-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0943745&HistoricalAwards=false
• 关键词: EMSW21; RTG; Research; Training; Group

The goal of this project is training of undergraduate students, graduate students, and postdocs at the research interface of combinatorics, geometry, and representation theory. This area includes enumerative geometry, geometric representation theory of infinite dimensional Lie algebras, corresponding quantized universal enveloping algebras, and of Hecke algebras. On the combinatorial side we will also focus on algebraic combinatorics and its applications. All these areas have seen fascinating progress in the last decade.The project will be conducted with active involvement of graduate and undergraduate students and post-docs. These areas of mathematics are closely related to many recent developments in mathematical physics (the mathematical side of theoretical physics), mostly to quantum field theory, string theory, and statistical mechanics. Combinatorial problems which will be addressed also have direct applications in biology, for instance in the study of phylogenetic trees. This grant (in combination with other grants) will be used to fund a number of training workshops and master-classes on hot research topics aimed at post-doctoral fellows, graduate, and undergraduate students.

该项目的目标是在组合学、几何和表示论的研究领域对本科生、研究生和博士后进行培训。 该领域包括枚举几何、无限维李代数的几何表示理论、相应的量化泛包络代数以及赫克代数。 在组合方面，我们还将关注代数组合及其应用。所有这些领域在过去十年中都取得了令人瞩目的进展。该项目将在研究生、本科生和博士后的积极参与下进行。 数学的这些领域与数学物理学（理论物理学的数学方面）的许多最新发展密切相关，主要与量子场论、弦理论和统计力学有关。 将要解决的组合问题在生物学中也有直接的应用，例如在系统发育树的研究中。 这笔赠款（与其他赠款一起）将用于资助针对博士后研究员、研究生和本科生的热门研究主题的一系列培训研讨会和大师班。