Automorphic Forms, Representations, and Combinatorics

自守形式、表示和组合

基本信息

批准号：
1205558
负责人：
Benjamin Brubaker
金额：
$ 3.04万
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：
2012
资助国家：
美国
起止时间：
2012-08-01 至 2013-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1205558&HistoricalAwards=false
关键词：
Automorphic Forms Representations Combinatorics

项目摘要

The conference "Automorphic forms, representations, and combinatorics" will take place at Stanford University from August 13--16, 2012, and highlight recent research by Daniel Bump and his many collaborators and students. Their results connect various matrix coefficients to the geometry and combinatorics of a certain class of singular algebraic varieties. Many of these constructions extend to matrix coefficients on metaplectic covers of reductive groups, certain central extensions closely linked to reciprocity laws in number theory. These extensions often lead to surprising connections with combinatorial representation theory. Related developments in number theory, automorphic forms, and random matrix theory will also be discussed in an effort to stimulate new connections among these fields.The conference will bring together a group of twenty international speakers who are leaders in the fields of number theory, automorphic forms, and combinatorial representation theory to discuss recent progress and suggest new directions of study. The conference program also aims to introduce a new generation of young mathematicians to these rapidly developing fields by offering some expository lectures, curating materials in an online website, and offering partial travel support for those without other sources of funding. A website for the conference may be found at math.mit.edu/~brubaker/bumpconf.html

“自同构形式、表示和组合”会议将于 2012 年 8 月 13 日至 16 日在斯坦福大学举行，重点介绍 Daniel Bump 及其众多合作者和学生的最新研究成果。他们的结果将各种矩阵系数与某一类奇异代数簇的几何和组合联系起来。这些构造中的许多都扩展到还原群的元逻辑覆盖上的矩阵系数，某些中心扩展与数论中的互易定律密切相关。这些扩展常常导致与组合表示理论令人惊讶的联系。还将讨论数论、自同构形式和随机矩阵理论的相关发展，以努力激发这些领域之间的新联系。会议将汇集 20 位国际演讲者，他们是数论、自同构领域的领导者形式和组合表示理论来讨论最新进展并提出新的研究方向。该会议计划还旨在通过提供一些说明性讲座、在在线网站上整理材料以及为那些没有其他资金来源的人提供部分旅行支持，向新一代年轻数学家介绍这些快速发展的领域。会议网站可在 math.mit.edu/~brubaker/bumpconf.html 找到