Perspectives in Lie Theory

谎言理论的观点

• 批准号: 1448873
• 负责人: Victor Kac
• 金额: $ 3.62万
• 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: 2015
• 资助国家: 美国
• 起止时间: 2015-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1448873&HistoricalAwards=false
• 关键词: Perspectives; Lie; Theory

An intensive research period "Perspectives in Lie Theory" will take place in Pisa, at Centro de Giorgi, from December 9, 2014 until February 28, 2015. It will consist of several activities, such as various symposia, mini-courses, research talks and multiple discussion sessions. This project is to support the participation of U.S.-based speakers in three mini-courses: "Vertex algebras, W-algebras, and applications" December 9-January 18, 2015; "Lie Theory and Representation Theory" January 19-February 6, 2015; and "Algebraic topology, geometric and combinatorial group theory" February 8-28, 2015; and to support the participation of U.S.-based junior or resource-restricted researchers in workshops and symposia held during the intensive research period. A record of all the activities and achievements of the program will be available on the webpage of the event (http://www.crm.sns.it/event/293/) and the proceedings will be published by Springer-Verlag in the INdAM series.Many important theories in mathematics find their motivation in physical problems; one of these is Lie theory, which could be seen as a study of generalized symmetries. It is a very sophisticated theory, presenting an explosion of activity at the moment. Lie theory has developed through the years in a broad range of interacting branches and directions, all requiring advanced techniques from different areas such as algebra, geometry, topology, combinatorics, and mathematical physics. Communication and scientific collaboration between mathematicians with different backgrounds is essential for the progress of such a theory. The intensive research period will therefore address the newest and most exciting achievements in Lie theory and will engage some of the most outstanding and active researchers working in the field. Specifically, the intensive research period will address: vertex algebras, their classical limits, and applications to the theory of integrable systems; representation theory of Lie groups, Lie algebras and generalizations; cluster algebras; non-commutative geometry and its relevance in representation theory; combinatorics and topology of toric and hyperplane arrangements and representations of Artin groups; configuration and loop spaces.

一个密集的研究期“谎言理论的观点”将于2014年12月9日至2015年2月28日在比萨的乔治中心举行。它将包括几项活动，如各种专题讨论会、小型课程、研究讲座和多场讨论会。该项目旨在支持美国的参与-在三个迷你课程的扬声器：“顶点代数，W-代数，和应用”2015年12月9日至1月18日;“李理论和表示理论”2015年1月19日至2月6日;和“代数拓扑，几何和组合群论”2015年2月8日至28日;并支持美国的参与-在密集研究期间举办的讲习班和专题讨论会上，该计划的所有活动和成就的记录将在该活动的网页上提供（http：//www.crm.sns.it/event/293/），会议记录将由Springer-Verlag在INdAM系列中出版。许多重要的数学理论在物理问题中找到了它们的动机;其中之一是Lie理论，它可以被视为广义对称性的研究。这是一个非常复杂的理论，目前呈现出爆炸式的活动。多年来，李理论已经在广泛的相互作用的分支和方向上发展，所有这些都需要来自不同领域的先进技术，如代数，几何，拓扑，组合学和数学物理。具有不同背景的数学家之间的交流和科学合作对于这一理论的发展至关重要。因此，密集的研究期间将讨论李群理论中最新和最令人兴奋的成就，并将吸引一些在该领域工作的最杰出和最活跃的研究人员。具体而言，密集的研究期间将解决：顶点代数，其经典的限制，并应用于可积系统的理论;李群，李代数和概括的表示理论;集群代数;非交换几何及其在表示理论的相关性;组合学和拓扑的环面和超平面安排和阿廷群表示;配置和循环空间。