Perspectives in Lie Theory

从2014年12月9日到2015年2月28日，位于乔治中心的比萨将举办一场名为《谎言理论的视角》的密集研究活动。它将包括多项活动，如各种研讨会、迷你课程、研究讲座和多个讨论环节。该项目旨在支持美国演讲者参加三个迷你课程：2015年12月9日至1月18日的《顶点代数、W-代数及其应用》；2015年1月19日至2月6日的《李论与表示理论》；2015年2月8日至28日的《代数拓扑、几何和组合群论》；以及支持美国初级或资源受限的研究人员参加密集研究期间举办的研讨会和座谈会。该计划的所有活动和成果的记录将在该活动的网页上获得(http://www.crm.sns.it/event/293/)和会议记录将由斯普林格-韦拉格在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；其中之一是李理论，它可以被视为对广义对称性的研究。这是一个非常复杂的理论，目前呈现出一种爆炸性的活动。多年来，李氏理论在广泛的相互作用的分支和方向上得到了发展，所有这些都需要来自不同领域的先进技术，如代数、几何、拓扑学、组合学和数学物理。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进步是必不可少的。因此，密集的研究期将介绍谎言理论的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。具体地说，密集的研究阶段将涉及：顶点代数，它们的经典极限，以及在可积系统理论中的应用；李群、李代数和推广的表示理论；簇代数；非交换几何及其在表示理论中的相关性；环面和超平面排列的组合学和拓扑学以及Artin群的表示；构型和循环空间。

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.