Perspectives in Lie Theory

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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.