Conference: The Interplay of Algebra and Geometry

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ABSTRACTPrincipal Investigator: Etingof, Pavel I. Proposal Number: DMS - 0935974 Institution: Massachusetts Institute of Technology Title: Conference: The Interplay of Algebra and GeometryThe one-week conference entitled "The Interplay of Algebra and Geometry" intends to present some of the most important and recent developments in representation theory. It will take place in Cortona (Italy), at the Palazzone, a conference location belonging to the Scuola Normale Superiore of Pisa, between June 14 and 20, 2009, on the occasion of Corrado De Concini's 60th birthday. The speakers will be distinguished mathematicians working in the areas of Lie groups, representation theory and related fields with an emphasis on the interplay of algebraic and geometric methods in representation theory. The main topics of the conference are: finite and infinite dimensional Lie groups and Lie algebras, representation theory of Lie algebras and algebraic groups, invariant theory, symmetric and wonderful varieties and their compactifications, quantum groups and quantum affine algebras, hyperplane and subspace arrangements and their compactifications.Representation theory is an area of mathematics that studies symmetry in linear spaces. It has important applications to quantum physics and chemistry. For instance, it allows one to incorporate the rotational symmetry of the space into the study of atoms, ultimately underlying the structure of the Periodic Table of chemical elements. Also, representation theory is one of the main tools in classifying elementary particles, and is a fundamental instrument of string theory, which aims to explain gravity quantum-mechanically. In addition, representation theory has applications to statistical physics, and to the theory of quantum computers. Recently, a great progress in representation theory was made thanks to applying deep ideas from geometry. In the other direction, representation theory may shed a new light on classical problems in geometry. The conference will highlight this interplay and will review some of the main achievements in this field.