Lie Groups, Representations and Discrete Mathematics

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Abstract for Lie Groups, Representations and Discrete Mathematics ConferenceFebruary 6-10, 2006The conference is part of a year-long program at the Institute for Advanced Study in Princeton, New Jersey on Lie Groups, Representations and Discrete Mathematics. The last two decades show some deep and surprising connections between questions and results in number theory in general, automorphic forms in particular and seemingly unrelated problems in discrete mathematics and computer science. These developments led to the constructions of Ramanujan graphs and complexes and to the solution of several long-standing problems. Many of these questions are related to the notion of expanders. This is a basic concept in combinatorics and computer science which found its way to the representation theory and the theory of discrete subgroups of Lie groups. Recently, it also found its use in 3-dimensional hyperbolic geometry.The goal of the conference is to bring together experts from these quite different areas of mathematics and computer science to present their work and to strengthen the potential cooperation between these scientists who usually do not meet or attend the same conferences.