SM: Arithmetic Groups and Their Applications in Combinatorics, Geometry and Topology

University Of Virginia Main Campus, Charlottesville VA

Investigators

Abstract

A workshop ``Arithmetic Groups and Their Applications in Combinatorics, Geometry and Topology" will be held April 15-18 on the campus of the University of Virginia in Charlottesville. The scientific program of the workshop will be composed of lectures delivered by the leading experts in the area from the US, Brazil, France and Israel, and will highlight the most significant results obtained in the last few years. Special attention will be given to such topics as the analysis of structural properties of arithmetic groups (virtual positivity of the first Betti number, congruence subgroup problem, bounded generation), their applications in algebraic geometry (fake projective planes and fake versions of other important algebraic varieties), in differential geometry and topology (hyperbolic 3-manifolds, isospectral locally symmetric spaces) and in combinatorics (construction of expanders). Arithmetic groups are special groups whose elements are matrices with integral entries. This notion, which can be traced back to the work of Gauss on integral quadratic form, plays a crucial role in many areas of mathematics including algebra and various parts of number theory (e.g., the theory of automorphic forms). In recent years, new applications of the theory of arithmetic groups have emerged in algebraic and differential geometry, Lie theory and combinatorics. The workshop will showcase important results involving arithmetic groups. The focus will be placed on making the methods of the theory of arithmetic groups accessible to researchers, particularly young ones, working in a variety of areas.