An Introduction to Approximate Subgroups

Emmanuel Breuillard  (Universite Paris-Sud XI)

10:30 am to 11:30 am, August 22nd, 2014   Science Building A1510

Abstract:

Approximate subgroups are finite subsets of a group that are almost closed under multiplication. They were introduced by Terence Tao about ten years ago. In this talk I will discuss the notion, some of its history, its connections with a variety of subjects including additive combinatorics, asymptotic group theory, riemannian geometry, and number theory. In particular I will describe a joint work with B. Green and T. Tao, in which we prove a structure theorem for approximate subgroups of an arbitrary group, which admits a number of geometric consequences including refinements of theorems of Gromov's such as the polynomial growth theorem and the almost flat manifolds theorem.

About the speaker:

Prof. Emmanuel Breuillard (Univ. Paris-Sud XI) is an invited speaker of ICM 2014 (Seoul).

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