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).

__Attachments:__