Date: Tuesday, February 02, 2016
Title: Superapproximation and its applications.
Abstract: Let G be a finitely generated subgroup of GL(n,Q). Under certain algebraic conditions, strong approximation describes the closure of G with respect to its congruence topology. Superapproximation essentially tells us how dense G is in its closure! Here is my plan for this talk:
1. I will start with the precise formulation of this property.
2. Some of the main results on this subject will be mentioned.
3. Some of the (unexpected) applications of superapproximation will be mentioned, e.g. BanachRuziewicz problem, orbit equivalence rigidity, variation of Galois representations.
4. Some of the auxiliary results that were needed in the proof of superapproximation will be mentioned: sumproduct phenomena, existence of small solutions.
Speaker: Alireza Salehi Golsefidy
Institution: UCSD
