Nonabelian arithmetic combinatorics and diophantine approximation 
Abstract: In the last ten years additive combinatorics has spread to group theory yielding a series of structure theorems for approximate subgroups, i.e. subsets that do not grow much under multiplication. Combined with diophantine considerations this has shed new light on the structure of dense subgroups of Lie groups and has had applications to spectral gap bounds, fast mixing of random walks, uniform exponential growth, Bernoulli convolutions and more. I will survey these developments. 

Web page: Alexandru I. Suciu  Comments to: i.loseu@neu.edu  
Posted: May 10, 2016  URL: http://www.math.neu.edu/bhmn/breuillard16.html 