Math 207A: Superapproximation




Course description:
Unlike my previous topics courses, this course will be a more surveystyle course with an emphasis on the main ideas rather than details of many proofs. The main concepts and more fundamental results will be discussed more thoroughly, but in order to cover all the main results on this growing topic, we skip the details of many of the proofs. As the title says, in this course, we will learn about superapproximation : the study of randomwalks on congruence quotients of subgroups of \(S\)arithmetic groups. We will mention some of many applications of this topic to other parts of mathematics: construction of expanders, affine sieve, sieve in groups, hyperbolic groups, Apollonian packing, Zaremba's conjecture, etc. Here are some of the articles that will be discussed in this course:


Notes related to lectures and supplementary materials:
I will share some of my notes here.
