Andreas Thom: Stability and invariant random subgroups III

The lecture was held within the framework of the Hausdorff Trimester Program: Logic and Algorithms in Group Theory.

Abstract:
Is a pair of almost commuting permutations close to a pair of commuting permutations? Arzhantseva and Paunescu answered a more precise form of this question positively. In this course, I will discuss methods to decide when almost solutions to equations in permutation groups are close to actual solutions of those equations. The course will contain a basic introduction to the theory of unimodular random networks as well as invariant random subgroups and explain their use in decision problems in graph theory and group theory.