Pure PGR Seminar - Equations in virtually nilpotent groups, Motiejus Valiunas (Southampton) Seminar

Event details

Given an equation in a group, one may ask what is the probability that randomly chosen elements will satisfy it. Although a priori this question only makes sense for finite groups, one may generalise it to the family of amenable groups, as they are endowed with a measure that assigns 'size' to any subset. In fact, they often possess many measures, and the size of a subset might depend on the choice of a measure. In the talk I will consider a particular subfamily of discrete amenable groups - finitely generated virtually nilpotent groups - computations in which can be described by a finite set of polynomials. I will explain why the size of the solution set of a given equation in such a group does not depend on the measure chosen.