Equations in virtually nilpotent groups

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• Motiejus Valiunas, University of Southampton
• Friday 03 November 2017, 15:00-16:00
• CMS, MR14.

If you have a question about this talk, please contact Nicolas Dupré.

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. This is joint work with Yago Antolin, Armando Martino and Enric Ventura.

This talk is part of the Junior Algebra/Logic/Number Theory seminar series.

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