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 and Number Theory seminar series.

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