### Growth of subsets

Geometry and Topology Seminar

12th March 2024, 2:00 pm – 3:00 pm

Fry Building, 2.04

The standard growth function of a finitely generated group counts the elements in the ball of radius n in the Cayley graph. We can modify this by only counting elements of some given subset of interest (for example a subgroup, or conjugacy class). We are concerned with both the asymptotics of this function, and the behaviour of the associated formal power series. In this talk I will discuss some work in progress on the growth of conjugacy classes in various classes of groups, before moving onto some more general results for subsets of virtually abelian groups. Joint work with Aram Dermenjian, and with Laura Ciobanu and Alex Levine.

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