Paula Lins spoke at an international algebra conference at the ICTS, India

Lincoln algebraist Dr Paula Lins was one of the invited speakers at the event “Combinatorial Methods in Enumerative Algebra” at the International Centre for Theoretical Sciences in Bengaluru, India.

Paula’s talk was about a recent work on zeta functions of groups counting twisted conjugacy classes.

Title: Zeta functions and applications to twisted conjugacy

Abstract:

In this talk, I will discuss zeta functions that count the number of twisted conjugacy classes of a fixed group.

Twisted conjugacy is a generalisation of the usual conjugacy, where we introduce a twist by an endomorphism. Specifically, given a group G and an automorphism f, we consider the action gx = gx f(g)^{-1}. The orbits of this action are known as twisted conjugacy classes, or Reidemeister classes.

Recent years have seen intensive investigation into the sizes of these classes. A major goal in this area is to classify groups where all classes are infinite. For groups that do not possess this property, the focus shifts to understanding the possible sizes of the classes, among all automorphisms.

In this talk, we will see that, as typical, these zeta functions admit Euler product decompositions with rational local factors, and we will explore how these zeta functions can be utilised to understand twisted conjugacy classes of certain nilpotent groups.