Paula Lins’s talk at the Algebra Seminar of the University of Warwick

Paula Lins gave an invited talk at the Algebra Seminar of the University of Warwick on 23 January 2025.

Title: Zeta functions and applications to the Reidemeister Spectrum

Abstract: 

In this talk, I will introduce zeta functions that count group-theoretical objects, specifically focusing on the number of twisted conjugacy classes within a group.

Twisted conjugacy is a generalization of the usual conjugacy, incorporating a twist by an endomorphism. 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 automorphisms give infinitely many classes. For groups that do not possess this property, the focus shifts to understanding the possible sizes of the classes across all automorphisms, known as the Reidemeister spectrum.

In this talk, we will explore how the zeta functions mentioned above can be used to understand twisted conjugacy classes of certain nilpotent groups.