Tobias Rossmann (University of Galway)

TITLE: Symbolic enumeration of orbits
 

ABSTRACT: In this talk, I will provide an overview of recent work on generating functions enumerating linear orbits and conjugacy classes of unipotent groups. We will study these generating functions by means of their linearised siblings, so-called "ask zeta functions", obtained by averaging over sizes of kernels in collections of matrices. The study of the latter functions involves a (sometimes surprising!) blend of techniques from algebra, combinatorics, and geometry.