Counting quiver representations over finite fields

By Fernando Rodriguez Villegas

These are notes (taken by E. Vitale) of a summer school held at the University of Bologna in the week of 22-26 May, 2023 as part of the program Quiver Representations, Quiver Varieties and Combinatorics.

This is the announcement for the course.

Counting representations of quivers over finite fields

In these lectures I will present the calculation of the title in the case of the star-shaped quivers related to character varieties based on my joint work with E. Letellier and T. Hausel. The starting point will be a formula of Hua for a general quiver. The basic tool used is the combinatorics of symmetric functions and generating functions, which I will discuss from scratch.