Alex Weekes (University of Saskatchewan)

Title: Quivers, Kac polynomials, and zastava spaces.

Abstract: Quivers (aka directed graphs) have many interesting ties to combinatorics, algebra, and geometry. We'll begin this talk by overviewing the basics of quiver representations, including Gabriel's Theorem, leading towards a theorem of Kac which counts quiver representations in terms of Kac polynomials. A remarkable theorem of Hua provides an explicit generating function for these Kac polynomials. We'll discuss how Hua's result can be interpreted in terms of certain interesting algebraic varieties called zastava spaces, via recent developments in mathematical physics (the theory of Coulomb branches). This talk is based on joint work with Dinakar Muthiah.

Venue

UQAM, 201, avenue du Président-Kennedy, PK-4323, Montréal