QM Research seminar: Graph potentials, TQFTs and mirror symmetry

Speaker: Pieter Belmans (University of Luxembourg)

Abstract:

Associated to decorated trivalent graphs I will describe a family of Laurent polynomials called graph potentials. These polynomials satisfy interesting symmetry and compatibility properties for different choices of graphs, leading to the construction of a topological quantum field theory which efficiently computes the classical periods as the partition function.

Under mirror symmetry graph potentials are related to moduli spaces of rank 2 bundles (with fixed determinant of odd degree) on a curve of genus g>1, which is a class of Fano varieties of dimension 3g-3. I will discuss how enumerative mirror symmetry relates classical periods to quantum periods in this setting. Time permitting I will touch upon aspects of homological mirror symmetry for these Fano varieties and their mirror partners. This is joint work with Sergey Galkin and Swarnava Mukhopadhyay.