Oberseminar Algebra und Geometrie

Talk by Pieter Belmans (Université du Luxembourg)

Graph potentials, TQFTs and mirror partners

Abstract: In a joint work with Sergey Galkin and Swarnava Mukhopadhyay we introduced a class of Laurent polynomials associated to decorated trivalent graphs which we called graph potentials. These Laurent polynomials satisfy interesting symmetry and compatibility properties, 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 $g\geq 2$, 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.