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Graph potentials, TQFTs and mirror partners

February 9, 2022 at 16:0017:00 CET

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.


February 9, 2022
16:00 – 17:00 CET


Frankfurt and Zoom


Alex Küronya
Martin Möller
Jakob Stix
Martin Ulirsch
Annette Werner