In a series of joint works with Pieter Belmans and Swarnava Mukhopadhyay we introduce graph potentials,
a collection of Laurent polynomials parametrized by trivalent graphs. We show how this collection gives rise to an infinite-dimensional 2d TQFT, and argue that it can be upgraded to a 4d TQFT of Donaldson-Floer type.
The original motivation for introduction of the graph potentials is the study of mirror symmetry for SU(2) character varieties on a surface, or equivalently moduli spaces of fixed determinant parabolic semi-stable rank 2 vector bundles on algebraic curves. We show that periods of graph potentials for graphs without leaves match enumerative geometry of moduli spaces in the case of odd degree determinant, when the respective variety is smooth.
Graph potentials: mirror symmetry for SU(2) character varieties and TQFT
18.05.2026 13:15 - 14:45
Organiser:
H. Grobner, A. Mellit, A. Minguez, B. Szendroi
Location: