Graph potentials and mirrors of moduli of rank two bundles on curves

Contact: Nicolas Addington

Graph potentials are Laurent polynomials associated with (colored) trivalent graphs that were introduced in a joint work with Belmans and Galkin. They naturally appear as Newton polynomials of natural toric degenerations of the moduli space of rank two bundles. In this talk we will first discuss how graph potentials compute quantum periods of the moduli space M of rank two bundles with fixed odd degree determinant and hence can be regarded as a partial mirror to M. From the viewpoint of mirror symmetry, we will show how the critical value decomposition of graph potentials is related to the semi-orthogonal decomposition of D^bCoh(M). If time permits we will also discuss a formula to efficiently compute the periods of graph potential via a TQFT. This is joint work with Pieter Belmans and Sergey Galkin.