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

Abstract: Graph potentials are Laurent polynomials associated to (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 view point of mirror symmetry, we will show how the critical value decomposition of graph potentials provides evidence for the conjectural semiorthogonal 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 a joint work with Pieter Belmans and Sergey Galkin.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html