Graph potentials as mirrors to moduli of vector bundles on curves

Abstract: In a joint work with Sergey Galkin and Swarnava Mukhopadhyay we have a class of Laurent polynomials associated to decorated trivalent graphs which we called graph potentials. These Laurent polynomials satisfy interesting symmetry and compatibility properties. Under mirror symmetry they 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 (parts of) the (enumerative / homological) mirror symmetry picture for Fano varieties, and then explain what we understand for this class of varieties and what we can say about the (conjectural) semiorthogonal decomposition of the derived category.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

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