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We consider the Fano variety $N$ parametrizing rank two bundles on a curve $C$ with fixed determinant of odd degree. These varieties have also appeared in symplectic geometry as character varieties. In the first part of this talk, we construct a weak Landau-Ginzburg mirror  i.e. certain Laurent polynomials $L$ in the following sense: The  constant term of the powers of $L$ computes  one-pointed descendent Gromov-Witten numbers of $N$. We will also outline how these potentials led to a conjectural decomposition of the $D^bCoh(N)$ which has now been proved by Tevelev etal.    In the second part of this talk, we study various properties of these mirror polynomials which we refer to as Graph Potentials. We first show that the birational type of the graph potential only depends on the homotopy type of the colored graph, and we use this to define a topological quantum field theory. A similar construction was recently introduced independently by Kontsevich--Odesskii under the name of multiplicative kernels. As an application  we  give an efficient computational method to compute its partition function answering the main question.    This is a joint work with Pieter Belmans and Sergey Galkin