Ribbon Graphs and Mirror Symmetry
Seminar Room 1, Newton Institute
Beginning with a ribbon graph with some extra structure, I will define a dg category, the "constructible plumbing model," which serves as a stand-in for the Fukaya category of the Riemann surface associated to the ribbon graph. When the graph has a combinatorial version of a torus fibration with section, I will define a one-dimensional algebraic curve, and prove that the dg category of vector bundles on the curve is equivalent to the constructible plumbing model, a version of homological mirror symmetry in one-dimension. I will also discuss the higher-dimensional case.
This talk is based on joint work with Nicolo' Sibilla and David Treumann.