Mirror Symmetry and Ribbon Graphs

In this talk I will explain how to construct a model
for the Fukaya category of punctured Riemann surfaces in terms of a sheaf
of dg-categories over a suitable category of ribbon graphs. The main
ingredients will be Nadler and Zaslow's work on cotangent bundles, and
Kontsevich' recent ideas on the locality of the Fukaya category of a Stein
manifold. Further, I will explain applications to homological mirror
symmetry for degenerate elliptic curves. This work is joint with David
Treumann and Eric Zaslow