Special Geometry and Physics Seminar: Vincent Bouchard, University of Alberta

Abstract:

In recent years, a unifying theme has been found for a surprising number of counting problems. It appears that in many seemingly unrelated contexts, generating functions for enumerative invariants satisfy a particular topological recursion, based on the geometry of a complex curve. As examples, Hurwitz theory, Gromov-Witten theory of the complex line, and open/closed Gromov-Witten theory of the three-dimensional complex plane and other toric Calabi-Yau threefolds are all encoded by the same topological recursion on certain complex curves. In this talk, I will first review applications of the topological recursion on genus zero curves, and then report on work in progress on studying the topological recursion for families of elliptic curves. In this context, the recursion produces an infinite tower of quasi-modular forms. The question is: to what counting problem should these quasi-modular forms be related?