"Generalized topological recursion and enumerative geometry"

Abstract: In recent years, it has become clear that the Eynard-Orantin topological recursion is a unifying theme in various enumerative geometric problems related to string theory. In this talk I will first review what the recursion is and how it encodes enumerative invariants in a number of contexts, including work in progress on new applications of the recursion to double Hurwitz numbers, with explicit relations to topological string theory on orbifolds. I will also study some of the fundamental properties of the recursion, and then define a newly found "generalized recursion" with a wider range of applicability than the original Eynard-Orantin recursion.