## Orbifold Hurwitz Numbers and Topological Recursion

Dr. Norman Do

(Monash)

Abstract

How many ways are there to map a genus g Riemann surface to the Riemann sphere? We obtain Hurwitz numbers by counting such maps with prescribed branching conditions. In recent work with Oliver Leigh and Paul Norbury, we show that a certain class of Hurwitz numbers is generated by topological recursion. The talk will be an advertisement for topological recursion, which appears in matrix models, enumeration of surface tilings, intersection theory on moduli spaces, enumerative geometry of threefolds, statistical mechanical models, quantum invariants of knots, topological string theory, and probably a lot more!