Geometry and Topology Seminar: Hurwitz numbers in geometry and physics.
31 January 2013 13:00 in CM221
Hurwitz numbers enumerate ramified coverings of the 2-sphere of a fixed topological type. Amazingly, the same numbers occur in many different contexts, in particular, they are related to geometry of the moduli spaces of curves via so-called ELSV formula. I am going to make a short overview of different interpretations of Hurwitz numbers and methods of computation. I'll explain their relation to the moduli
spaces of curves, and another relation to the random matrix models (in fact, I'll use a mathematical replacement for the random matrix theory given by topological recursion for some multi-differentials on Riemann surfaces. The latter one I'll explain from the very beginning).