Topological recursion for generalized Hurwitz numbers

Abstract: The topological recursion or Chekhov-Eunard-Orantin recursion is an inductive procedure for an explicit computation of correlator functions appearing in a large number of problems in mathematical physics, from matrix integrals and Gromov-Witten invariants to enumerations of maps and meromorphic functions with prescribed singularities. In spite of existence of a huge number of known cases where this procedure does work, its validity and universality still remains mysterious in much extend. We develop a new tool based on the theory of KP hierarchy that allows one not only formally prove it in a unified way for a wide class of problems but also to understand its true nature and the origin. These problems include enumeration various kinds of Hurwitz numbers: ordinary ones, orbifold, double, monotone, r-spin Hurwitz numbers, as well as enumeration of (hyper) maps and extends much beyond. The talk is based on a joint work with B.Bychkov, P.Dunin-Barkowski, S.Shadrin.

HEP - theorymathematical physicsalgebraic geometrycombinatoricsexactly solvable and integrable systems

Audience: researchers in the discipline

IBS-CGP Mathematical Physics Seminar

Series comments: Registration is required at cgp.ibs.re.kr/activities/talkregistration