Maxim Kazarian (HSE & Skoltech, Moscow)
Tuesday, October 19, 2021 - 14:00
HU Berlin, Institut für Physik, IRIS-Haus
Zum Großen Windkanal 2, 12489 Berlin-Adlershof, Raum 1'021,
Hybrid seminar: Algebra, Geometry and Physics (HU Berlin/MPIM Bonn)
Gaetan Borot (HU Berlin), Yuri Manin (MPIM)
The topological recursion or Chekhov-Eynard-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.
submitted by Gaetan Borot (