U. Haifa Algebra seminar: Wednesday, November 30, 2022. Speaker: Petr Dunin-Barkowski (HSE Moscow). Title: “Generalized double Hurwitz numbers, topological recursion, and ELSV-type formulas”.

Date:            Wednesday, November 30, 2022 at 12:00 PM 

Place:           Room 614, Science & Education Building, U. Haifa

Speaker:    Petr Dunin-Barkowski (HSE Moscow)

Title: Generalized double Hurwitz numbers, topological recursion, and ELSV-type formulas

Abstract: In the talk, I’ll briefly recall the origin and the main properties of spectral curve topological recursion, and then I will describe in more detail our results on explicit closed algebraic formulas for generating functions of generalized double Hurwitz numbers, and how this allows proving topological recursion for a wide class of problems. After that I’ll talk about the implications for the so-called ELSV-type formulas (relating Hurwitz-type numbers to intersection numbers on the moduli spaces of algebraic curves); in particular, I’ll explain how this almost immediately gives proofs (of a purely combinatorial-algebraic nature) of the original ELSV formula and of its r-spin generalization (originally conjectured by D.Zvonkine).

The talk is based on a series of joint works with B.Bychkov, M.Kazarian, and S.Shadrin, arXiv:2008.13123, 2012.14723, 2106.08368, 2206.14792.   

This talk can be thought of as a continuation of Boris Bychkov’s talk on November, 23.