Séminaires : Géométrie énumérative

Equipe(s) : aa, tga,
Responsables :Penka Georgieva, Elba Garcia-Failde, Ilia Itenberg, Alessandro Chiodo
Email des responsables : penka.georgieva@imj-prg.fr
Salle : 1516 - 413
Adresse :Jussieu

URL: https://webusers.imj-prg.fr/~penka.georgieva/EGSeminar.html

Orateur(s) Boris Bychkov - University of Haifa,
Titre Topological recursion for generalized double Hurwitz numbers
Horaire14:00 à 15:00

Topological recursion is a remarkable universal recursive procedure that has been found in many enumerative geometry problems, from combinatorics of maps, to random matrices, Gromov-Witten invariants, Hurwitz numbers, Mirzakhani's hyperbolic volumes of moduli spaces, knot polynomials. A recursion needs an initial data: a spectral curve, and the recursion defines the sequence of invariants of that spectral curve. 

In the talk I will define the topological recursion, spectral curves and their invariants, and illustrate it with examples; I will introduce the Fock space formalism which proved to be very efficient for computing TR-invariants for the various classes of Hurwitz-type numbers and I will describe our results on explicit closed algebraic formulas for generating functions of generalized double Hurwitz numbers, and how this allows to prove topological recursion for a wide class of problems.

If time permits 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). The talk is based on the series of joint works with P. Dunin-Barkowski, M. Kazarian and S. Shadrin.