Laboratory Colloquium - Richard Schoen (UC Irvine), Sergey Lando (NRU HSE)

17:00 Sergey Lando (NRU HSE). Combinatorial solutions to integrable hierarchies

Abstract: Since Witten’s work around 1990, it is well known that properly collected Gromov-Witten invariants (of all genera) of certain varieties constitute solutions to integrable hierarchies of partial differential equations. This is true, in particular, for the Kontsevich-Witten potential of a point, which is a solution to the Korteweg – de Vries hierarchy, and, as proven by Okounkov in 2000, for simple Hurwitz numbers, which form a solution to the Kadomtsev-Petviashvili hierarchy. Hurwitz numbers, which enumerate ramified coverings of the 2-sphere, also can be expressed in terms of properly equipped graphs. In the talk, we will discuss a natural question about which classes of graph invariants possess a similar property. The talk is based on a joint work with S.Chmutov (Ohio State University) and M.Kazarian. 
No specific preliminary knowledge is required.