Speaker:  Alexandr Orlov (Institute of Oceanology, RAS)

Date and time: 19.10.2022, 17:00 (GMT +03:00)

Title: Graphs, Hamiltonian systems and Hurwitz numbers

Abstract: The quantum Calogero equation at the point of free fermions can be considered as an equation written in terms of the eigenvalues of some matrix X, and the Hamiltonian can be written as the Casimir operator, an element of the center of the universal enveloping algebra. This equation also makes sense of the generalized Mironov-Morozov-Natanzon cut-an-join equation (it generalizes the Guldon-Jackson cut-and-join equation, which describes the composition of a transposition with an element of a symmetric group in terms of the action of a differential operator on a polynomial of many variables). I will consider generalizations of this equation obtained for a set of matrices $X_1,\dots,X_n$, and classes of their solutions constructed using bipartite graphs, and also tell you about the connection of these problems with the enumeration of coverings of the Riemann surface with an embedded graph (Hurwitz numbers).

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com