Seminar on W-algebras and Integrable Systems

[Boris Dubrovin]

Dear All,

Next two meetings of the Seminar on W-algebras and Integrable Systems will take place on

Friday, July 8, 11:00 - 12:30, Room 136 of SISSA Main Building

Speaker: Boris Dubrovin (SISSA)

Title: Computing tau-functions from integrable PDEs

Abstract: A simple and efficient procedure of computing logarithmic expansion of tau-functions of solutions to integrable systems will be explained. It will be applied to computing the Witten - Kontsevich intersection numbers on the moduli spaces of algebraic curves as well as the correlators of Hermitian random matrices. The talk is based on a series of joint papers with Marco Bertola and Di Yang (2015-16).



Wednesday, July 13, 14:30 - 16:00, Room 136 of SISSA Main Building

Speaker: Sylvain Carpentier (MIT)

Title: Integrable rational differential operators

Abstract: We will discuss sufficient and necessary conditions for a rational differential operator L=AB^{-1} to generate a Lenard-Magri scheme of integrability. Provided that L can be applied infinitely many times  to a root function, the functions in the hierarchy pairwise commute if and only if L lies in a class
of rational operators that we call integrable. If we assume moreover that L is weakly non-local and preserves a Z/2Z-grading of the algebra of functions, we show that one can always construct an integrable  hierarchy starting from any function in Ker B.

Everybody is welcome.

Boris Dubrovin