Title: Differential equations and quantum groups
Speaker: Valerio Toledano Laredo (Northeastern University)
Abstract: Quantum groups were introduced in the mid-eighties by Drinfeld and Jimbo as the algebraic backbone of the Quantum Inverse Scattering Method of Statistical Mechanics. They were soon found to have a host of other applications: to low-dimensional topology, representation theory, and algebraic geometry to name a few.
This talk will concentrate on one aspect of quantum groups, namely their uncanny ability to describe the monodromy of integrable systems of partial differential equations attached to semisimple Lie algebras.
This phenomenon was originally discovered by Drinfeld and Kohno in the early 90s in connection with the Knizhnik-Zamolodchikov equations of Conformal Field Theory. More recently, I proved that quantum groups also describe the monodromy of the so-called Casimir equations of a semisimple Lie algebra g and, in recent joint work with Andrea Appel (USC) that this continues to hold for any symmetrisable Kac-Moody algebra g.
Colloquium URL: https://web.math.osu.edu/colloquium/
