Speaker: Sachin Gautam
Title: Monodromy problems in representation theory
Abstract: Quantum groups are certain Hopf algebras introduced in the eighties by Drinfeld and Jimbo. Among other things, Drinfeld (and Kohno) proved that the quantum groups are natural receptacles for the monodromy of certain first order PDE's, called Knizhnik-Zamolodchikov equations. In this talk, I will introduce the analytic and algebraic characters of this story and go over the statement of the Kohno-Drinfeld theorem. I will also explain a few variants of this theorem, some of them still conjectural, which hint at interesting connections between representation theory and the problem of computing monodromy.
Note: This is part of the Invitations to Mathematics lecture series given each year in Autumn and Spring semesters. Pre-candidacy students can sign up for this lecture series by registering for one or two credit hours of Math 6193, class #16988 (with Prof H. Moscovici).
