EVENT DETAILS AND ABSTRACT

Title: Virasoro constraints in Drinfeld-Sokolov hierarchies
Speaker: Pavel Safronov
Speaker Info: UT Austin
Brief Description:
Special Note:
Abstract:

A conjecture of Witten proved by Kontsevich states that the generating function of intersection numbers on the moduli spaces of curves satisfies equations of the Korteweg-de Vries hierarchy together with certain conditions known as the Virasoro constraints. I will discuss these constraints in a more general setting of Drinfeld-Sokolov hierarchies, which are certain flows on the moduli space of principal bundles with a reduction at a point. The Virasoro constraints are then naturally interpreted in terms of a connection compatible with the reduction at the marked point. Pretalk is to introduce main characters of the actual talk, such as moduli of bundles, Drinfeld-Sokolov hierarchy, and Krichever's construction if time permits.