Time: Thursday Dec. 6, 10:00-12:00.

Speaker: Dr. Gehao Wang (Peking University).

Title: A Review on Hurwitz Tau-function and Kontsevich-Witten Tau-function

Abstract:
The tau-functions have played an important role in the study of non-commuting symmetries of the KP and KdV hierarchies. One of the known facts is that tau functions of the KP hierarchy are actually elements of the orbit of the vacuum state under a group action, namely the Lie group of the infinite dimensional Lie algebra $gl(\infty)$. In this talk, we will first give a review on two important tau-functions: Hurwitz tau-function, i.e. the exponent of a generating function of single Hurwitz numbers, and Kontsevich-Witten tau-function known as the potential function for Kontsevich integral over spaces of Hermitian matrices. Then we will investigate possible relations between them via the Lie group action.

Venue: Room 09 at Quan-Zhai (全斋), Beijing International Center for Mathematical Research, Peking University.