Colloquium| Institute of Mathematical Sciences
Time：Thursday, Apirl 22nd, 2021, 14:00-15:00
Location：R408, IMS
Speaker: Prof. Xiaobo Liu, Peking University
Abstract: Generating functions of intersection numbers of certain tautological classes on moduli spaces of stable curves provide geometric solutions to integrable systems. Notable examples are the Kontsevich-Witten tau function and Brezin-Gross-Witten tau function. Both of them are tau-functions of the KdV hierarchy. Recently Mironov-Morozov and Alexandrov conjectured that these tau functions can be represented as linear combinations of Schur's Q-polynomial with simple coefficients. In this talk I will describe proofs of these conjectures and a similar conjecture for generalized BGW tau functions. This is a joint work with Chenglang Yang.