Colloquium

Schur Q-polynomials and intersection numbers on moduli spaces of curves

  • Speaker: Xiaobo Liu (Peking University)

  • Time: Dec 9, 2022, 16:30-17:30

  • Location: Tencent Meeting ID 492-509-938

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. Using matrix models, Mironov-Morozov gave a formula expressing Kontsevich-Witten tau function as an expansion of Schur's Q-polynomial with simple coefficients. This formula was called Mironov-Morozov conjecture by Alexandrov. A similar formula was also conjectured by Alexandrov for Brezin-Gross-Witten tau function. In this talk I will describe two proofs of these formulas using Virasoro constraints and cut-and-join operators. The talk is based on joint works with Chenglang Yang.