题目: On the uniform large genus asymptotics for Brezin-Gross-Witten numbers and Witten's intersection numbers

报告人: 杨迪教授（中国科学技术大学）

时间: 2025年11月7日, 上午10:00-11:00

地点: 理科楼 A304

摘要: Brezin-Gross-Witten numbers and Witten's intersection numbers are two families of rational numbers, which have physical origins and topological meanings. Their partition functions are particular tau-functions of the KdV hierarchy, satisfying an infinite set of linear constraints called Virasoro constraints. In this seminar, we study arithmetic and combinatorial properties for these numbers (monotonicity, integrality, rational functions, and etc., several of which are still conjectural), and in particular give their uniform large genus asymptotics. Applications to particular solutions of the Painleve II hierarchy and of the Painleve I equation are given. The talk is based on joint works with Jindong Guo, Paul Norbury and Don Zagier.