报告人：杨迪 教授（中国科学技术大学）

时间：2026年01月30日 10:00-

腾讯会议ID：748 823 951

摘要：Br\'ezin--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 conjectural), and in particular give their uniform large genus asymptotics. Applications to particular solutions of the Painlev\'e II hierarchy and of the Painlev\'e I equation are given. The talk is based on joint works with Jindong Guo, Paul Norbury and Don Zagier.

邀请人：杨依灵

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