活动地点：CMS 202

活动类型：学术报告

主讲人：杨迪 教授

活动时间：2024-07-09 16:00:00--2024-07-09 17:00:00

活动内容：

杨迪教授专题学术报告 

 

报告题目：Mapping Partition Functions and the Mapping Universality Conjecture

报告人：杨迪  教授（中国科学技术大学）

时间：2024年7月9日（周二）下午4:00

地点：数学中心202教室

Abstract：Let G be the infinite group of formal power series of one variable near the identity with group law given by composition. We introduce the G-action on partition functions of Witten--Kontsevich (WK) type. In particular, each element of G sends the WK partition function to a new partition function, which we call the WK mapping partition function. We show that the genus zero part of its logarithm is independent of elements of G, and derive the loop equation for its higher genus parts. We then show that the Dubrovin--Zhang hierarchy for the WK mapping partition function is a bihamiltonian perturbation of the Riemann--Hopf hierarchy possessing a tau-structure, and conjecture that it is a universal object for all such perturbations.