Open Hurwitz numbers and the mKP hierarchy

YMSC Topology Seminar

Organizers：

陈伟彦、高鸿灏、黄意、林剑锋、邱宇、孙巍峰

Speaker：

Alexandr Buryak (HSE University)

Time：

Fri., 15:30-16:30, Feb. 27, 2026

Venue：

C654, Shuangqing Complex Building A

Zoom meeting ID: 405 416 0815, PW: 111111

Title：

Open Hurwitz numbers and the mKP hierarchy

Abstract:

We give a natural definition of open Hurwitz numbers, where the weight of each ramified covering includes an integer parameter N taken to the power that is equal to the number of boundary components of a Riemann surface with boundary mapping to the complex projective line. We prove that the resulting sequence of partition functions, depending on N, is a tau-sequence of the mKP hierarchy, or in other words it is a sequence of tau-functions of the KP hierarchy where each tau-function is obtained from the previous one by a Backlund-Darboux transformation. Our result is motivated by a previous observation of Alexandrov and the first two authors that the refined intersection numbers on the moduli spaces of Riemann surfaces with boundary give a tau-sequence of the mKP hierarchy.