Seminars on Gromov-Witten Theory
Spring Quarter 2011
Fridays 4:10 - 6:00
Organizer: Motohico Mulase
This term we meet on Fridays 4:10 to 6:00.
Professor Kanehisa Takasaki of Kyoto University will be visiting Davis during the week of March 28. He will give us several lectures, including introductory talks on integrable systems and Sato Grassmannians. His schedule will be announced on this page.
April 1. Professor Kanehisa Takasaki (Kyoto University): "Generalized string equations for Hurwitz numbers."
Generating functions of almost-simple and double Hurwitz numbers for the Riemann sphere are known to become special tau functions of the KP and Toda hierarchies. This talk presents recent results on the generating function of duble Hurwitz numbers. Generalized string equations for the Lax and Orlov--Schulman operators are derived. These equations turn out to have a meaningful classical limit in the dispersionless Toda hierarchy. Solving these equations reveals a relation with Lambert's W-function. This seems to show another approach to various roles of the W-function in Hurwitz numbers.