Title：Hurwitz numbers and the cut-and-join equation

Speaker：Zhang, Hanxiong （中国矿业大学）

Time：2019年3月21日       上午  10:00-11:30

Room：东区管理科研楼   0029cc金沙贵宾会1418室

Abstract：Hurwitz numbers are classical objects in enumerative geometry. In this introductory talk, I will review the geometric and algebraic definitions of Hurwitz numbers, and explain why these two definitions are equivalent. Then I will  introduce the generating function of Hurwitz numbers using symmetric functions, which turns out to be a solution of the cut-and-join equation. Its link with integrable hierarchies via Boson-Fermion correspondence will also be gently addressed.