活动地点：CMS 201

活动类型：学术报告

主讲人：刘思齐教授

活动时间：2018-04-11 09:00:00--2018-04-11 09:50:00

活动内容：

刘思齐教授专题学术报告

 

 

报告题目：Matrix Integral, Hodge Integral, and Integrable system 

报告人：刘思齐  教授（清华大学数学系）

 

时间：2018年4月11日（周三）上午9:00-9:50

 

地点：数学中心201教室 

Abstract: Matrix integral is a classical topic in mathematics. It is introduced by physicist E. Wigner, and has many interesting applications in physics, probability theory, mathematical statistics, numerical analysis, and number theory. It is revealed by the celebrated Witten conjecture that matrix integral is also the bridge among two-dimensional quantum gravity, the moduli space of stable curves, and the Korteweg-de Vries (KdV) hierarchy. Hodge integrals are the integrals of certain natural cohomological classes on the moduli space of stable curves, which are very important in modern mathematical physics. In our previous work, we showed that the generating function of certain Hodge integrals is related to the GUE matrix model and the Volterra hierarchy. We also conjecture a generalization of this correspondence. Recently, we prove this generalization.