Matrix Integral, Hodge Integral, and Integrable systems
报告题目(Title)：Matrix Integral, Hodge Integral, and Integrable systems
报告人(Speaker)：刘思齐 教授（清华大学）
地点(Place)：腾讯会议ID: 453 850 0147
时间(Time)：2021年7月7日(周三)，16:00-17:00
邀请人(Inviter)：王灯山
报告摘要
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.
主讲人简介
刘思齐，清华大学数学科学系的教授，国家优秀青年科学基金和国家杰出青年科学基金获得者，主要研究可积的演化偏微分方程在各种坐标变换作用下的分类，以及相应的分类定理对诸如Gromov-Witten不变量理论、奇点理论等数学物理中其它领域的应用。
