**Speaker**：Xiaomeng Xu

**Abstract**:

In this report, we will first give a brief introduction to the multivalued solutions of a class of differential equations with singularities and the Gelfand Zeitlin type canonical basis in representation theory. Then we will discuss how to use the asymptotic analysis of the solutions of this kind of equations to naturally get the above canonical basis and cactus group effect on it, so we will give the analysis and explanation of some discrete problems in representation theory. Our workrelieson the compactness of a class of well-knownnonlinear partial differential equations, and more understanding of such equations will produce important applications in representation theory and field theory.

**Time: ****December 27th 11:00**

**Venue：****Lecture Hall,1th Floor, School of Mathematics and Statistics**

**Speaker Introduction:**

Xiaomeng Xu is an assistant professor in Peking University. He graduated from Henan University in 2010, received his master's degree from Peking University in 2013, a doctor's degree from the University of Geneva in 2016, and a postdoctoral degree from MIT in 2016-2019. His main research fields are representation theory, symplectic geometry, singularity theory and its application in mathematical physics. He has published many papers in Comm. Math. Phys, Int. Math. Res. Not .