The i-quantum groups are certain quantum algebras arising from the study of quantum symmetric pairs. They are defined by generators and relations and are embedded as coideal subalgebras of the quantum linear groups. Moreover, the restriction of the famous quantum Schur-Weyl duality pair for quantum linear groups and Hecke algebras of type A gives a duality pair for an i-quantum group and the Hecke algebras of type B. This new duality was discovered by H. Bao and W. Wang. Moreover, Bao, Kujawa, Li and Wang developed a geometric setting of the duality, including some fundamental multiplication formulas and the modified i-quantum group. In this talk, I report a new realization for the i-quantum group $U^j(n)$ and it’s applications to representations of finite orthogonal groups. This is joint work with Yadi Wu.

研究生和大学生的差别是什么？研究生应具备怎样的素质？从大学生到研究生的过程就是从学习到研究、从集体到个体的过程。当一名研究生，要做好充分的准备，要有良好的心态。报告人根据自己三十多年来指导研究生的经验，结合个人成长经历，谈谈研究生阶段应该重视的方面，对研究生的成长提出建议。

We propose a flow to study the Chern-Yamabe problem and discuss the long time existence of the flow. In the balanced case we show that the Chern-Yamabe problem is the Euler-Lagrange equation of some functional. The monotonicity of the functional along the flow is derived. We also show that the functional is not bounded from below.

代数簇是代数几何的主要研究对象。双有理代数几何是代数几何的经典分支之一。光滑代数簇有很多好的性质，但有奇点的代数簇在双有理代数几何中自然出现。本次报告将介绍双有理代数几何关于奇点的基本问题，以及近期与Caucher Birkar在这方面的部分进展。

A formula of dimensions for the spaces of generalized theta functions on moduli spaces of parabolic bundles on a curve of genus g , the so called Verlinde formula, was predicted by Rational Conformal Field Theories. The proof of Verlinde formula by identifying the spaces of generalized theta functions with the spaces of conformal blocks from physics was given in last century mainly by Beauville and Faltings (so called infinite dimensional proof). Under various conditions, many mathematicians tried to give proofs of Verlinde formula without using of conformal blocks, which are called finite dimensional proofs by Beauville. In this talk, we give unconditionally a purely algebro-geometric proof of Verlinde formula.

Block-wise missing data are becoming increasingly common in highdimensional biomedical, social, psychological, and environmental studies. As a result, we need efficient dimension-reduction methods for extracting important information for predictions under such data. Existing dimension-reduction methods and feature combinations are ineffective for handling block-wise missing data. We propose a factor-model imputation approach that targets block-wise missing data, and use an imputed factor regression for the dimension reduction and prediction. Specically, we first perform screening to identify the important features. Then, we impute these features based on the factor model, and build a factor regression model to predict the response variable based on the imputed features. The proposed method utilizes the essential information from all observed data as a result of the factor structure of the model. Furthermore,

In this talk, two geometric variational problems, so-called partitioning problems for bounded domains will be discussed. Type-I is on area minimizing hypersurfaces with volume constraint and Type-II is on area minimizing ones with wetting area constraint. The stationary points for Type-I are free boundary CMC hypersurfaces while the ones for Type-II are minimal hypersurfaces with constant contact angle. When the bounded domain is a Euclidean ball, the global minimizers have been classified in 1970's. We will talk about the classification of the local minimizers for these problems. Moreover, we give Morse index estimate for such variational problems.

We use the deformation methods to obtain the strictly log concavity of solution of a class Hessian equation in bounded convex domain in R^3, as an application we get the Brunn–Minkowski inequality for the Hessian eigenvalue and characterize the equality case in bounded strictly convex domain in R^3.