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.

题目：An Introduction to Stability of Traveling Wave Solutions in Free Interface Problems报告人：Claude-Michel Brauner (Tongji and Bordeaux (France) Univ.)地点：致远楼108室时间：2020-11-19, 12-03, 12-17（星期四）上午8：00—10：00In this round of talks, we intend to discuss a method especially suitable for the analysis of stability of traveling waves in free interface problems. For convenience, ...

We will talk about Minkowski type inquality, weighted Alexandrov-Fenchel inequality for the mean convex star-shaped hypersurfaces in Reissner-Nordstrom-anti-deSitter manifold and Penrose type inequality for asymptotically locally hyperbolic manifolds in which can be realized as graphs over Reissner-Nordstrom-anti-deSitter manifold.

由一列球或矩形确定的上极限集是丢番图逼近中两类基本的集合, 一个源自于Dirichlet定理另一个源自于Minkowski定理. 由球确定的上极限集的度量理论已经非常丰富/完备, 然而由矩形确定的上极限集的研究却非常滞后, 甚至一些基本问题都尚未完全解决. 在此报告中, 通过引入“矩形的无处不在性/满测性”, 我们确定了由矩形生成的上极限集的Hausdorff理论的一般原理.