In this talk, we will present two formulas on scalar curvatures of canonical Hermitian connections on an almost Hermitian manifold. Then we will show some inequalities of various total scalar curvatures and some characterization results. Finally, we will talk about some applications. This is a joint work with Jixiang Fu.

In this talk, we will introduce some topics on mean curvature flow (MCF) and minimal submanifolds about their relationship and interreaction, including the rigidity on the second fundamental form, Bernstein type theorem for entire graphs, and applications of MCF on minimal submanifolds.

题目：The Maximum Principle报告人：徐兴旺 教授（南京大学）地点：致远楼101室时间：2019年10月24日15：00-16:00欢迎广大师生参加

imbo Michio教授曾任京都大学，东京大学教授，现任立教大学特任教授，京都大学，东京大学名誉教授。

The (classical) Minkowski problem asked for sufficient and necessary conditions such that a finite Borel measure on the sphere is the surface area measure of a convex body. Its solution, based on works by Minkowski, Aleksandrov and Fenchel & Jessen, is one of the centerpieces of the classical Brunn-Minkowski theory. There are two far-reaching extensions of the classical Brunn-Minkowski theory, the Lp-Brunn-Minkowski theory and the dual Brunn-Minkowskitheory. In the talk we will discuss the analog of the (classical) Minkowski problem within the dual Brunn-Minkowski theory

This paper develops an asymptotic theory of nonlinear least squares estimation by establishing a new framework that can be easily applied to various nonlinear regression models with heteroscedasticity. This paper explores an application of the framework to nonlinear regression models with nonstationarity and heteroscedasticity. In addition to these main results, this paper provides a maximum inequality for a class of martingales and establishes some new results on convergence to a local time and convergence to a mixture of normal distributions.

In this report, we first introduce some backgrounds of delay differential equations and then consider the Galerkin method to solve the vanishing delay differential equations under uniform and quasi-graded mesh. The global convergence and local superconvergence results are obtained. Based on the local superconvergence results, several postprocessing techniques to accelerate the global convergence are proposed. State dependent delay differential equations are also considered. Theoretical expectations are confirmed by numerical experiments.

We consider the logarithmic Minkowski inequality which is equivalent to several problems in convex geometric analysis and is still an open problem in dimension greater than 2. Among the problems equivalent to the logarithmic Minkowski inequality is the uniqueness of solutions to the logarithmic Minkowski problem. We present yet a new connection to a uniqueness of a Minkowski problem, namely if a given centro-affine Minkowski problem has unique solution (up to special linear group of transformations), then the corresponding logarithmic Minkowski inequality holds.