Clustering of extremes usually has a large societal impact. The extremal index, a number in the unit interval, is a key parameter in modelling the clustering of extremes. We build a connection between the extremal index and the stable tail dependence function, which enables us to compute the value of extremal indices for some time series models. We also construct a nonparametric estimator of the extremal index and an estimation procedure to verify D(d)(un) condition, a local dependence condition often assumed when studying extremal index. We prove that the estimators are asymptotically normal.

We study the regularity of the Gromov-Hausdorff limits of Riemannian manifolds with bounded Bakry-Emery Ricci curvature, which include the Ricci soliton and bounded Ricci curvature cases. Our main results are the generalizations of the works of Cheeger-Colding-Tian-Naber when the manifolds are volume noncollapsed. The new ingredients here are a Bishop-Gromov type relative volume comparison theorem on the original manifold without involving weight, and proving that the C/α harmonic radius can be bounded from below, which has relaxed Anderson's result. Our proof of the Codimension 4 Theorem essentially follows the guideline of Cheeger-Naber, but we managed to shorten the proof by using Green's function and a linear algebra argument of R. Bamler. These are joint works with Qi S. Zhang.

In this talk, I will present some recent results on the compactness of the solutions to the Yamabe problem on manifolds with boundary. The compactness of Yamabe problem was introduced by Schoen in 1988. There have been a lot of works on this topic later on. This is a joint work with Sergio Almaraz and Olivaine Queiroz.

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.