本报告将介绍一些关于运动策略演变的偏微分方程模型，具体内容包括单个物种模型，竞争物种模型，以及连续种群模型。我们将通过数学分析和数值模拟，试图回答什么样的空间移动策略是进化稳定的。本报告的大部分内容会适合于研究生和高年级本科生。

It is a survey talk. The aim is to give an introduction to the Kahler-Ricci flow, with emphasis on the surgeries and singularity analysis. The full picture fits into the Analytic Minimal Model Program by Ricci flow which is proposed by Song-Tian.

题目：Blow-up Phenomenon of the Prescribed Q-curvature Flow on 4-manifolds报告人：张宏 副研究员（中国科技大学数学科学学院）时间：2018年10月26日（周五）下午16：00-17:00地点：致远楼101室欢迎广大师生参加

In Riemannian geometry, collapse imposes strong geometric and topological restrictions on the spaces on which it occurs. In the case of Alexandrov spaces, which generalize Riemannian manifolds with a lower sectioanl curvature bound, collapse is fairly well understood in dimension three. In this talk I will discuss the topology of sufficiently collapsed Alexandrov 3-spaces: when the space is irreducible, it is modeled on one of the eight three-dimensional dimensional Thurston geometries, excluding the hyperbolic one. This extends a result of Shioya and Yamaguchi,

Field data are an important source of reliability information for many commercial products. Because field data are often collected by the maintenance department, information on failed and returned units is well maintained. Nevertheless, information on unreturned units is generally unavailable. The unavailability leads to truncation in the lifetime data. This study proposes a data augmentation algorithm for this type of truncated field return data with returned failures available only. The algorithm is based on an idea to reveal the hidden unobserved lifetimes. Theoretical justifications of the procedure for augmenting the hidden unobserved are given. On the other hand, the algorithm is iterative in nature. Asymptotic properties of the estimators from the iterations are investigated.

In this talk, we will talk about the classification of rational vertex operator algebras. First, we will talk about the background and motivations of our results. Then we will talk about some basic results in the theory of vertex operator algebras. Finally, we will about about the classification of extensions of some important vertex operator algebras.

For the time-fractional phase field models, the corresponding energy dissipation law has not been well studied on both the continuous level and the discrete level. In this talk, we shall address these open issues. More precisely, we prove that the time-fractional phase field models indeed admit an energy dissipation law of an integral type. In the discrete level, we propose a class of finite difference schemes that can inherit the theoretical energy stability. Our discussion covers the time-fractional gradient systems, including the time-fractional Allen-Cahn equation, the time-fractional Cahn-Hilliard equation, and the time-fractional molecular beam epitaxy models. Moreover, a numerical study of the coarsening rate of random initial states depending on the fractional parameter $/alpha$ reveals that there are several coarsening stages for all the three models, while there exist a $-/alpha/3$ power law coarsening stage for both

The Dynkin Diagram and the Stiefel Diagram are ”visualizations” of Lie groups (or their root systems) which are very familiar to geometers and topologists. We propose an ”enhanced” Coxeter Plane as a third visualization. This has a purely Lie-theoretic definition, but it arises most naturally from a certain isomonodromic family of meromorphic connections, constructed as a special case of the Toda equations - an integrable system. This is joint work with Nan-Kuo Ho.

In this talk, we first recall the Donaldson- Uhlenbeck-Yau theorem which states that Hermitian-Einstein equation must be solvable on a stable holomorphic vector bundle, and introduce our recent works on the Hermitian-Einstein equation, Bogomolov type inequality and the Hermitian Yang- Mills flow.

we develop a global geometric method to study variations of complex structures over Kahler manifolds. More precisely, by using operators from Hodge theory on a complete Kahler manifold, we obtain closed formulas for holomorphic canonical forms under global variations of complex structures and present several applications including solving the general Belrtami equations and the Kuranishi obstruction equations in deformation theory of complex structures.