The index $\ind(\F)$ of a fixed point class $\F$ is a classical invariant in Nielsen fixed point theory. In this talk, for graph selfmaps, we introduce a new invariant $\ichr(\F)$ called the improved characteristic, and show that the two homotopy invariants mentioned above are exactly the same. Since the improved characteristic is totally determined by the endomorphism of the fundamental group, we give a group-theoretical approach to compute indices of fixed point classes of graph selfmaps. As consequences, we give some applicaitons on fixed words of endomorphisms of free groups. This is joint work with Zhao Xuezhi.

题目：Learning Multiscale Models Using Nonlocal Upscaling报告人：Prof. Eric Chung （香港中文大学）地点：致远楼101室时间：2021年3月31日 下午2:00--3:00欢迎各位参加

We get optimal lower bounds for the eigenvalues of the submanifold Dirac operator on locally reducible Riemannian manifolds in terms of intrinsic and extrinsic expressions. The limiting-cases are also studied. As a corollary, one gets several known results in this direction.

在本次报告中，我们将讨论一类复Monge-Ampere型偏微分方程及其在复几何中的应用。

Isoperimetric problem is to determine a convex body of maximum volume with fixed surface area and is equivalent to the isoperimetric inequality. The Minkowski problem in differential geometry asked for necessary and sufficient conditions such that a positive smooth function on the sphere is the Gauss curvature of a convex hypersurface.This problem has been solved by Nirenberg, Pogorelov, Cheng-Yau and others. Those two problems are among the most important and closely related problems in mathematics. We will address Minkowskin problems in integral and convex geometry that are inspired by Lutwak-Yang-Zhang.

本报告以罗氏集团这几年在数学与医疗学科交叉的尝试和中国医疗健康的现状、机遇与挑战为切入点，对医疗健康领域中不同尺度的数学问题进行了具体的举例，重点介绍了罗氏集团和牛津大学、苏黎世大学以及同济大学在这些领域的合作模式和拟解决的具体问题，并对未来数学学科与医疗学科的交叉、应用与落地提出了展望。

In this talk, I will discuss the Li-Yau-Hamilton estimates for the heat equation and nonlinear parabolic equations. Moreover, I will talk about some applications.

教师：Dr. Sanae Rujivan (Walailak University)课程时间 The first course takes in Dec. 28, 2020, following by 7 courses (Jan 13, 15, 18, 21, 22, 25, 26，2021，every time 1 hour from 14:00),课程目的 introducing one class of continuous-time stochastic processes known as Ito processes widely used in quantitative finance to describe stock price dynamics. Furthermore, this course introduces two import...