In this talk, we discuss the generalization of Lappan's theorem to higher dimensional complex projective space.

I plan to review the connection between central extension of sln(A) coordinated by a unital associative algebra A and the cyclic homology of A due to Kassel and Loday. Then, I am going to present its generalization in unitary Lie algebras obtained by Y. Gao and its further generalizations in Lie superalgebra cases, including the H. Chen and J. Sun’s work on slm|n(A) and my joint work with Z. Chang on ortho-symplectic, periplectic and queer Lie superalgebras.

众所周知存在从ADE型Hecke代数到对应类型的Temperley-Lieb代数的自然满同态。我们发现从非ADE型Hecke代数也具有到某些类型的Temperley-Lieb代数的有趣的同态。利用这种同态能够恰好“实现”出二面体型Hecke代数的所有二维不可约表示。在这些同态的构造过程中意外遇见了切比雪夫多项式。

众所周知存在从ADE型Hecke代数到对应类型的Temperley-Lieb代数的自然满同态。我们发现从非ADE型Hecke代数也具有到某些类型的Temperley-Lieb代数的有趣的同态。利用这种同态能够恰好“实现”出二面体型Hecke代数的所有二维不可约表示。在这些同态的构造过程中意外遇见了切比雪夫多项式。

Let M be a compact smooth oriented manifold. The set of isotopy classes of orientation-preserving self-diffeomorphism of M is a group through composition of maps, which is called the mapping class group of M. In this talk, we mainly concern with the mapping class groups of high dimensional manifolds. This talk divides into three parts. In the first part, we will recall some basic definitions and propositions of mapping class groups of high dimensional manifolds. In the second part, we will discuss the calculations of the mapping class groups of standard spheres, exotic spheres and product of spheres. In the third part, we will say something about the mapping class groups of HP2-like manifolds. This work is joint with Yang Su.

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.