2020年拓扑学系列学术报告

报告人：杜晓明 副教授（华南理工大学）

时间：2020年10月11日 18：00-19:00

地点：https://meeting.tencent.com/s/bmW8KMI7mZHc

会议 ID：867 915 607

题目：辨认曲面形状的工具：Teichmuller 空间

摘要：Teichmuller 空间是记录曲面几何结构的重要工具，同时也给出曲面几何结构之间差距的有效衡量方式。我会讲一下：为什么要讨论这些几何结构，引入几何结构之间的距离时会遇到哪些细节问题，如何在技术上克服这些问题。

报告人：杨会军 副教授（河南大学）

时间：2020年10月11日 20:00-21:00

地点：https://meeting.tencent.com/s/bmW8KMI7mZHc

会议 ID：867 915 607

题目：The existence of contact structures on 9-manifolds

摘要：We give necessary and sufficient conditions for

a closed orientable $9$-manifold $M$ to admit an almost contact structure.

The conditions are stated in terms of the Stiefel-Whitney classes of $M$ and

other more subtle homotopy invariants of $M$.

By a fundamental result of Borman, Eliashberg and Murphy,

$M$ admits an almost contact structure if and only if $M$ admits an over-twisted contact structure.

Hence we give necessary and sufficient conditions for $M$ to admit

an over-twisted contact structure and we prove that

if $N$ is another closed $9$-manifold which is homotop

y equivalent to $M$,

then $M$ admits an over-twisted contact structure if and only if $N$ does.

In addition, for $W_{i}(M)$ the $i$th integral Stiefel-Whitney class of $M$,

we prove that if $W_3(M) = 0$ then $W_7(M) = 0$.

This is a joint work with Professor Diarmuid Crowley.

报告人：钟立楠 副教授（华南师范大学）

时间：2020年10月17日 10：00-11:00

地点：https://meeting.tencent.com/s/JXV2GIm6l4WH

会议 ID：214 977 811

题目：Detection of a nontrivial product in the stable homotopy groups of spheres

摘要：To determine the stable homotopy groups of spheres is one of the central problems in homotopy theory. One of the main tools to approach it is the classical Adams spectral sequence. In this talk we discuss some nontrivial products in the stable homotopy groups of spheres.

报告人：陈亮 副教授（东北师范大学）

时间：2020年10月17日 16：00-17:00

地点：https://meeting.tencent.com/s/JXV2GIm6l4WH

会议 ID：214 977 811

题目：Geometry of submanifolds from duality viewpoint

摘要：Singularity and degeneracy destroy the structure of manifolds and give rise to essential difficulties in researching the deteriorative manifolds. Thus, it is crucial to develop new methods for investigating the singular or degenerate submanifolds. By characterizing the inner connection between pseudo spheres in semi-Euclidean space, the Legendrian duality is an effective method developed by the L. Chen and Izumiya in 2009 for studying the submanifolds in non-flat space. Specially, the Legendrian duality is applicable for studying the singular or degenerate submanifolds. In this talk, using the singularity theory of mappings, we investigate the geometrical properties of the (singular or degenerate) submanifolds immersed in non-flat space from the viewpoint of duality.

报告人：孙大为 副教授（河南工业大学）

时间：2020年10月17日 18：00-19:00

地点：https://meeting.tencent.com/s/JXV2GIm6l4WH

会议 ID：214 977 811

题目：Hofer metric on the group of Hamiltonian diffeomorphisms

摘要：In this talk we will introduce some extensions of the Hofer metric on the group of Hamiltonian diffeomorphisms. We show that the extended Hofer metric and the Hofer metric coincides under some conditions, give the constructions of the Hofer type metric on some Poisson manifolds.