Differential Geometry seminar

Organizer:Xiaokui Yang, Yingying Zhang
Time: 2021-11-1 ~
Venue:Zoom Online


Upcoming Talks:

Speaker: Pak-Yeung Chan (UCSD)

Abstract: Ricci soliton arises naturally in the singularity analysis of the Ricci flow. Steady Ricci soliton is closely related to the Type II limit solution to the Ricci flow. There are two generic curvature decays for complete noncompact steady gradient Ricci soliton, namely linear and exponential decays. It is unclear if these are the only two possible decays. We show that this dichotomy holds for four dimensional complete noncompact non Ricci flat steady gradient Ricci soliton with at least linear curvature decay and proper potential function. A similar dichotomy is also shown in higher dimensions under the additional assumption that the Ricci curvature is nonnegative near infinity. As an application, we prove some classification results on steady soliton with fast curvature decay and obtain a dichotomy on the asymptotic geometry at spatial infinity. This talk is based on a joint work with Bo Zhu.
Location: Online (Zoom)


Past Talks

Zuoqin Wang (USTC)

Title: Abstract: Given a $G$-invariant elliptic pseudodifferential operator on a compact Riemannian $G$-manifold $M$, we study its equivariant spectral invariants. I will explain the role of symplectic geometry in studying the $G$-equivariant spectrum. In particular, I will show how to apply symplectic techniques to study equivariant inverse spectral problems for $G$-invariant Schrodinger operators, the main tool being a generalized Legendre transform in the abelian case, and a generalized Legendre relation in the nonabelian case. This is based on joint works with V. Guillemin (MIT).

Time: 12/16/2012, Thursday, 10:00-11:00amLocation: Online (Tencent meeting)Meeting ID: 531-442-663腾讯会议链接: https://meeting.tencent.com/dm/ATZbbgViVT47

Speaker: Title: Brief Introduction to Genera and Applications.

Abstract: The cobordism invariants, genera, play fundamental roles in manifold topology. Some specific genera, like A-hat genus, L-genus, Witten genus and elliptic genus are the topological pillars of the Atiyah-Singer index theory, spin geometry and string geometry. In this minicourse, we will give a brief introduction to genera starting from very basic knowledge and introduce some applications of genera in physics in particular anomaly cancellation problem, and in geometry concerning group actions and curvatures.

Location: Online Meeting ID: 607-3894-1091

Xin Zhou (Cornell University)

Time: Dec 7 Tuesday, 10:00-11:00am (Beijing Time)



password: 858040

Speaker: Title: Minimal graphs and related flows in warped product manifolds.

Abstract: In this talk we report our series of results on minimal graphs and related problems in warped product (WP) manifolds. Our motivation is to view WP manifolds as canonical manifolds in the certain sense. Then we introduce our results on minimal graphs, mean curvature flows, inverse mean curvature flows and two types of area minimizing problems in some WP manifolds. This includes of some recent works joint with Gao, Qiang.

Time: Dec 2, Thursday, 10:00-11:00amLocation: Online (Tencent meeting)Meeting ID: 156 932 865腾讯会议链接:https://meeting.tencent.com/dm/l5dKmDmCYF2H


Time: Dec 1st, Wednesday, 15:30-16:30

Location: Online (Tencent meeting)Meeting ID: 731 188 239腾讯会议链接:https://meeting.tencent.com/dm/iY2sUcxC2kNh<p font-size:16px;font-variant-numeric:normal;font-variant-east-asian:normal;line-height:30px;padding:0px;text-align:justify;white-space:normal;"="" style="margin-top: 0px; margin-bottom: 0px; padding: 0px; text-align: justify; line-height: 30px;">

题目: 微分几何中的几类几何流

报告人: 李逸 教授(东南大学)

腾讯会议号: 272 360 965

时间: 2021-11-20 14:00-15:00

Abstract: 本报告主要讨论产生于微分几何和广义相对论中的几类几何流的分析和几何性质。


题目:The Hirzebruch genera, symmetric functions and multiple zeta values

报告人: 李平 教授(同济大学)

腾讯会议号: 272 360 965

时间: 2021-11-20 15:30-16:30


Title: The convergence and rigidity of mean curvature flow in arbitrary codimension  

Speaker: Prof.  Entao Zhao (Zhejiang University)  

Tencent Meeting ID:  168 504 661  

Time: 2021-11-06, 14:00-15:00  

Abstract: In this talk, I will first review the rigidity and sphere theorems for submanifolds, which are motivations of our research on mean curvature flow. Then I will discuss some convergence results for mean curvature flow of arbitrary codimension. At last, I will talk about our recent results on the rigidity of ancient mean curvature flow under curvature pinching conditions.

This talk is based on the joint works with Prof. Kefeng Liu, Prof. Hongwei Xu and Dr. Li Lei.

Title:Poincare inequality on area-minimizing hypersurfaces  

Speaker: Prof. Qi Ding (Fudan University)  

Tencent Meeting ID:   168 504 661  

Time:  2021-11-06, 15:30-16:30  

Abstract: In this talk, I will talk about Neumann-Poincare inequality on area-minimizing hypersurfaces in Euclidean space and manifolds of almost nonnegative Ricci curvature.