Program
Geometric Analysis Seminar
Student No.:50
Time:15:20-16:30, Dec.14-Jun.3
Instructor:Xu Guoyi, Zhang Yingying  
Place:Conference Room 1, Jin Chun Yuan West Bldg.
Starting Date:2018-12-14
Ending Date:2019-1-3

2018-12-14, 15:20-16:20

Speaker: Lihan Wang

Place: Conference Room 1, Jin Chun Yuan West Bldg.

Title: Symplectic Laplacians, boundary conditions and cohomology

Abstract:
Symplectic Laplacians are introduced by Tseng and Yau in 2012, which are related to a system of supersymmetric equations from physics. These Laplacians behave different from usual ones in Rimannian case and Complex case. They contain both 2nd and 4th order operators. In this talk, we will discuss these operators and their relations with cohomologies on compact symplectic manifolds with boundary. For this purpose, we will introduce new boundary conditions for differential forms on symplectic manifolds. Their properties and importance will be discussed.


2018-12-27, 15:30-16:30

Speaker: 孙奥 Sun Ao

Place: Conference Room 3, Jin Chun Yuan West Bldg.

Title: Some Properties of Mean Curvature Flow

Abstract:
Mean Curvature Flow is a geometric heat flow evolves to minimize the area of the submanifold. In this talk, I will discuss some properties of the mean curvature flow and I will focus on the differential geometric approach to the study of mean curvature flow.


2018-12-28, 15:30-16:30

Speaker: 孙奥 Sun Ao

Place: Conference Room 1, Jin Chun Yuan West Bldg.

Title: Singularities of Mean Curvature Flow

Abstract:
The major problem of the study of the mean curvature flow is to understand the singularities. There are several models of the singularities, and the most important model is the self-shrinkers. The self-shrinkers are homothetic shrinking solutions of mean curvature flow. They are also the minimal submanifolds of the Gaussian space, so one of the approaches to study self-shrinker is using the techniques in minimal surface theory. In this talk, I will discuss some recent progress on the research of self-shrinkers. In particular, I will discuss the structure theory of self-shrinkers in R^3.


2019-1-3, 15:30-16:30

Speaker: 孙奥 Sun Ao

Place: Conference Room 3, Jin Chun Yuan West Bldg.

Title: Entropy and Generic Singularities of Mean Curvature Flow

Abstract:
In the significant paper "Generic mean curvature flow I; generic singularities", Colding and Minicozzi used entropy to study the singularities of the mean curvature flow and obtained many interesting and important results. In particular, they introduced the notion of entropy stability of the singularities, and it plays an important role in the dynamics of mean curvature flow. In this talk, I will discuss their ideas. Moreover, I will show how to use their idea to study a generic case of the multiplicity one conjecture of mean curvature flow.