Speaker: 郑涛（北京理工大学）

Time: 14:00-15:00, Dec.11  2024

Venue: 数学中心研讨室（至善楼602）

Online: Zoom: 811 5638 1768（Password: msrc）

Title: Fully Nonlinear Equations on Almost Hermitian Manifolds

Abstract:

In this talk, we will introduce some preliminaries of almost complex geometry. Then we will discuss some fully nonlinear equations on almost Hermitian manifolds, including continuity equations and geometric flows of almost Hermitian metrics, and some extensions on Sasakian manifolds.

Cirriculum Vitae:

郑涛，北京理工大学数学与统计学院助理教授，研究方向是复流形上的蒙日-安培方程，研究成果发表在Adv. Math.、J. Funct. Anal.、IMRN等学术杂志上，主持国家自然科学基金委青年基金和面上项目。

Speaker: 程亮（华中师范大学）

Time: 14:30-16:30, Dec.15  2024

Venue: 数学中心研讨室（至善楼602）

Online: Zoom: 811 5638 1768（Password: msrc）

Title: Isoperimetric, logarithmic Sobolev inequalities and  scalar curvature rigidity

Abstract:

The rigidity properties regarding lower scalar curvature bounds are one of important topics in the study of differential geometry. Most of rigidity theorems regarding scalar curvature were obtained by two methods - minimal hypersurfaces and Dirac operators. We will talk about our recent work about scalar curvature rigidity theorems regarding isoperimetric profile, logarithmic Sobolev inequality and Perelman's \mu-functional by using different methods.