中科院数学与系统科学研究院
数学研究所
几何分析研讨班
报告人：朱超娜 博士 (中科院数学所)
题 目：Improved Moser-Trudinger-Onofri inequality under constraints
时 间：2021.02.01（星期一）, 09:00-11:00
地 点：腾讯会议ID 348 6898 7444
摘 要：We will talk about the recent work of A. Chang and Hang about Moser-Trudinger-Onofri inequality. In this work, they proved some refinements of concentration compactness principle for Sobolev space W^{1,2} on a smooth compact Riemannian surface, which are crucial in showing their main theorem that extending Aubin’s classical theorem on S^2 for functions with zero first order moments of the area element to higher order moments cases.
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报告人： 周 杰 博士 (清华大学)
题 目：Topological structure of varifold and its quantitative stability
时 间：2021.02.02（星期二）, 09:00-11:00
地 点：腾讯会议ID 348 6898 7444
摘 要：Varifolds with generalized mean curvature can be regarded as weak conception of manifolds in the category of measure theory. In this talk, we care about two questions.
1.(Regularity) Under what kind of curvature condition, a varifold admit a topological manifold structure?
2. (Stability) Is a varifold close to (in the sense of Radon measure convergence) a manifold homeomorphic to the manifold?
We will give a quantitative result under a critical curvature condition, which is related to a generalized Li-Yau inequality for the Willmore Energy.
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报告人：侯松波 副教授 (中国农业大学)
题 目：Existence of solutions to Chern -Simons-Higgs equations on graphs
时 间：2021.02.03（星期三）, 09:00-11:00
地 点：腾讯会议ID 348 6898 7444
摘 要：In this talk, we discuss the existence of solutions to a generalized Chern-Simons-Higgs equations on graphs. We also discuss the existence of solutions to the Chern-Simons-Higgs equation, which completes the results of An Huang, Yong Lin and Shing-Tung Yau (Commun. Math. Phys. 377, 613-621 (2020)).
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报告人： 桂耀挺 博士 (中国科学技术大学)
题 目：Positive mass theorem for a spin manifold and its generalization on a singular space
时 间：2021.02.04（星期四）, 09:00-11:00
地 点：腾讯会议ID 348 6898 7444
摘 要：In this talk, we shall prove the positive mass theorem for a spin manifold which is locally conformal flat. The proof contains a construction of test spinor and a simplification of Witten’s original argument. We shall also discuss some generalizations of this result to singular paces with co-dimension two singularities.
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报告人：毕宇晨 博士 (中科院数学所)
题 目：Convergence of the mean field equation in even dimension
时 间：2021.02.05（星期五）, 09:00-11:00
地 点：腾讯会议ID 348 6898 7444
摘 要：In this talk, I will introduce our recent results about the mean field equation. Under some geometric conditions, we show the convergence of the solution for arbitrary initial energy. For the sake of simplicity，I will focus on the two dimensional flat tours case.
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