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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Gibbons' conjecture and Liouville theorem for master equations
主方程 Gibbons猜想 Liouville定理
2023/11/29
In this talk, we will discuss some of our recent work on the master equation involving the fully fractional heat operator. Specifically, we will present two main results. The first one pertains to a g...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Introduction to Allard’s regularity theorem（II）
阿拉德 正则性定理 导论
2023/5/17
We continue to discuss the proof of the Allard regularity theorem. In the second presentation, we will focus on the harmonic approximation and the iteration argument for getting the decay of the tilt-...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Introduction to Allard’s regularity theorem（I）
阿拉德 正则性 定理 导论
2023/5/10
In this short seminar, we will discuss the proof of the Allard regularity theorem, which is an $\epsilon$-regularity theorem for the mean curvature equation in the Geometric Measure Theory(GMT) settin...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Borel—Wei—Bott theorem for Derived Flag Schemes
派生 标志方案 博雷尔-魏-博特定理
2023/4/13
The framework of derived algebraic geometry (DAG), developed by Toen-Vezzosi, Lurie and many others, allows us to extend Grothendieck’s theory of flag schemes of sheaves to the cases of complexes. In ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Berndtsson’s proof of the Bourgain-Milman theorem
伯恩松 布尔根-米尔曼定理 证明
2023/4/28
I will give a report on the Bourgain-Milman theorem. Berndtsson used complex methods to give a proof. I’ll talk about his papers. However, the best constant for the Bourgain-Milman theorem is still un...
A simple proof of Sarkozy's theorem
Sarkozy's theorem Number Theory Classical Analysis and ODEs
2011/8/23
Abstract: It is a striking and elegant fact (proved independently by Furstenberg and Sarkozy) that in any subset of the natural numbers of positive upper density there necessarily exist two distinct e...
Extending Landau's Theorem on Dirichlet Series with Non-Negative Coefficients
Extending Landau's Theorem Non-Negative Coefficients
2010/11/26
A classical theorem of Landau states that, if an ordinary Dirichlet series has non-negative coefficients, then it has a singularity on the real line at its abscissae of absolute convergence.