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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On a Bogomolov type vanishing theorem
Bogomolov型 消失定理 代数几何
2023/11/29
The Bogomolv theorem holds great importance in algebraic geometry, particularly in the field of birational geometry. During this presentation, we will introduce our recent work on a variant of the Bog...
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：The Cerednik--Drinfeld uniformization theorem
Cerednik-Drinfeld 一致化定理 Drinfeld半平面 Shimura曲线
2023/11/13
In this talk we relate the Drinfeld half plane studiedso far in the seminar with certain Shimura curves.which are of more global arithmetic interest. Therelation is expressed in a certain uniformizati...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Cartan-Helgason theorem for quaternionic symmetric pairs
四元数 对称对 Cartan-Helgason定理
2023/11/7
we present a joint work with Clemens Weiske and Genkai Zhang (Sweden). It shows a branching law for compact symmetric pairs K\subset G of quaternionic type. Precisely to say, K is a product of a simpl...
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：Fill-ins and Positive Mass theorem
填充 正质量定理 AH流形
2023/5/15
In this talk, we shall use fill-in to give a new description of the positive mass theorem. By using this, we shall show that PMT on AH manifolds implies PMT on AF manifolds. This talk is based on the ...
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：Extensions of Projection Theorem in Banach Spaces
投影定理 巴拿赫空间 扩展
2023/5/4
In this talk, we first recall classic projection theorem for closed convex subsets in a Hilbert space. Then we introduce two extensions of the projection theorem in the Banach space where one is estab...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On Bernstein Theorem of Affine Maximal Hypersurface
仿射 极大超曲面 伯恩斯坦定理
2023/4/13
Bernstein problem for affine maximal type hypersurfaces has been a core problem in affine geometry. A conjecture proposed firstly by Chern (Proc. Japan-United States Sem., Tokyo, 1977, 17-30) for enti...
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：A Liouville’s theorem for some Monge-Ampère type equations
蒙日-安培型方程 刘维尔定理 单调准局部质量类型量
2023/4/13
We study a Monge-Ampère type equation which interpolates the sigma_2-Yamabe equation in conformal geometry and the 2-Hessian equation. In dimension 4, we prove a corresponding Liouville’s theorem. Our...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonsplitting of the Hilbert Exact Sequence and the Principal Chebotarev Density Theorem
希尔伯特精确序列 主切 博塔列夫密度定理 非分裂
2023/4/18
Let $K/k$ be a finite Galois extension of number fields, and let $H_K$ be the Hilbert class field of $K$. We find a way to verify the nonsplitting of the short exact sequence
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The Quantum Perron-Frobenius Theorem
量子力学 Perron-Frobenius Theorem 量子对称性
2023/4/23
We establish the quantum Perron-Frobenius theorem on quantum symmtries. We characterize the structure of the Perron-Frobenius eigenvector space using quantum Fourier analysis (in the sense of picture ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Quasi-invariant theorem on the Gaussian path space
高斯路径 空间 准不变定理
2023/4/27
In this talk, we will first introduce a class of Gaussian processes, and prove the quasi-invariant theorem with respect to the Gaussian Wiener measure, which is the law of the associated Gaussian proc...
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...