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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Siegel Zeros and Applications
西格尔零点 Landau-Siegel零点 大黎曼猜想 狄利克雷L函数
2023/4/24
Siegel zeros are real zeros of L-functions that are very close to 1, the non-existence of which was conjectured as a direct consequence of the Grand Riemann Hypothesis (GRH). In this talk, we will sta...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An introduction to the Hypergraph Regularity Lemma and its Applications 3
超图 规律性引理 超图正则引理 汉密尔顿循环
2023/4/26
In this talk, we give an example to illustrate how to use the hypergraph regularity lemmas. The absorbing method due to R?dl, Schacht and Szemerédi is a powerful tool in proving hypergraph Hamilton cy...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An introduction to the Hypergraph Regularity Lemma and its Applications 2
超图 规律性引理 超图正则引理 汉密尔顿循环
2023/4/26
In this talk, we first introduce the definitions of equitable partitions and state the hypergraph regularity lemma due to R?dl and Schacht. Then, we give the conception of reduced hypergraphs and its ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An introduction to the Hypergraph Regularity Lemma and its Applications 1
超图 规律性引理 超图正则引理 汉密尔顿循环
2023/4/26
Hypergraph regularity lemmas are generalizations of Szemerédi's regularity lemma for graphs, which has been proved to be a powerful tool with many subsequent. In this talk, we first give a brief intro...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Carleman estimates for some stochastic partial differential equations and applications
随机 偏微分方程 卡勒曼估计
2023/5/5
This talk is concerned with the controllability, observability and inverse problems for two types of stochastic partial differential equations, which are degenerate/singular stochastic parabolic equat...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Bilinear approaches in soliton theory I: Hirota direct method and its applications in (1+1)-dimensions
孤子理论 双线性方法 广田直接法 （1+1）维
2023/5/6
We will talk about the Hirota direct method and its applications to soliton solutions in (1+1)-dimensions. Both known and new examples of soliton equations will be discussed, and generalized bilinear ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The constant rank theorem and its applications
常秩定理 半线性方程组 规定曲率 克里斯托费尔-闵可夫斯基问题 魏因加滕曲率问题
2023/5/6
The constant rank theorem was initially developed by Caffarelli-Friedman in 1985 in two-dimensions for convex solutions of semilinear equations. Later, Korevaar-Lewis extended the result to higher dim...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Semiclassical oscillating functions of isotropic type and their applications
各向同型 半经典 振荡函数
2023/5/8
Rapidly oscillating functions associated with Lagrangian submanifolds play a fundamental role in semiclassical analysis. In this talk I will describe how to associate classes of semiclassical oscillat...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Oka manifolds and applications (V)
奥卡歧管 应用 奥卡流形理论
2023/5/8
In this series of talks, I will present some recent developments in the theory of Oka manifolds and their applications. After a brief review of the classical Oka-Grauert theory, I shall recall the not...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Oka manifolds and applications (III)
奥卡歧管 奥卡流形理论 奥卡-格雷特理论
2023/5/10
In this series of talks, I will present some recent developments in the theory of Oka manifolds and their applications. After a brief review of the classical Oka-Grauert theory, I shall recall the not...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Oka manifolds and applications (II)
奥卡歧管 奥卡流形理论 奥卡-格雷特理论
2023/5/10
In this series of talks, I will present some recent developments in the theory of Oka manifolds and their applications. After a brief review of the classical Oka-Grauert theory, I shall recall the not...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Oka manifolds and applications (I
奥卡歧管 奥卡流形理论 奥卡-格雷特理论
2023/5/10
In this series of talks, I will present some recent developments in the theory of Oka manifolds and their applications. After a brief review of the classical Oka-Grauert theory, I shall recall the not...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Paley-Wiener type theorems and their applications
Paley-Wiener型定理 Clifford代数环境 函数空间
2023/5/15
In this talk I will briefly introduce some Paley-Wiener type theorems in the Clifford algebra setting. The PW type theorems are related to a decomposition of some function spaces. Using the PW type th...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Birkhoff genericity for points on curves in expanding horospheres and Diophantine applications
星座图 曲线 Birkhoff泛型 丢番图应用
2023/5/16
Let $\{a(t):t \in \mathbb{R}\}$ be a diagonalizable subgroup of $SL(d,\mathbb{R})$ for which the expanded horosphere $U$ is abelian. By the Birkhoff ergodic theorem, for any point $x \in SL(d,\mathbb{...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Oka manifolds and applications (I)
奥卡流形 应用 复流形
2023/5/16
In this series of talks, I will present some recent developments in the theory of Oka manifolds and their applications. After a brief review of the classical Oka-Grauert theory, I shall recall the not...