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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rooted trees, Hopf algebras and rough paths
有根树 Hopf代数 粗路径
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2023/11/15
In this talk, we first recall some classical Hopf algebras on rooted trees, including Connes-Kreimer Hopf algebra and Loday-Ronco Hopf algebra. Then we give a combinatorial description of the coproduc...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Projective Manifolds with Pseudoeffective Cotangent Bundle II
伪有效 余切丛 射影流形
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2023/11/15
The Keller-Segel system is known to exhibit rich dynamical behaviors including singularity formation with self-similarity structure. The talk presents recent developments in the study of blowup for th...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the dimension of limit sets on the real projective plane via stationary measures
实射 影平面 极限集 维数 平稳测度
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2023/11/15
I will present a dimension jump result of limit sets on RP^2 for representations of surface groups in SL(3,R). For Anosov representations, we prove the equality between the Hausdorff dimension and the...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On deformation limit in deformation theory
变形理论 变形极限 射影流形
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2023/11/15
This talk mainly concerns the projective, Moishezon and Kahler loci of a family. We first introduce four conjectures on this topic and then the works of the deformation limit of projective manifolds a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Algebraic topology of digraphs and its applications
有向图 代数拓扑 图论
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2023/11/15
High-order interaction occurs in various complex network, such as social network, bionetwork and network medicine. Comparing with that there are a lot of well-developed math tools (from graph theory) ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Prescribing sigma-2 curvature and boundary mean curvature on compact manifolds
紧致流形 sigma-2曲率 边界平均曲率
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2023/11/15
On a smooth compact manifold of dimensions three and four with totally non-umbilic boundary，imposing non-negativity assumptions on curvatures of the background metric, we establish that there exists a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Weak values as statistical estimation
统计估计 弱值 量子可观测值 最小方差
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2023/11/15
Given a quantum observable and a state, one can construct a classical observable, such that it is the optimal estimate of the quantum observable, in the sense of minimum variance. We demonstrate how t...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Toric Algebras and Matroids
Toric代数 拟阵 复曲面代数
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2023/11/13
In the first lecture I will give an introduction to toric algebras. A toric algebra can be seen as a monomial subalgebra, or as a quotient of a polynomial ring by a binomial prime ideal. We will discu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Several topics related to nonlinear Schrodinger equation-(I)
非线性 薛定谔方程 量子力学
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2023/11/13
The nonlinear Schrodinger (NLS) equation is a fundamental equation in the theory of integrable system and in many physical areas. In this talk, we will address several topics related to NLS equation, ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Several topics related to nonlinear Schrodinger equation-(II)
非线性 薛定谔方程 量子力学
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2023/11/13
The nonlinear Schrodinger (NLS) equation is a fundamental equation in the theory of integrable system and in many physical areas. In this talk, we will address several topics related to NLS equation, ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An inverse Lax-Wendroff procedure for finite difference schemes on the Cartesian grids
笛卡尔网格 有限差分格式 Lax-Wendroff逆过程
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2023/11/13
In this talk, we introduce the so-called inverse Lax-Wendroff (ILW) boundary treatment for finite difference approximations on the Cartesian mesh. As the domain boundary may intersect with the grid in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Rigidity results in mapping class groups and homeomorphism groups
映射类群 同胚群 刚性结果
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2023/11/13
Mapping class groups and homeomorphism groups are symmetry groups of surfaces and all manifolds. They are usually very rigid, in the sense that their automorphism groups only consist of conjugation. I...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Heisenberg-Pauli-Weyl uncertainty principle based on Phase derivatives
相位导数 Heisenberg Pauli-Weyl不确定性原理
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2023/11/13
In this talk we introduce some recent developments of Heisenberg-Pauli-Weyl uncertainty principle in the different settings.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some improved Caffarelli-Kohn-Nirenberg inequalities and uncertainty principles
Caffarelli Kohn-Nierberg不等式 不确定性原理
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2023/11/13
In this talk we introduce some improved Caffarelli-Kohn-Nirenberg inequalities and uncertainty principle for complex- and vector-valued functions on ?n, which is a further study of the results given i...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Multiple solutions for a Kirchhoff-type fractional coupled problem with p-Laplacian
p-Laplacian算子 Kirchhoff型分数 耦合问题 多重解
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2023/11/13
We discuss a class of two-parameters coupled Kirchhoff-type fractional differential equations. Two differentiated methods are used to prove the existence of two solutions to the equation. The fundamen...