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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：Algebraic Structures from Integral Equations
积分方程 代数结构 代数分析
2023/11/29
Even though the research style of algebra and analysis are quite different, many algebraic structures naturally arose from analysis, differential equations and integral equations, inspiring further ap...
郭位，香港城市大学校长及校杰出教授，目前担任IEEE Transactions on Reliability 主编。郭教授于2000年当选美国国家工程院院士，后又获选为台湾中央研究院院士及中国工程院外籍院士。他同时也是国际品管学管学院（IAQ）院士，国际工业工程学（IIE）会员、美国品管学会（ASQ）会员、运筹学和管理学研究协会（INFORMS）、美国标准协会（ASA）及国际电机电子工程学会（IE...
中国人民大学高瓴人工智能学院召开“第二届计算经济学研究与应用”研讨会（图）
计算经济学 函数 模型 区块链
2024/1/31
2023年11月8日，由中国人民大学高瓴人工智能学院主办的第二届计算经济学研究与应用研讨会顺利召开。北京大学前沿计算研究中心讲席教授邓小铁，中科院计算所前瞻研究实验室、处理器芯片重点实验室研究员孙晓明，中国科学院数学与系统科学研究院研究员陈旭瑾，清华大学计算机科学与技术系教授陈婧，中国科学院计算技术研究所研究员张家琳，北京交通大学经济管理学院教授曹志刚，谷歌研究科学家左淞，中国科学院数学与系统科学...
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
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：Rooted trees, Hopf algebras and rough paths
有根树 Hopf代数 粗路径
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：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
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：Algebraic topology of digraphs and its applications
有向图 代数拓扑 图论
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：On deformation limit in deformation theory
变形理论 变形极限 射影流形
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：Projective Manifolds with Pseudoeffective Cotangent Bundle II
伪有效 余切丛 射影流形
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...
曲面求交是计算机辅助设计（CAD）的基础操作，求交算法的拓扑稳定性是CAD系统稳定性的重要保障之一。样条曲面间的交线通常无法被准确参数化，这是造成CAD模型水密性问题的根源之一。在曲面求交中，在满足工业环境精度和效率要求的前提下，将交线的多分支、重分支、临近分支、小环、奇点全部正确计算是CAD领域的挑战性难题。
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
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
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：On several bi-Hamiltonian systems
双哈密顿系统 齐次Hamitionan算子 相容三元组
2023/11/13
Recently, based on the classification of the second and third order homogeneous Hamitionan operators Lorenzoni and his collaborators classified compatible trios of two-component homogeneous Hamiltonia...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：New revival phenomena for bidirectional dispersive hyperbolic equations
双向离散 双曲型方程 新复活现象
2023/11/13
In this talk, the dispersive revival and fractalization phenomena for bidirectional dispersive equations on a bounded interval subject to periodic boundary conditions and discontinuous initial profile...