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The finite-time stabilization problem is considered for a class of multi-input multi-output nonlinear systems composed of several different subsystems that are coupled with unknown nonlinearities, pos...
In this paper, we prove that the \(L^p(\mathbb {R}^d)\) norm of the maximal truncated Riesz transform in terms of the \(L^p(\mathbb {R}^d)\) norm of Riesz transform is dimension-free for any \(2\le p<...
形状梯度流系统演化有限元方法的收敛性分析
形状梯度流 系统演化 有限元方法 收敛性分析
2023/12/13
As a specific type of shape gradient descent algorithm, shape gradient flow is widely used for shape optimization problems constrained by partial differential equations. In this approach, the constrai...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Occupation fields for Markov loops
马尔可夫循环 占用域 格林函数
2023/11/29
In this talk, we introduce occupation fields for vertices and oriented edges and compute their distributions. More precisely, under the Markov loop measure, the expected number for crossings of an ori...
丘成桐（Shing-Tung Yau），数学家。美国国籍。生于中国广东省汕头市。1966－1969在香港中文大学数学系就读。1971年获美国伯克利加州大学博士学位。1974－1987年任美国斯坦福大学、普林斯顿高等研究院、圣地亚哥加州大学数学教授。1987年至今任哈佛大学数学教授。美国国家科学院院士(1993)，美国纽约科学院院士，美国艺术与科学院院士。曾获菲尔兹奖(1982)、克雷福德数学奖(1...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Adaptive stabilization of non-cooperative stochastic differential games
非合作 随机微分对策 自适应镇定
2023/11/29
We considers the adaptive stabilization problem for a basic class of linear-quadratic non-cooperative stochastic differential games when the systems matrices are unknown to the regulator and the playe...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Coexistence of nonempty Fatou sets and Julia sets with interior for transcendental Hénon maps
超Hénon映射 非空Fatou集 Julia集 内部共存性
2023/11/29
A Hénon map is a map of the form H(z, w) = (f(z) + aw, z). A main focus of interest are the Fatou sets and the Julia sets. In this lecture I will show that it is possible that the Fatou set and the Ju...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Proofs of two or infinity conjectures for Reeb orbits and closed geodesics
Reeb轨道 闭测地线 两个 无穷大猜想
2023/11/29
In this talk, we give a proof of the conjecture of Hofer-Wysocki-Zehnder published in 2003 asserting that a smooth and autonomous Hamiltonian flow on R4 has either two or infinitely many simple period...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convex sets with Oka complements
Oka补 凸集 Oka流形
2023/11/29
It is now known that the complement of any polynomially convex compact set K in C^n is an Oka manifold. In particular this holds if K is convex. I will discuss a recent result, joint with Forstneri?, ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The Proper Basis for Zero-dimensional Polynomial Ideals
零维 多项式理想 正确基 Grobner基
2023/11/29
The Grobner basis for a zero-dimensional polynomial ideal comprises a univariate polynomial in the least variable. The elimination process in Buchberger's algorithm unnecessarily involves the least va...
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：On the Gauss maps of complete minimal surfaces in Rm
Rm 完全极小曲面 高斯映射
2023/12/11
We prove that if the Gauss map of a minimal surface immersed in Rm omits a generic hypersurface of large enough degree, then it must be constant.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： The C0 estimate of the cscK equation
cscK方程 C0估计 ABP最大值原理
2023/12/11
We report the work of Chen-Cheng on the existence of cscK metrics. In this talk I will mainly focus on the C0 estimate, which is derived using the ABP maximum principle.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent progress on steady Prandtl equation and Tollmien-Schlichting waves
稳定 Prandtl方程 Tollmien-Schlichting波
2023/11/9
The Prandtl equation introduced by Prandtl in 1904 is a basic equation describling the behavior of the fluid near the boundary at high Reynolds number regime. In this talk, I will first introduce some...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A 1.344-approximation algorithm for the vertex cover problem
顶点覆盖问题 1.344 近似算法
2023/12/11
We present an algorithm for the vertex cover problem by combining the LP relaxation and the random edge-reductions. The algorithm has the expected approximation ratio of 1.344.