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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...
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：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：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：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.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Pleijel identity
Pleijel恒等式 光滑边界 Blaschke–Petkantschin
2023/10/16
Let K be a planar convex body with C^1 boundary. Consider a random line G intersecting K. In [1] Pleijel discovered an identity expressing the integral functional of the length of the chord G ∩ K in t...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Singular integral and geometry
奇异积分 几何 谐波分析
2023/5/8
The geometric considerations enter in a decisive way in many questions of harmonic analysis. For example, the estimation of the Fourier transform of surface-carried measure, which played a key role in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stability conditions and quadratic differentials
稳定性条件 二次微分 三角分类
2023/5/6
Stability conditions on triangulated categories are introduced by Bridgeland. For 3-Calabi-Yau triangulated categories from quivers with potentials, the space of stability conditions on this triangula...
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...