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中国科学院金属所确定布尔可满足性问题计算复杂性下限（图）
拓扑结构 自旋纠缠 公式计算
2023/11/23
中国科学院金属研究所研究员张志东在计算机领域计算复杂性理论研究方面取得重要进展，确定了布尔可满足性问题的计算复杂度下限。相关研究成果发表在《数学》（Mathematics）上。
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：Some Applications of Nevanlinna Theory
Nevanlinna理论 指数多项式 算术性质 Green Griffiths-Lang猜想
2023/11/29
In this talk, we will introduce some applications of Nevanlinna theory to “arithmetic properties” of exponential polynomials and some special cases of Green-Griffiths-Lang conjecture with moving targe...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：C1,1/3- very weak solutions to the two dimensional Monge–Ampère equation
二维 Monge–Ampère方程 C1,1/3极弱解
2023/11/29
For any θ<1/3 , we show that very weak solutions to the two-dimensional Monge–Ampère equation with regularity C1,θ are dense in the space of continuous functions. This result is shown by a convex inte...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The Brauer-Manin obstruction on algebraic stacks
代数栈 Brauer-Manin阻塞 Hasse原理
2023/11/29
The Brauer-Manin obstruction is an old topic in local-global principle of varieties. I will talk about Brauer-Manin obstruction on algebraic stacks and extend some classical results such as the exact ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars："Sobolev extensions"(5)&(6)
Sobolev扩展 Whitney扩展 技术变体
2023/11/29
I will give an introduction to Sobolev extensions, including the use of variants of the Whitney extension technique. I will concentrate on the basics of the theory.
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 a Bogomolov type vanishing theorem
Bogomolov型 消失定理 代数几何
2023/11/29
The Bogomolv theorem holds great importance in algebraic geometry, particularly in the field of birational geometry. During this presentation, we will introduce our recent work on a variant of the Bog...
研究确定布尔可满足性问题计算复杂性下限
布尔 可满足性问题 复杂性下限
2023/12/14
中国科学院金属研究所研究员张志东在计算复杂性理论研究方面取得重要进展，确定了布尔可满足性问题的计算复杂度下限。近日，相关研究成果发表于Mathematics。
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
2023/11/29
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：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...
