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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Random phase approximation for the mean-field electron gas （3）
平均场 电子气 随机相位近似
2023/11/29
Random phase approximation (RPA) was proposed by Bohm and Pines in four seminal papers during 1951-1953 to describe the correlation of fermions, namely the correction to the Hartree-Fock theory. While...
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：Approximation and computation for the linear and nonlinear eigenvalue problems in photonic crystals
光子晶体 线性非线性特征值问题 近似 计算
2023/5/15
In this talk, we discuss the approximation and computation for the linear and nonlinear eigenvalue problems in photonic crystals. We discretize the shifted Maxwell operator with edge finite elements a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On forward/inverse spectral problems, approximation problems and multiple integral formulae for non-smooth solitons
非光滑孤子 正/逆谱问题 近似问题 多重积分公式
2023/4/28
A class of nonlinear integrable PDEs admit non-smooth solitary wave solutions as certain special weak solutions. These solutions can be used to capture main attributes of solutions of these PDEs, e.g....
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Pandora Box Problem with Nonobligatory Inspection: Hardness and Approximation Scheme
潘多拉盒问题 非强制性检查 硬度 近似方案
2023/4/14
Weitzman (1979) introduced the Pandora Box problem as a model for sequential search with inspection costs, and gave an elegant index-based policy that attains provably optimal expected payoff. In vari...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stochastic approximation methods for nonconvex constrained optimization
非凸 约束优化 随机逼近方法
2023/4/14
Nonconvex constrained optimization (NCO) has been one of the important research fields in optimization community. It has widely appeared in many application fields. However, challenges for solving NCO...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Arithmetic purity of strong approximation for complete toric varieties
完整 复曲面品种 强近似 算术纯度
2023/4/18
In this talk, I will discuss arithmetic purity of strong approximation : motivations and related results. Finally, for complete toric varieties, I will briefly explain my work on this topic.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Approximation Distillation of Quantum Coherence
量子相干性 近似蒸馏 相干资源理论
2023/4/18
Coherence distillation is a basic information-theoretic task in the resource theory of coherence. In this talk, I will report the framework of the approximate coherence distillation under strictly inc...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Improved Approximation Ratios of Fixed-Price Mechanisms in Bilateral Trades
双边贸易 固定价格机制 近似比率
2023/4/18
We study the performance of fixed-price mechanisms in the bilateral trade problem. We improve the approximation ratios of welfare-optimal mechanisms in several settings. In particular, when we have on...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A Landscape View of Eigenvalues Approximation
特征值近似 景观视图 无序系统
2023/4/24
Waves of all sorts, including electromagnetic waves, acoustic waves, and mechanical vibrations, play a role in shaping our world. In disordered systems, the transport of waves is hindered, resulting i...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：ENERGY, POINTWISE, AND FREE BOUNDARY APPROXIMATION OF THE OBSTACLE PROBLEM FOR NONLOCAL OPERATORS
非局部 算子障碍物 自由边界 近似
2023/4/28
We consider the obstacle problem for a nonlocal elliptic operator, like the integral fractional Laplacian of order $s \in (0,1)$. We derive regularity results in weighted Sobolev spaces, where the wei...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Towards a zero-one law for improvements to Dirichlet's approximation theorem
Dirichlet近似定理 改进 零一定律
2023/5/10
In this talk we discuss a notion of $\psi$-Dirichlet in Diophantine approximation which concerns improving Dirichlet’s approximation theorem to a general approximating function $\psi$. This notion was...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Strong approximation and integral quadratic forms over affine curves
仿射曲线 强近似 积分二次形式
2023/5/9
Let $k$ be a field of characteristic 0 and let $C$ be the a smooth affine curve over $k$. We will first discuss applications of strong approximation to the theory of integral quadratic forms over $C$....
Two pillar theories in physics – general relativity and quantum mechanics – stand up well on their own, but are incompatible with each other.
2018算子代数中的逼近性质及遍历理论研讨会（Workshop on Approximation Properties in Operator Algebras and Ergodic Theory）
2018 算子代数中的逼近性质及遍历理论 研讨会
2017/12/20
Modeling non-commutative phenomena in finite dimensional matrix algebras is a central theme of the program Quantitative Linear Algebra. This workshop will focus on a variety of concrete questions aro...