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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：No blow-up by nonlinear It? noise for the Euler equations
非线性 爆炸 欧拉方程 噪声
2023/5/17
We consider the incompressible Euler equations in two or three dimensions and we show that the addition of a suitable multiplicative It? noise with superlinear growth prevents a smooth solution from b...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Introduction to Allard’s regularity theorem（II）
阿拉德 正则性定理 导论
2023/5/17
We continue to discuss the proof of the Allard regularity theorem. In the second presentation, we will focus on the harmonic approximation and the iteration argument for getting the decay of the tilt-...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Fill-ins and Positive Mass theorem
填充 正质量定理 AH流形
2023/5/15
In this talk, we shall use fill-in to give a new description of the positive mass theorem. By using this, we shall show that PMT on AH manifolds implies PMT on AF manifolds. This talk is based on the ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The pseudoeffective cone on projective manifolds
射影流形 赝有效锥 全纯线丛
2023/5/15
We report the work of Boucksom-Demailly-Paun-Peternell, which shows that a holomorphic line bundle on a projective manifold is pseudoeffective iff its degree on any member of a covering family of curv...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Social Learning and Strategic Pricing with Rating Systems
评级系统 社交学习 战略定价
2023/5/15
Despite widespread use in online transactions, rating systems only provide summary statistics of buyers' diverse opinions at best. To investigate the consequences of this coarse form of information ag...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Geometry of Landau-Ginzburg Model
朗道-金茨堡模型 几何 非紧复流形M
2023/5/15
An LG model (M, f) is given by a noncompact complex manifold M and the holomorphic function f defined on it, which is an important model in string theory. Because of the mirror symmetry conjecture, th...
国家重点研发计划“数学和应用研究”重点专项青年科学家项目启动会暨实施方案论证会举行（图）
北大 数学 重点专项
2023/6/16
2023年4月28日下午，由北京大学作为牵头单位承担的国家重点研发计划“数学和应用研究”重点专项青年科学家项目“数据与机理融合的金融风险预警方法研究”启动会暨实施方案论证会在北京大学中关新园举行。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Analysis of distributed SG algorithm
分布式 SG算法 分析
2023/5/12
In this talk, a distributed stochastic gradient (SG) algorithm is proposed where the estimators are aimed to collectively estimate an unknown time-invariant parameter from a set of noisy measurements ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Hausdorff dimension, singular vectors and divergent trajectories
豪斯多夫维数 奇异向量 发散轨迹
2023/5/12
In this talk, I will give a survey of results related to the problem of computing Hausdorff dimension of various dynamically defined sets, such as singular vectors. The aim is to try to describe the l...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The complexity of computing Markov perfect equilibrium in general-sum stochastic games
一般 随机博弈 马尔可夫完美均衡 计算复杂性
2023/5/12
Similar to the role of Markov decision processes in reinforcement learning, Markov games (also known as stochastic games) form the basis for the study of multi-agent reinforcement learning and sequenc...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Coupling by change of measures for dimension-free Harnack inequality
无维 哈纳克不等式 测度 耦合
2023/5/12
简要介绍概率论中的耦合方法及其在基础数学中的应用。引入新的变测度耦合，以简单的随机微分方程为例，将其应用于建立无穷维Harnack不等式、Bisnut导数公式和分布积分公式。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：离散型数学在信息科学中的一些应用
离散 数学 信息科学
2023/5/12
上世纪六十年代以来，随着数字通信技术的快速发展，离散型数学（组合设计和图论，数论，代数以及有限域上代数几何）逐渐成为通信许多应用领域的重要数学工具。本报告沿着六十年来历史发展的足迹，通俗介绍在代数纠错码和信息安全方面一些重要发展和数学问题，以实际例子说明数学所起的作用。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Derivation of the Vlasov equation from quantum many-body Fermionic systems with singular interaction
奇异相互作用 量子多体 费米子系统 弗拉索夫方程
2023/5/12
We consider the combined mean-field and semiclassical limit for a system of the N fermions interacting through singular potentials. We prove the uniformly in the Planck constant h propagation of quant...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Solitons and Breathers in the modulus KdV equations
模量 KdV方程 孤子 呼吸器
2023/5/12
Compared to the soliton solutions, the breathers, which are constructed in the mKdV or Gardner equation via integrability methods, are less studied. In our numerical study, we show the interactions be...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：中国式现代化与积极应对人口老龄化战略
中国式现代化 积极应对 人口老龄化
2023/5/10
人口快速老龄化、超大规模老年人口是中国式现代化面临的重要国情。当下，中国正面临人口老龄化加速发展期与实现中国式现代化过程叠加的发展新阶段，创造有利于经济高质量发展的人口条件，以及形成适应人口老龄化的经济发展新模式，是中国社会主义现代化发展的必由之路。因此，要以积极的态度看待人口老龄化带来的风险和挑战，挖掘老龄社会中存在的机遇，并主动应对人口老龄化问题，从根本上解决造成人口老龄化不断加速的难点、痛点...