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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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Introduction to Allard’s regularity theorem（I）
阿拉德 正则性 定理 导论
2023/5/10
In this short seminar, we will discuss the proof of the Allard regularity theorem, which is an $\epsilon$-regularity theorem for the mean curvature equation in the Geometric Measure Theory(GMT) settin...
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：Numerical PDEs for Fluid-Structure Interaction (FSI) Problems
流固耦合 数值 偏微分方程
2023/5/8
The interaction of a flexible structure with a flowing fluid in which it is submersed or by which it is surrounded gives rise to a rich variety of physical phenomena with applications in many fields o...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：两水平非正规因子设计的构造
两水平 非正规因子 设计 构造
2023/5/6
因子设计可分为正规设计和非正规设计，其中正规设计结构简单，试验次数被限制在2的幂次上。非正规设计结构复杂，但具有较为灵活的试验次数，并可用于估计更多的因子效应。作为一类特殊的非正规设计，平行平面设计受到了越来越多的关注。正规设计也被称为单平面设计，由来自同一家族的几个单平面行并置得到的设计被称为平行平面设计。由三个平行平面构成的平行平面设计是最常用的非正规设计。将其推广到具有f个平面的平行平面设计...
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：Projective measure without Projective Baire
投射贝尔 投射测量 勒贝格可测
2023/5/6
In this talk, I will give some of the context and a sketch of the proof of the following result which I proved a while ago: It is consistent (relative to a Mahlo catrdinal) that there is a projective ...
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：An Inexact Projected Subgradient Method on Hadamard manifolds
哈达玛流形 不精确投影 亚梯度方法
2023/5/4
In this talk, we extend a recently established subgradient method for the computation of Riemannian metrics that optimizes certain singular value functions associated with dynamical systems. This exte...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On strongly quasiconvex functions: existence results and proximal point algorithms
强准孔函数 存在结果 近端点算法
2023/5/4
The class of strongly quasiconvex functions was introduced in the famous paper of B.T. Polyak in 1966. It is the natural extension of the class of strongly convex functions, its applications emcompass...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the transcendental Morse inequality
先验 莫尔斯不等式 射影流形 可动锥 对偶性
2023/5/4
We report the work “Duality between the pseudoeffective and the movable cone of a projective manifold” of Witt Nystrom, where he proved the transcendental Morse inequality for projective manifolds.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Fields with a generic multiplicative endomorphism
通用乘法 自同态 域
2023/5/4
The theory of fields expanded by a unary function symbol for a multiplicative endomorphism admits a model-companion, we denote it ACFH. It is a new example of an NSOP1 theory which is not simple. I wi...