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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：Arnold conjecture and advances in Floer theory
阿诺德猜想 弗洛尔理论 哈密顿微分同胚
2023/5/4
In 1960s, Arnold conjectured that the number of fixed points of a Hamiltonian diffeomorphism of a symplectic manifold should be (much) greater than its counterpart for a general diffeomorphism. This c...
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：Solving hidden number problem with lattice sieving
晶格筛分 隐数问题 格约简算法
2023/4/28
Lattice reduction algorithms have been proved to be one of the most powerful and versatile tools in public key cryptanalysis. In this talk, we primarily concentrate on lattice attacks against (EC)DSA ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：带约束的差分隐私
带约束 差分隐私 中国科学院数学与系统科学研究院
2023/4/13
本报告首先主要介绍差分隐私的基本知识，然后介绍最近关于带约束差分隐私的工作。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Challenges and Beneficiations of differential privacy in transfer learning and federated learning
迁移学习 联邦学习 差分隐私
2023/4/13
Differential privacy is one of the most common techniques in privacy-preserving machine learning due to its rigorous math definition and theoretical results. Transfer learning and Federated learning a...
刘凯，男， 1983年4月出生，教授，博导、硕导，研究生学历，2009年博士毕业于山东大学和芬兰约恩苏大学。联系方式:liukai@ncu.edu.cn.2017年12月评为教授，2019年评为博导，南昌大学首批赣江青年学者，2017年获得江西省杰出青年人才项目资助，2014年9月-2015年8月国家留学基金委资助东芬兰大学访问学者，主持国家自然科学基金4项，主持江西省自然科学基金4项，发表SCI...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Meromorphic differentials and Teichmüller space
亚纯微分 泰希米勒空间 全纯二次微分
2023/4/17
In the late 1980s, Nigel Hitchin and Michael Wolf independently discovered a parametrization of the Teichmüller space of a compact surface by holomorphic quadratic differentials. In this talk, I will ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Uniqueness of BV Solution for Compressible Euler Equations
可压缩 欧拉方程 BV解 唯一性
2023/4/17
Compressible Euler equations are a typical system of hyperbolic conservation laws, whose solution forms shock waves in general. It is well known that global BV solutions of system of hyperbolic conser...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonsplitting of the Hilbert Exact Sequence and the Principal Chebotarev Density Theorem
希尔伯特精确序列 主切 博塔列夫密度定理 非分裂
2023/4/18
Let $K/k$ be a finite Galois extension of number fields, and let $H_K$ be the Hilbert class field of $K$. We find a way to verify the nonsplitting of the short exact sequence
非精确两层网格法的新型收敛性分析方法（张晨松）
非精确 两层网格法 收敛性 分析方法
2023/2/22
Two-grid methods with exact solution of the Galerkin coarse-grid system have been well studied by the multigrid community: an elegant identity has been established to characterize the convergence fact...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the preservation of second integrals by RK methods
RK方法 保存 第二积分
2023/4/25
One can elucidate integrability properties of ODEs by knowing the existence of second integrals. However, little is known about how they are preserved, if at all, under numerical methods. In this talk...
Sobolev不等式关于梯度的最优稳定性（张翼）
Sobolev不等式 梯度 最优稳定性
2023/2/22
We prove a sharp quantitative version of the p-Sobolev inequality for any 1
2022年12月9日上午，国家重点研发计划“数学和应用研究”重点专项“可解释深度学习的微分嵌入与最优传输理论”项目启动会暨实施方案论证会在西安交通大学顺利召开。项目咨询专家西安交通大学徐宗本院士、中国科学院数学与系统科学研究院高小山研究员、上海科技大学生物医学工程学院院长沈定刚教授、中山大学朱熹平教授、纽约州立大学石溪分校顾险峰教授、北京大学张志华教授参会指导。西安交通大学副校长别朝红教授、科技部...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Weak multisymplectic spectral integrators with a resolution of Gibbs phenomenon
吉布斯现象 分辨率 弱多辛谱 积分器
2023/4/28
We will report our recent work on weak multisymplectic spectral integrators for a wide range of nonsmooth Hamiltonian partial differential equations, which appear in quite a few physical applications ...