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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Primal Dual Alternating Proximal Gradient Algorithms for Nonsmooth Nonconvex Minimax Problems with Coupled Linear Constraints
耦合 线性约束 非光滑 非凸极小问题 基本对偶交替 近端梯度算法
2023/4/14
Nonconvex minimax problems have attracted wide attention in machine learning, signal processing and many other fields in recent years. In this paper, we propose a primal dual alternating proximal grad...
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：Chevalley formulae for the motivic Chern classes of the Schubert cells
舒伯特 细胞动机陈类 切瓦利公式
2023/4/14
The motivic Chern classes of the Schubert cells are the K-theoretic generalizations of the Chern-Schwartz-MacPherson classes in homology. I will report some joint work in progress with L. Mihalcea and...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Best subset selection via distance covariance
距离协方差 最佳子集 回归分析
2023/4/14
Best subset selection is an important problem in regression analysis,which has many applications in computer science and medicine. However, the existing best subset selection methods have some limitat...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A simpler proof of the Frank-Lieb inequality on the Heisenberg group
海森堡群 Frank-Lieb inequality 更简单证明
2023/4/14
I will discuss the Hardy-Littlewood integral inequality with sharp constant on the Heisenberg goup proved by Frank and Lieb. I will outline a simpler proof which bypasses the sophisticated argument fo...
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：SOME PROPERTIES OF STATIONARY CONTINUOUS STATE BRANCHING PROCESSES
稳态 连续状态 分支过程 性质
2023/4/14
We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant po...
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：On the stability of multi-dimensional rarefaction waves
多维 稀薄波 稳定性
2023/4/17
In his pioneering work in 1860, Riemann proposed the Riemann problem and solved it for isentropic gas in terms of shocks and rarefaction waves. It eventually became the foundation of the theory of one...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Prismatization over k
k 棱柱化 棱镜F规
2023/4/17
Discuss [Bha, §3.1-3.3]. Please cover §3.1 and §3.3. You can recall/admit materials in §3.2 for some discussions in §3.3.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A structure-preserving parametric finite element method (PFEM) for geometric PDEs and applications
几何偏微分方程 结构保持 参数有限元
2023/4/17
In this talk, I begin with a review of different geometric flows (PDEs) including mean curvature (curve shortening) flow,surface diffusion flow, Willmore flow, etc., which arise from materials science...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Expanding cone and homogeneous dynamics
膨胀锥体 均匀动力学 非紧致简单李群
2023/4/17
We introduce the notion of expanding cone of a noncompact simple Lie group. This allows us to extend several results in homogeneous dynamics to more general settings. We show how this notion is used i...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On cancellation laws in cardinal arithmetic without the axiom of choice
选择公理 基数算术 取消定律
2023/4/17
We survey known results concerning cancellation laws in cardinal arithmetic without the axiom of choice. These results include the cancellation law for Dedekind finite cardinals in cardinal addition a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Steady gradient Ricci solitons with positive curvature
正曲率 稳态梯度 利玛窦孤子
2023/4/17
We will construct some new examples of steady gradient Ricci solitons with positive curvature operator. Moreover, for any 3D steady gradient Ricci soliton with positive curvature, if it is asymptotic ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：超大规模连接信息理论极限分析
超大规模 连接信息 理论极限 分析
2023/4/17
超大规模连接被认为是6G的五大典型场景之一，具有小包传输和用户随机接入的特点。本研究针对该场景进行了有限块长信息理论极限分析，推导了在多天线准静态瑞利衰落信道中，用户随机接入系统时能量效率的非渐近理论界，量化了活跃用户数是否已知、信道状态信息是否已知以及是否共享同一码本对系统性能的影响。