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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convex sets with Oka complements
Oka补 凸集 Oka流形
2023/11/29
It is now known that the complement of any polynomially convex compact set K in C^n is an Oka manifold. In particular this holds if K is convex. I will discuss a recent result, joint with Forstneri?, ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed volume of infinite-dimensional convex compact sets II
无限维 凸紧集 混合体积
2023/11/6
Using the results presented in the previous lecture, namely the generalization of the Tsirelson's theorem [2] to mixed volumes, we calculate the mixed volume of the closed convex hulls of the two orth...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed volume of infinite-dimensional convex compact sets I
无限维 凸紧集 混合体积
2023/11/6
Let K be a convex compact subset of a separable Hilbert space H. One of the most important geometric characteristics of K is its intrinsic volumes. In the finitedimensionalcase (K ? R^d), the intrinsi...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convex integration and non-uniqueness of weak solutions for viscous fluids
粘性流体弱解 凸积分 非唯一性
2023/4/23
In this talk, I will discuss the method of convex integration and its applications on non-uniqueness of weak solutions to the hyper-viscous incompressible Navier-Stokes equations as well as the hypo-v...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The logarithmic Brunn-Minkowski inequality conjecture in convex geometry
凸几何 对数 布伦-闵可夫斯基 不等式猜想
2023/4/21
The logarithmic Brunn-Minkowski inequality conjecture is one of the most intriguing challenges in convex geometry since 2012. Notably, this conjectured inequality is stronger than the celebrated Brunn...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mixed-binary Convex Quadratic Optimization and Its Applications in Inference with Sparsity
二元凸 二次优化 稀疏推理
2023/4/14
Sparsity is a naturally occurring characteristic in many real-world applications including signal denoising, outlier detection, and finance. On one hand, sparsity assumption allows people to tackle in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：First-order methods for convex optimization and monotone inclusions under local Lipschitz conditions
局部利普希茨条件 凸优化 单调夹杂物 一阶方法
2023/5/6
In this talk, we first consider convex optimization whose smooth components have a locally Lipschitz continuous gradient and propose a first-order method for finding an epsilon-KKT solution. We then c...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stochastic Navier-Stokes equations via convex integration
凸积分 随机 纳维-斯托克斯方程
2023/5/8
In this talk I will talk about our recent work on the three dimensional stochastic Navier-Stokes equations via convex integration method. First we establish non-uniqueness in law, existence and non-un...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Volume preserving Gauss curvature flow of convex hypersurfaces in the hyperbolic space
双曲空间 凸超曲面 保体积 高斯曲率流
2023/5/15
In this talk, we discuss Y. Wei, B. Yang and T. Zhou’s preprint arXiv:2210.06035, in which they consider volume preserving curvature flows of smooth, closed and convex hypersurfaces in hyperbolic spac...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Distributed Event-Triggered Algorithm for Convex Optimization with Coupled Constraints
耦合约束凸优化 分布式事件 触发算法
2023/5/17
This talk concerns the nonsmooth distributed optimization problem via multi-agent network with the coupled equality and inequality constraints. The considered global optimization problem is to minimiz...