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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convergence and Implicit Regularization of Deep Learning Optimizers
深度学习 优化 收敛 隐式正则化
2023/4/13
In this talk, I will present our recent work on the convergence/generalization analysis for the popular optimizers in deep learning. (1) We establish the convergence for Adam under (L0,L1 ) smoothness...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Syntomic cohomology in characteristic p
特征p 同调 Syntomic cohomology
2023/4/13
Discuss [Bha, §4.4-4.5]. One reasonable plan is to focus on §4.5 and use it as motivation to introduce materials in §4.4.
This is a periodic series learning seminar organized by Koji Shimizu and Shiz...
北京大学召开数学高层次人才自主培养质量提升专题研讨会（图）
北大 数学 人才培养
2023/6/16
2023年4月3日下午，北京大学数学高层次人才自主培养质量提升专题研讨会在理科一号楼1366会议室举行。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Combinatorial statistics: a common theme and a few examples
组合统计 霰弹枪组装 随机图匹配
2023/4/13
In this talk, I will overview the general flavor for the topic of “combinatorial statistics”, and I will describe some recent progress on shotgun assembling problems as well as random graph matching p...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：椭圆型偏微分方程有关的正则性问题 椭圆型偏微分方程有关的正则性问题
椭圆型偏微分方程 正则性问题 Calderon-Zygmund估计 Schauder估计
2023/4/18
简介椭圆型方程正则性的基本结果，综述弱正则数据下其方程解的Calderon-Zygmund估计和Schauder估计的基本方法和近期进展，分析非线性椭圆方程组的部分正则性和处处正则问题，介绍我们在有关问题上的一些研究。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：椭圆型偏微分方程有关的正则性问题
椭圆型 偏微分方程 正则性问题
2023/4/13
简介椭圆型方程正则性的基本结果，综述弱正则数据下其方程解的Calderon-Zygmund估计和Schauder估计的基本方法和近期进展，分析非线性椭圆方程组的部分正则性和处处正则问题，介绍我们在有关问题上的一些研究。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Ergodicity of non-stationary stochastic processes
非平稳 随机过程 遍历性
2023/4/13
I will discuss the ergodicity of two kinds of non-stationary processes: random periodic processes and random quasi-periodic processes. I will describe periodic measures, quasi-periodic measures and th...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data
平滑数据 二维布西内斯 三维欧拉方程 稳定近似 自相似爆炸
2023/4/13
Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. In this talk, we will first review recent progress in singu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Zeros of complete symmetric polynomials over finite fields
有限域 完全对称 多项式 零点
2023/4/13
Wan and Zhang have recently obtained a nontrivial lower bound for the number of zeros of complete symmetric polynomials over finite fields, and proposed a problem whether their bound can be improved. ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：2-representations and 2-vector bundles
2 向量丛 群论
2023/4/13
In this talk I will introduce some basic concepts in higher category and some details of the construction in the first talk. I will introduce crossed modules and the example of strict 2-representation...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On Bernstein Theorem of Affine Maximal Hypersurface
仿射 极大超曲面 伯恩斯坦定理
2023/4/13
Bernstein problem for affine maximal type hypersurfaces has been a core problem in affine geometry. A conjecture proposed firstly by Chern (Proc. Japan-United States Sem., Tokyo, 1977, 17-30) for enti...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Two families of $n$-rectangle nonconforming finite elements for sixth-order elliptic equations
六阶椭圆方程 矩形 有限元族
2023/4/13
We propose two families of nonconforming finite elements on $n$-rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent property and the approximation ability of ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Mean curvature flow coming out of cones
圆锥体 流出 平均曲率流
2023/4/13
We study mean curvature flows (MCFs) coming out of cones. As cones are singular at the origin, the evolution is generally not unique. A special case of such flows is known as the self-expanders. We wi...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Borel—Wei—Bott theorem for Derived Flag Schemes
派生 标志方案 博雷尔-魏-博特定理
2023/4/13
The framework of derived algebraic geometry (DAG), developed by Toen-Vezzosi, Lurie and many others, allows us to extend Grothendieck’s theory of flag schemes of sheaves to the cases of complexes. In ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the L2 rate of convergence in the limit from the Hartree to the Vlasov–Poisson Equation
哈特里到弗拉索夫 泊松方程 极限 L2收敛率
2023/4/13
We consider the semiclassical limit from the Hartree equation with Coulomb interaction potential to the Vlasov–Poisson equation. Using a new stability estimate for the difference of the square roots o...