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北京大学110周年庆·数学学人 | 张恭庆：我的数学人生（图）
张恭庆 北大 数学
2023/6/16
2023年，北京大学数学学科迎来成立110周年，百十年经风雨而续薪火，再回首忆往昔而向未来。站在这个有着特别意义的节点上，我们推出了“110周年庆系列文章”栏目，以人物专访、回忆征稿等形式，回望北大数学学人一路走来的足迹以及学科发展历程。
一簇线性收敛的有向图上的分布式动量方法
一簇线性收敛 有向图上 分布式 动量方法
2023/6/13
We consider the distributed optimization to minimize a sum of smooth and strongly convex local objective functions over directed graphs. Using row- and column-stochastic weights, we propose a family o...
中国科学院物理研究所铁基超导体中超导与奇异金属态在压力下的共存共灭现象（图）
铁基超导体 奇异金属态 函数
2023/6/28
低温下电阻随温度的线性变化是奇异金属态的一个重要特征，在非常规超导材料中经常发现。高温超导电性对这种奇异金属态的依赖关系一直是高温超导机理研究中备受关注的问题，可能隐含了破解高温超导机理的“密码”。一般情况下，高温超导体的电阻随温度的变化既包含线性项，也包含温度的平方项，近似可用一个温度的幂律函数，R(T) = R0 + ATα, 或是R (T) = R0+ AT + BT2 来描述。幂指数 α=...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Fill-ins and Positive Mass theorem
填充 正质量定理 AH流形
2023/5/15
In this talk, we shall use fill-in to give a new description of the positive mass theorem. By using this, we shall show that PMT on AH manifolds implies PMT on AF manifolds. This talk is based on the ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The pseudoeffective cone on projective manifolds
射影流形 赝有效锥 全纯线丛
2023/5/15
We report the work of Boucksom-Demailly-Paun-Peternell, which shows that a holomorphic line bundle on a projective manifold is pseudoeffective iff its degree on any member of a covering family of curv...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Geometry of Landau-Ginzburg Model
朗道-金茨堡模型 几何 非紧复流形M
2023/5/15
An LG model (M, f) is given by a noncompact complex manifold M and the holomorphic function f defined on it, which is an important model in string theory. Because of the mirror symmetry conjecture, th...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Coupling by change of measures for dimension-free Harnack inequality
无维 哈纳克不等式 测度 耦合
2023/5/12
简要介绍概率论中的耦合方法及其在基础数学中的应用。引入新的变测度耦合，以简单的随机微分方程为例，将其应用于建立无穷维Harnack不等式、Bisnut导数公式和分布积分公式。
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：Balanced Boolean Functions with Good Autocorrelation Spectra and Their Applications
自相关谱 平衡 布尔函数
2023/4/26
In this talk we consider the maximum absolute value in the autocorrelation spectrum (not considering the zero point) of balanced Boolean function. The long-standing open question in this area is to ob...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Smoothing invariant is equivalent to harmonic
平滑不变 等价 谐波 调和函数
2023/4/23
It is well known that harmonic function is smoothing invariant when convolved with the standard mollifier, which gives a quick proof of the smoothness of the harmonic function. In this talk, we will c...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Liouville theorems for superlinear parabolic problems
超线性 抛物线问题 刘维尔定理
2023/4/21
We first consider positive classical solutions to a semilinear heat equation and discuss the associated Liouville-type theorems and their consequences on a priori estimates of solutions (in particular...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Bergman reproducing kernels for nearly holomorphic functions on bounded symmetric domains
伯格曼 有界对称域 近乎全纯函数 核
2023/4/17
Nearly holomorphic functions on symmetric domains are defined by Shimura as polynomial of differential of Kaehler potential with holomorphic coefficients. We find the corresponding Bergman reproducing...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Bergman reproducing kernels for nearly holomorphic functions on bounded symmetric domains
伯格曼 有界对称域 近乎全纯函数 核
2023/4/23
Nearly holomorphic functions on symmetric domains are defined by Shimura as polynomial of differential of Kaehler potential with holomorphic coefficients. We find the corresponding Bergman reproducing...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Differentiability of volume functions for big classes
大类 体积函数 可微性
2023/4/17
We report a recent paper of Witt Nystrom, where he proved the differentiability of volume functions using deformation to the normal cone.