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2024年1月26日，国家自然科学基金基础科学中心项目“流形上的几何、分析和计算”2023年项目进展暨战略发展研讨会在中国科学院数学与系统科学研究院（以下简称数学院）召开。国家自然科学基金委（以下简称基金委）党组成员、副主任江松院士、数理科学部数学处赵桂萍副处长、数理科学部综合与战略规划处陈国长副处长、数理科学部数学处王小虎项目主任，咨询专家王小云院士、张平文院士、张伟平院士，以及周向宇、郭雷、席...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some Applications of Nevanlinna Theory
Nevanlinna理论 指数多项式 算术性质 Green Griffiths-Lang猜想
2023/11/23
In this talk, we will introduce some applications of Nevanlinna theory to “arithmetic properties” of exponential polynomials and some special cases of Green-Griffiths-Lang conjecture with moving targe...
中国人民大学高瓴人工智能学院召开“第二届计算经济学研究与应用”研讨会（图）
计算经济学 函数 模型 区块链
2023/11/14
2023年11月8日，由中国人民大学高瓴人工智能学院主办的第二届计算经济学研究与应用研讨会顺利召开。北京大学前沿计算研究中心讲席教授邓小铁，中科院计算所前瞻研究实验室、处理器芯片重点实验室研究员孙晓明，中国科学院数学与系统科学研究院研究员陈旭瑾，清华大学计算机科学与技术系教授陈婧，中国科学院计算技术研究所研究员张家琳，北京交通大学经济管理学院教授曹志刚，谷歌研究科学家左淞，中国科学院数学与系统科学...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Prescribing sigma-2 curvature and boundary mean curvature on compact manifolds
紧致流形 sigma-2曲率 边界平均曲率
2023/11/14
On a smooth compact manifold of dimensions three and four with totally non-umbilic boundary，imposing non-negativity assumptions on curvatures of the background metric, we establish that there exists a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Liouville Properties on gradient shrinking Ricci solitons with constant scalar curvature
常标量 曲率梯度收缩 Ricci孤子 Liouville性质
2023/10/30
In this talk we show that bounded harmonic functions are constant on gradient shrinking Ricci solitons with CSC by frequency function method. As an application, we show that the space of harmonic func...
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
2023/9/1
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
2023/9/1
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：Some Results on Partial Inverse Spanning Tree Problems
部分逆生成树 有权函数 非循环边子集
2023/8/29
Given a graph G with weight function w and an acyclic edge subset E', the partial inverse spanning tree problem on (G, w; E') is to find a new weight function w* so that E' can be extended to a maximu...
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
2023/5/13
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
2023/5/13
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
2023/5/12
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
2023/5/10
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
2023/5/3
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
2023/5/3
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
2023/4/25
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...