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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
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2023/11/29
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Projective Manifolds with Pseudoeffective Cotangent Bundle II
伪有效 余切丛 射影流形
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2023/11/15
The Keller-Segel system is known to exhibit rich dynamical behaviors including singularity formation with self-similarity structure. The talk presents recent developments in the study of blowup for th...
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
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2023/11/15
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
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2023/11/13
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
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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
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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：Some Results on Partial Inverse Spanning Tree Problems
部分逆生成树 有权函数 非循环边子集
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2023/11/6
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
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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
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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
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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
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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
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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
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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
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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
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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...