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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...
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...
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 ...
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...
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...
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...
在微分几何中,和乐群描述了向量沿闭曲线平移后与原向量的差别,反映了黎曼流形的整体微分几何性质。Berger对黎曼流形可能的和乐群进行了分类。特殊特殊和乐群黎曼流形是不同于SO(n)的可定向黎曼流形,包括Calabi-丘流形、超Kahler流形、G2流形和Spin(7)流形。这些特殊特殊和乐群黎曼流形本身具有极其丰富的结构,与多个数学分支产生深刻的联系,并且在物理上也非常重要。在此报告中,我们将介绍...
2020年Greene和Lobb利用复二维空间的拉格朗日子流形分类简洁地解决了光滑约当曲线的矩形钉子存在性问题。我们将以此为引,从定性和定量两个角度介绍拉格朗日子流形分类的进展,应用和问题。
丢番图逼近中经典的Dirichlet逼近定理给出了用有理向量逼近给定实向量时误差与分母之间的关系。1969年前后,Davenport和Schmidt定义了Dirichlet可改进向量,这些实向量被有理向量逼近时误差比Dirichlet逼近定理给出的更小;他们证明了这些向量构成了R^n中的一个Lebesgue零测集,并提出了如下问题:R^n中光滑曲线上的Dirichlet可改进向量是否仍然是零测的。...
The motivation to study manifolds with scalar curvature bounded from below comes from Mathematical General Relativity and Riemannian Geometry. In this talk, I'll first briefly introduce some problems ...
I will present the joint work with Jialun Li and Pratyush Sarkar in the talk. As a final work to establish that the frame flows for geometrically finite hyperbolic manifolds of arbitrary dimensions ar...
The well-known Simons cone suggests that singularities may exist in a stable minimal hypersurface in Riemannian manifolds of dimension greater than 7, locally modeled on stable minimal hypercones. It ...
The moduli space of a smooth manifold X is defined to be the classifying space of its diffeomorphism group. Understanding the cohomology group of this space is important because elements in this group...
In this series of talks, I will present some recent developments in the theory of Oka manifolds and their applications. After a brief review of the classical Oka-Grauert theory, I shall recall the not...

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