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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Metric geometric aspects of Einstein manifolds
Einstein流形 度量几何 爱因斯坦流形 黎曼几何
2023/11/29
This lecture concerns the metric Riemannian geometry of Einstein manifolds, which is a central theme in modern differential geometry and is deeply connected to a large variety of fundamental problems ...
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
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
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：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：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：Deformation rigidity of Fano manifolds
法诺歧管 变形刚度 光滑射影品种X
2023/4/17
A smooth projective variety X is called rigid if any deformation of X is isomorphic to itself. A first example is the projective space, but in general it is a subtle and difficult problem to prove the...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Lines on holomorphic contact manifolds and a generalization of (2,3,5)-distributions to higher dimensions
全纯接触流形 线和 （2，3，5） 高维度推广
2023/4/19
Since the celebrated work by Cartan, distributions with small growth vector (2,3,5) have been studied extensively. In the holomorphic setting, there is a natural correspondence between holomorphic (2,...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Researches on manifolds with scalar curvature bounded from below
标量曲率 有界 流形
2023/4/25
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 ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Exponential mixing of frame flows for geometrically finite hyperbolic manifolds with cusps
几何有限 双曲流形带尖 框架流 指数混合
2023/4/28
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Exponential mixing of frame flows for geometrically finite hyperbolic manifolds with cusps
几何有限 双曲流形带尖 框架流 指数混合
2023/5/4
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Suspension Homotopy of 4-manifolds And the Second 2-local Cohomotopy Sets
4-流形 悬浮同伦 第二个 2-局部 同伦集合
2023/4/28
In this talk we study the homotopy type of the (double) suspension of an orientable, closed, connected 4-manifold M, whose integral homology can have 2-torsion. Moreover, the decomposition results are...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Generic Regularity for All Minimal Hypersurfaces in 8-Manifolds
8流形 最小超曲面 通用规则性
2023/5/5
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 ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Homological instability for the moduli space of smooth 4-manifolds
光滑 4-流形模空间 同调不稳定性
2023/5/5
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Oka manifolds and applications (V)
奥卡歧管 应用 奥卡流形理论
2023/5/8
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Oka manifolds and applications (III)
奥卡歧管 奥卡流形理论 奥卡-格雷特理论
2023/5/10
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...