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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 ...
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...
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...
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...
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...
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,...
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...
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...
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...
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...
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...
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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