The seminar usually holds on Wednesday from 9:00-10:00 online. For more details, please visit
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Wednesday, February 19, 10:00-11:00 (Special time), Zoom link
(ID: 856 1651 6569, Code: 333115)
Man-Chun Lee (The Chinese University of Hong Kong) - Gap theorem on manifolds using Ricci flow - Abstract
In Kahler geometry, it was proved by Ni that curvature on nonflat Kahler manifold with nonnegative bisectional curvature cannot decay too fast at infinity. In this talk, we will discuss how Ricci flow can be used to prove the Riemannian gap theorem.
We will also discuss how the method related to existence of expanding soliton. This is based on joint work with P.-Y Chan.
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Wednesday, February 26, 16:30-17:30 (Special time), Zoom link
(ID: 830 0129 8209, Code: 397524)
Costante Bellettini (University College London) - PDE analysis on stable minimal hypersurfaces - Abstract
We consider properly immersed two-sided stable minimal hypersurfaces of dimension n. We illustrate the validity of curvature estimates for n \leq 6 (and associated Bernstein-type properties with an extrinsic area growth assumption). For n \geq 7 we illustrate sheeting results around "flat points".
The proofs rely on intrinsic (nonlinear) PDE analysis. The two main results extend respectively the analogous Schoen-Simon-Yau estimates (obtained for n \leq 5) and the Schoen-Simon sheeting theorem (valid for embeddings).
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Wednesday, March 5, 9:00-10:00, Zoom link
(ID: 838 2171 0038, Code: 506511)
Chuanjing Zhang (Ningbo University) - The L^p-approximate critical Hermitian structure on Higgs bundles - Abstract
In this talk, we consider the asymptotic behavior of the perturbed Hermitian-Yang-Mills equation, and prove the existence of L^p-approximate critical Hermitian structure on Higgs bundles. Then we give some applications. These works are joint with Chao Li, Shiyu Zhang and Professor Xi Zhang.
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Wednesday, March 12, 9:00-10:00, Zoom link
(ID: 897 1771 2616, Code: 909921)
Demetre Kazaras (Michigan State University) - Scalar curvature and codimension 2 collapse - Abstract
This talk is about the structure of Riemannian 3-manifolds satisfying a lower bound on their scalar curvature. These manifolds are models for spatial geometry in general relativity. Our motivational question will be "How flat is an isolated gravitational system with very little total mass?"
Objects like gravity wells and black holes can distort geometry without accumulating much mass, making this a subtle question. In addition to discussing progress, I will present a "drawstring" construction, which modifies a manifold near a given curve, reducing its length with negligible damage to a scalar curvature lower bound.
Unexpected examples are produced with relevance to a few problems. This construction extends ideas of Basilio-Dodziuk-Sormani and Lee-Naber-Neumayer, and is based on joint work with Kai Xu.
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Wednesday, March 19, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
Max Hallgren (Rutgers University) - TBA - Abstract
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Wednesday, March 26, 16:00-17:00 (Special time), Zoom link
(ID: TBA, Code: TBA)
Konstantinos Leskas (University of Athens) - TBA - Abstract
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Wednesday, April 2, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
Chi Li (Rutgers University) - TBA - Abstract
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Wednesday, April 9, 16:00-17:00 (Special time), Zoom link
(ID: TBA, Code: TBA)
Yang Li (Cambridge University) - TBA - Abstract
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Wednesday, April 16, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
Chenzi Jin (University of Maryland) - TBA - Abstract
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Wednesday, April 23, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
TBA (TBA) - TBA - Abstract
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Wednesday, April 30, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
TBA (TBA) - TBA - Abstract
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Wednesday, May 14, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
Yi Lai (University of California, Irvine) - TBA - Abstract
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Wednesday, May 21, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
TBA (TBA) - TBA - Abstract
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Wednesday, May 28, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
TBA (TBA) - TBA - Abstract
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Wednesday, June 4, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
TBA (TBA) - TBA - Abstract