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: 861 8198 8793, Code: 608224)
Max Hallgren (Rutgers University) - Finite-Time Singularities of the Ricci Flow on Kähler Surfaces - Abstract
By work of Song-Weinkove, it is understood that the Ricci flow on any Kähler surface can canonically be continued through singularities in a continuous way until its volume collapses. This talk will discuss recent progress in understanding a more detailed picture of the singularity formation in this context.
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Wednesday, March 26, 16:00-17:00 (Special time), Zoom link
(ID: 881 0044 4833, Code: 926627)
Konstantinos Leskas (University of Athens) - Smooth approximations for CMC hypersurfaces with isolated singularities - Abstract
In this talk we consider a constant mean curvature (CMC) hypersurface in R^8, with an isolated singularity, that minimizes the prescribed mean curvature functional. We show that in a ball centered at the singularity there exist a sequence of smooth CMC hypersurfaces that converges to the initial one.
The proof relies on the Hardt-Simon foliation for area minimizing cones in R^8. The result extends the Hardt-Simon smooth approximation theorem, established for area minimizers.
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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)
Xiaoxiang Chai (Pohang University of Science and Technology) - TBA - Abstract
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Wednesday, May 28, 15:00-16:00 (Special time), Zoom link
(ID: TBA, Code: TBA)
Thibaut Delcroix (Université de Montpellier) - TBA - Abstract
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Wednesday, June 4, 16:00-17:00 (Special time), Zoom link
(ID: TBA, Code: TBA)
Henri Guenancia (Université de Bordeaux) - TBA - Abstract