The seminar usually holds on Wednesday. For more details, please visit
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Wednesday, February 21, 9:00-10:00, Zoom link
(ID: 828 0478 1311, Code: 635902)
Gang Liu (East China Normal University) - Complete Kahler manifolds with nonnegative Ricci curvature - Abstract
We discuss some recent results on complete Kahler manifolds with nonnegative Ricci curvature:
1. the invariance of average of scalar curvature at infinity
2. boundedness of integral of higher power of Ric
3. A rigidity result for Kahler Ricci flat metric
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Wednesday, February 28, 9:00-10:00, Zoom link
(ID: 811 2485 6853, Code: 301398)
Yuan Yuan (Syracuse University) - Function theory on quotient domains - Abstract
Let $f: D \rightarrow \Omega$ be a proper holomorphic map between two bounded domains. $\Omega$ is a quotient domain of $D$ if there exists a finite group $G$ such that $\Omega = X / G$.
The function theory on $\Omega$ can be studied by transforming to $D$. In this way, we may study the Bergman projection, the Szeg\H{o} projection and the $\bar\partial$ problem on $\Omega$.
In this talk, we will mainly discuss the recent work on the Szeg\H{o} projection.
We will introduce a boundary value problem for holomorphic functions on $D$ which enables us to define the Hardy space on $\Omega$ and derive a Bell type transformation formula for the Szego projection on $\Omega$.
This definition of the Hardy space is different from the existing one in the literature and is a natural generalization of that on the planar domain considered by Lanzani-Stein.
When $D$ is the unit ball or the polydisc, we provide a sufficient condition for the solution to the boundary value problem. We further obtain the sharp $L^p$ estimates for Szego projections on some quotient domains in $\mathbb{C}^2$.
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Wednesday, March 6, 9:00-10:00, Zoom link
(ID: 834 8910 4525, Code: 783607)
Jingbo Wan (Columbia University) - Rigidity of Area Non-Increasing Maps - Abstract
In this talk, we discuss the approach of Mean Curvature Flow to demonstrate that area non-increasing maps between certain positively curved closed manifolds are rigid. Specifically, this implies that an area non-increasing self-map of $CP^n, n \geq 2$, is either homotopically trivial or is an isometry, answering a question by Tsai-Tsui-Wang.
Moreover, by coupling the Mean Curvature Flow for the graph of a map with Ricci Flows for the domain and the target, we can also study the rigidity of area non-increasing maps from closed manifolds with positive 1-isotropic curvature (PIC1) to closed Einstein manifolds, where Prof. Brendle's PIC1 Sphere Theorem is applied.
The key to studying the rigidity of area non-increasing maps under various curvature conditions lies in the application of the Strong Maximum Principle along the MCF/MCF-RF. We will focus our attention on one particular case to illustrate the SMP argument. This is a joint work with Professor Man-Chun Lee and Professor Luen-Fai Tam from CUHK.
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Thursday (Special day), March 14, 9:00-10:00, Zoom link
(ID: 842 9937 0734, Code: 296730)
Artem Pulemotov (The University of Queensland) - Palais--Smale sequences for the prescribed Ricci curvature functional - Abstract
On homogeneous spaces, solutions to the prescribed Ricci curvature equation coincide with the critical points of the scalar curvature functional subject to a constraint. We provide a complete description of Palais--Smale sequences for this functional.
As an application, we obtain new existence results for the prescribed Ricci curvature equation, which enables us to observe previously unseen phenomena. Joint work with Wolfgang Ziller (University of Pennsylvania).
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Wednesday, March 20, 9:00-10:00, Zoom link
(ID: 867 7258 6499, Code: 188353)
Bo Zhu (Texas A&M University) - Metric invariants of manifolds and Llarull rigidity theorem on four-manifolds - Abstract
This talk will focus on some metric invariants of Riemannian manifolds, which were introduced by Gromov in the 1980s. I will first introduce several metric invariants of Riemannian manifolds and then explore its connection with curvature on manifolds.
After that, I will talk about our recent progress on Llarull rigidity theorem on four-dimensional manifolds.
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Wednesday, March 27, 9:00-10:00, Zoom link
(ID: 836 0795 5992, Code: 960544)
Antoine Song (California Institute of Technology) - Minimal surfaces in spheres from random permutations - Abstract
The main result I will discuss states that there exists a sequence of closed minimal surfaces in high-dimensional Euclidean spheres which converge (around most points) to the hyperbolic plane.
The proof is based on a surprising connection between minimal surfaces in spheres, random permutations and convergence of unitary representations.
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Wednesday, April 3, 9:00-10:00, Zoom link
(ID: 861 1625 0516, Code: 824116)
Tran-Trung Nghiem (University of Montpellier) - Calabi-Yau metrics on complex symmetric spaces - Abstract
On complex symmetric spaces of rank one, Stenzel constructed explicit examples of Calabi-Yau metrics with smooth cross-section asymptotic cone. A new feature in higher rank is that the possible candidates for asymptotic cones generally have singular cross-section.
After an introduction and survey of known results, I will present an existence theorem of Calabi-Yau metrics on symmetric spaces of rank two with asymptotic cone having singular cross-section.
This provides new examples of Calabi-Yau manifolds with irregular asymptotic cone besides the only known example of Conlon-Hein, and covers the rank two symmetric spaces left by Biquard-Delcroix.
The metrics on the decomposable cases turn out to be asymptotically a product of two Stenzel cones. If time allows, I will also try to explain why some special symmetric spaces of rank two don't have any invariant Calabi-Yau metrics with a given asymptotic cone,
using an obstruction on the valuation induced by such metric if exists.
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Wednesday, April 10, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
Erik Hupp (Northwestern University) - TBA - Abstract
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Wednesday, April 17, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
Jian Wang (Stony Brook University) - TBA - Abstract
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Wednesday, April 24, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
Kai Xu (Duke University) - TBA - Abstract
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Wednesday, May 8, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
Yanir A. Rubinstein (University of Maryland) - TBA - Abstract
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Wednesday, May 15, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
Bin Wang (The Chinese University of Hong Kong) - TBA - Abstract
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Wednesday, May 22, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
TBA - TBA - Abstract
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Wednesday, May 29, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
TBA - TBA - Abstract
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Wednesday, June 5, 9:00-10:00, Zoom link
(ID: TBA, Code: TBA)
TBA - TBA - Abstract