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Geometry

Organizers:  Otis Chodosh & Greg Parker

Upcoming Events

Feb
19
Date3:15 PM
Location
383N
Speaker
Thomas Koerber (Vienna)

 The Riemannian Penrose inequality is a fundamental result in mathematical relativity. It has been a long-standing conjecture of G. Huisken that an analogous result should hold in the context of extrinsic geometry. In this talk, I will present recent joint work with M. Eichmair that…

Past Events

Jan
15
Date3:15 PM
Location
383N
Speaker
Yipeng Wang (Columbia)

A central problem in differential geometry is understanding how the geometry of a boundary determines the geometry of its interior. Gromov's fill-in problem suggests that when a closed Riemannian manifold is filled with a region of large curvature, the extrinsic curvature of the boundary must be…

Dec
11
Date3:15 PM
Location
383N
Speaker
Tristan Rivière (ETH)

We will illustrate by examples the role of canonical families in solving minmax problems. We will then propose a desingularisation of Marques-Neves-Ros canonical family leading to a new proof of the Willmore conjecture in dimension 3 and opening the way for considering the Willmore Problem in…

Dec
04
Date3:15 PM
Location
383N
Speaker
Nikolay Bogachev (University of Toronto)

Hyperbolic reflection groups appear in various fields of mathematics such as algebraic geometry, discrete subgroups of Lie groups, geometric group theory, geometric topology, and number theory. Cofinite and cocompact hyperbolic reflection groups have the following feature: their fundamental…

Nov
20
Date3:15 PM
Location
383N
Speaker
Greg Parker (Stanford)

The study of singularities of minimal submanifolds has a long history, with isolated singularities being the best understood case. The next simplest case is that of minimal submanifolds with families with singularities locally modeled on the product of an isolated conical singularity and a…

Nov
13
Date3:15 PM
Location
383N
Speaker
Clifford Taubes (Harvard University)

The Vafa Witten equations on 4-manifolds are the variational equations of a functional that generalizes one of the Chern-Simons functionals for SL(2;C) connections on 3-manifolds (and it reduces to that on products of a 3-manifold with the circle).  Being that the moduli space of solutions…

Nov
06
Date3:15 PM
Location
383N
Speaker
Doug Stryker (Princeton)

The existence problem for minimal hypersurfaces (or more generally prescribed mean curvature hypersurfaces) in complete noncompact manifolds is fundamental, but little is known. Min-max provides a powerful framework for existence in closed manifolds, but relies critically on compactness. I…

Oct
30
Date3:15 PM
Location
383N
Speaker
Rudi Zeidler (Münster)

I will explain a certain topological construction of positive scalar curvature metrics with uniformly Euclidean ($L^\infty$) point singularities. This provides counterexamples to a conjecture of Schoen. It also shows that there are metrics with uniformly Euclidean point singularities which…

Oct
23
Date3:15 PM
Location
383N
Speaker
Albachiara Cogo (University of Tübingen)

Riemannian structures of limited regularity arise naturally in the realm of geometric PDEs, especially in relation to physical models. Since the work of Sabitov-Shefel and De Turck-Kazdan in the late seventies, it is well known that the optimal regularity of a Riemannian structure is governed by…

Oct
16
Date3:15 PM
Location
383N
Speaker
Aria Halavati (NYU)

Entire critical points of the abelian Higgs functional are known to blow down to generalized minimal submanifolds (of codimension 2). In this talk we prove an Allard type large-scale regularity result for the zero set of solutions. In the "multiplicity one" regime, we show the uniqueness of blow…

Oct
09
Date3:15 PM
Location
383N
Speaker
Costante Bellettini (UCL)

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…