University of Tennessee - Geometric analysis seminar
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Fall 2022
Wednesday, Sept. 14, 1600-1700, Ayers 112
Tim Buttsworth (University of Queensland/Penn State)
Title: The Einstein–Hilbert functional along Ebin geodesics.
Abstract: Given a closed manifold M, the set S of Riemannian metrics with prescribed volume form V is totally geodesic with respect to the Ebin metric; by a classical result of Moser, S contains all possible Riemannian structures on M. In this talk, I will describe some classical results on the behaviour of the Einstein–Hilbert functional on S, and how these results have been used to construct new Einstein metrics. I will also describe a new result that applies when M is at least five-dimensional: given a Riemannian metric g in S, there is an open and dense set of Ebin geodesics on S starting at g (in the smooth Whitney topology), along which scalar curvature converges to – infinity uniformly on M. This is joint work with Christoph Böhm and Brian Clark.
Wednesday, Oct. 26, 1610-1700, Ayers 112
Sven Hirch (Duke University)
Title: Spacetime harmonic functions and a Hawking mass monotonicity formula for initial data sets.
Abstract: One of the central results in mathematical relativity is the positive mass theorem which has first been proven by Schoen-Yau using the Jang equation, and Witten using spinors. We show how level-sets of spacetime harmonic functions can be used to give a new proof of the spacetime positive mass theorem and demonstrate how this leads to an optimal rigidity statement. This is based on joint work with Demetre Kazaras, Marcus Khuri and Yiyue Zhang.
Wednesday, Nov. 2, 1610-1700, Ayers 112
Baris Coskunuzer (University of Texas at Dallas)
Title: Minimal Surfaces in Hyperbolic 3-manifolds.
Abstract: In this talk, we will show the existence of smoothly embedded closed minimal surfaces in infinite volume hyperbolic 3-manifolds. The talk will be non-technical, and accessible to graduate students.
Wednesday, Nov. 16, 1610-1700, Ayers 112
Jose Espinar (Universita de Cadiz)
Title: On Fraser-Li conjecture with anti-prismatic symmetry and one boundary component.
Abstract: Let $\sigma _1$ be the first Steklov eigenvalue on an embedded free boundary minimal surface in $B ^3$. We show that an embedded free boundary minimal surface $\Sigma_g$ of genus $g\ge 1$, one boundary component and anti-prismatic symmetry satisfy $\sigma_1 (\Sigma _g) =1$. In particular, the family constructed by Kapouleas-Wiygul satisfies a such condition.
Wednesday, Nov. 30, 1610-1700, Ayers 112
Sathyanarayanan Rengaswami (University of Tennessee Knoxville)
Title: TBA
Abstract:TBA
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