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08:40 AM - 09:00 AM
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Welcome
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- Location
- SLMath: Eisenbud Auditorium
- Video
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09:00 AM - 10:00 AM
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Hypersurfaces with non-negative scalar curvature
Lan-Hsuan Huang (University of Connecticut)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
- Since the time of Gauss, geometers have been interested in the interplay between the intrinsic structure of hypersurfaces and their extrinsic geometry from the ambient space. Many classical results discuss the sectional curvature. For example, it is known that a complete hypersurface in Euclidean space with non-negative sectional curvature is either convex or a generalized hypercylinder.
In a series of joint work with Damin Wu, we study hypersurfaces with non-negative scalar curvature. We prove that a closed hypersurface with nonnegative scalar curvature must be weakly mean convex. In general, vanishing scalar curvature causes analytical difficulties because the scalar curvature operator may not be elliptic. We tackle the problem by studying the level sets of a height function, which is motivated by general relativity. We further extend our proof to unbounded hypersurfaces which are asymptotically flat at infinity and obtain applications in the positive mass theorem and the Penrose inequality.
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Huang
215 KB application/pdf
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10:15 AM - 10:45 AM
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Tea
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- Location
- SLMath: Atrium
- Video
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10:45 AM - 11:45 AM
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Binary black holes in strong field gravity, gravitational waves and electromagnetic signatures from their accretion disks
Manuela Campanelli (Rochester Institute of Technology)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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12:00 PM - 12:30 PM
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Geometrostatics: The Geometry of Static Spacetimes in General Relativity
Carla Cederbaum (Tübingen University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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12:45 PM - 02:15 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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02:15 PM - 03:15 PM
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A vector field approach for sharp local well-posedness of quasiliner wave equations
Qian Wang (University of Oxford)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
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- Supplements
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Wang
89.6 KB application/pdf
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Wang
459 KB application/pdf
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03:30 PM - 04:00 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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04:00 PM - 04:30 PM
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On Hamilton’s Ricci flow and Bartnik’s construction of metrics of prescribed scalar curvature
Chen-Yun Lin (University of Connecticut)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
- Riemannian 3-manifolds with prescribed scalar curvature arise naturally in general relativity as spacelike hypersurfaces in the underlying spacetime. In 1993, Bartnik introduced a quasi-spherical construction of metrics of prescribed scalar curvature on 3-manifolds. This quasi-spherical ansatz has a background foliation with round metrics and converts the problem into a semi-linear parabolic equation. It is also known by work of R. Hamilton and B. Chow that the evolution under the Ricci flow of an arbitrary initial metric $g_0$ on $S^2$, suitably normalized, exists for all time and converges to the round metric.
In this talk, we describe a construction of metrics of prescribed scalar curvature using solutions to the Ricci flow. Considering background foliations given by Ricci flow solutions, we obtain a parabolic equation similar to Bartnik’s. We discuss conditions on the scalar curvature that guarantees the solvability of the parabolic equation, and thus the existence of asymptotically flat 3-metrics with a prescribed inner boundary. In particular, many examples of asymptotically flat 3-metrics with outermost minimal surfaces are obtained
- Supplements
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Lin
176 KB application/pdf
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04:45 PM - 05:15 PM
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From perturbation to observation: measuring the response of neutron stars
Jocelyn Read (California State University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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Read
9.14 MB application/pdf
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05:30 PM - 06:15 PM
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Panel Discussion
Andrea Bertozzi (University of California, Los Angeles), Manuela Campanelli (Rochester Institute of Technology), Carla Cederbaum (Tübingen University), Alexi Hoeft (Rutgers University), Christina Sormani (CUNY, Graduate Center; Herbert H. Lehman College, CUNY), Iva Stavrov (Lewis and Clark College)
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- Location
- SLMath: Commons Room
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07:00 PM - 09:00 PM
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Dinner at Taste of the Himalayas
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