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09:15 AM - 09:30 AM
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Welcome
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
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- Supplements
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09:30 AM - 10:30 AM
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Simple nonlinear waves on curved manifolds
Piotr Bizon (Jagiellonian University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
- My talk will be concerned with semilinear wave equations posed on curved manifolds. I will discuss several simple examples illustrating how a non-flat geometry of the domain affects the global behavior of solutions.
- Supplements
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Bizon
1.96 MB application/pdf
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10:30 AM - 11:00 AM
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Tea
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- Location
- SLMath: Atrium
- Video
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11:00 AM - 12:00 PM
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Stability and instability of spatially homogeneous solutions in the T^2 symmetric setting
Hans Ringström (Royal Institute of Technology (KTH))
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
- Solutions to Einstein's equations with a high degree of symmetry play an important role in guiding our understanding of general relativity. It is therefore natural to ask: to what extent are these solutions representative? In the talk we give examples both of stability and instability and relate the results to more general conjectures. In particular, we illustrate the strong dependence of the conclusions on the presence/absence of a positive cosmological constant
- Supplements
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12:00 PM - 01:15 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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01:15 PM - 02:15 PM
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Conservation laws for the wave equation and applications
Stefanos Aretakis (Princeton University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
- We will present recent results regarding conservation laws for the wave equation on null hypersurfaces. We will show that an important example of a null hypersurface admitting such conserved quantities is the event horizon of extremal black holes. We will also show that a global analysis of the wave equation on such backgrounds implies that certain derivatives of solutions to the wave equation asymptotically blow up along the event horizon of such backgrounds. In the second part of the talk we will present a complete characterization of null hypersurfaces admitting conservation laws. For this, we will introduce and study the gluing problem for characteristic initial data and show that the only obstruction to gluing is in fact the existence of such conservation laws.
- Supplements
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02:20 PM - 03:15 PM
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Asymptotically Flat Graphs with Small Mass
Lan-Hsuan Huang (University of Connecticut)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
- The Riemannian positive mass theorem and its rigidity is recently proven for asymptotically flat hypersurfaces in Euclidean space in all dimensions. The rigidity says that the hyperplane is the only asymptotically flat hypersurface with nonnegative scalar curvature whose ADM mass is zero. In this talk, we consider a class of asymptotically flat graphs with small positive mass and show that the graph is effectively close to a hyperplane if the mass is small. This is a joint work with Dan Lee
- Supplements
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Huang
178 KB application/pdf
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03:15 PM - 03:45 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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04:10 PM - 05:00 PM
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MSRI/Evans Lecture: On an information-theoretical interpolation inequality
VILLANI Cedric (Institute Henri Poincare)
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- Location
- UC Berkeley, 60 Evans Hall
- Video
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- Abstract
- In this talk I will review the history and use of an information-theoretical inequality introduced by Otto and I at the end of the nineties, which we called the HWI inequality; how it was used recently in some large-dimension results.
- Supplements
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