Convergence and Low Regularity in General Relativity: April 29-May 3, 2019

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Workshop: Convergence and Low Regularity in General Relativity

April 29-May 3, 2019

Organized by: Philippe LeFloch, Jeff Jauregui, Mike Anderson, Christina Sormani

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To truly address the many open questions that persist in Mathematical General Relativity, one cannot restrict oneself to smooth metrics and strong notions of convergence.   One must apply Lebesgue, Sobolev, Sormani-Wenger Intrinsic Flat, and possibly Gromov-Hausdorff convergence to handle sequences of manifolds that naturally arise when studying notions of mass.  These weak notions of convergence and perhaps others are needed to rigorously define stability and almost rigidity in both Riemannian and Lorentzian General Relativity.  It has become increasingly important to define low regularity metrics and explicitly describe how they may be considered as having nonnegative scalar curvature, or more generally satisfying Einstein’s Equation or the Constraint Equations.  This workshop brings together geometers with results on convergence in low regularity with geometric analysts specializing in low regularity general relativity.

 

Talk Schedule


Time Title Speaker Location
9:00am introduce topics Christina Sormani SCGP 102
10:00am Tea N/A SCGP Cafe
10:30am “On the stability of the positive mass theorem for asymptotically
hyperbolic graphs”		 Armando Cabrera SCGP 102
11:15am Noncollapsed degeneration of Einstein 4-manifolds Tristan Ozuch SCGP 102
12:00pm Ellipticity of Bartnik boundary data for vacuum spacetimes Zhongshan An SCGP 102
12:45pm Lunch N/A SCGP Cafe
2:15pm Compactness Theorem for Rotationally Symmetric Riemannian Manifolds with Positive Scalar Curvature. Part 2 Changliang Wang
3:00pm Compactness Theorem for Rotationally Symmetric Riemannian Manifolds with Positive Scalar Curvature. Part 1 Wenchuan Tian SCGP 102
3:30pm Tea Time N/A SCGP Cafe
4:00pm Low regularity aspects of the Jang equation Anna Sakovich SCGP 102

Time Title Speaker Location
9:00am Conformal groups of pseudo-Finsler structures Abdelghani Zeghib SCGP 102
10:00am Tea N/A SCGP Cafe
10:30am Flat and intrinsic flat convergence of graphical tori with lower
scalar curvature bounds. Part 1		 Christian Ketterer SCGP 102
11:15am Flat and intrinsic flat convergence of graphical tori with lower
scalar curvature bounds. Part 2		 Raquel Perales Aguilar scgp 102
11:45am lunch N/A SCGP Cafe
1:00pm SCGP Weekly Talk: Philippe LeFloch SCGP Weekly Talk: Philippe LeFloch 102
2:15pm Well-posed viscous cosmology? Open questions and first steps Shabnam Beheshti SCGP 102
3:00pm 4-dimensional cobordisms of positive scalar curvature and metric singularities Demetre Kazaras scgp 102
3:30pm Tea Time N/A SCGP Cafe
4:00pm An optimal transport formulation of the Einstein equations of general relativity Andrea Mondino SCGP 102

Time Title Speaker Location
9:00am Entropy Rigidities for RCD Space Xianzhe Dai SCGP 102
10:00am Tea N/A SCGP Cafe
10:30am Alexandrov geometry for Lorentzian-pseudometrics Stephanie Alexander SCGP 102
11:45am Simple Characterization of the Causal Boundary and Continuous Extension of the Spacetime Metric Stacey Harris SCGP 102
12:45pm lunch N/A SCGP Cafe
2:15pm Lorentzian length spaces Clemens Saemann SCGP 102
3:00pm Spacetime Extensions of the Big Bang Eric Ling SCGP 102
3:30pm Tea Time N/A SCGP Cafe
4:00pm The Conformal Method in Low Sobolev Regularity David Maxwell SCGP 102

Time Title Speaker Location
9:00am Global evolution of self-gravitating matter in T2 symmetry Bruno Le Floch SCGP 102
10:00am Tea N/A SCGP Cafe
10:30am Constrained deformations of manifolds with positive scalar curvature metrics Chao Li SCGP 102
11:45am Embedding of metric measure spaces in L^2 via heat kernel Shouhei Honda SCGP 102
12:45pm Lunch N/A SCGP Cafe
2:15pm The Einstein-Infeld-Hoffmann legacy in mathematical relativity Michael Kiessling SCGP 102
3:00pm Energy-momentum conservation for spacetimes with singularities Annegret Yvonne Burtscher SCGP 102
3:30pm Tea Time N/A SCGP Cafe
4:00pm Semi-local simple connectedness of non-collapsing Ricci limit spaces Guofang Wei SCGP 102

Time Title Speaker Location
9:00am “null mean curvature” flow and marginally outer trapped surfaces. Theodora Bourni SCGP 102
10:00am Tea N/A SCGP Cafe
10:30am Stationary Vacuum Black Holes in Higher Dimensions Marcus Khuri SCGP 102
11:45am Lower semicontinuity of ADM mass under Sormani-Wenger convergence Dan Lee SCGP 102
12:45pm Lunch N/A SCGP Cafe
2:15pm Quantum Laws of Motion for Singularities of Spacetime A. Shadi Tahvildar-Zadeh SCGP 102
3:30pm Tea Time N/A SCGP Cafe
4:00pm   Closing Discussion SCGP 102