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Mathematical Problems in General Relativity: January 19 – 23, 2015

Organized by Philippe LeFloch, Mike Anderson, Sergiu Klainerman, and Jared Speck

Dates: January 19 – 23, 2015

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Einstein’s field equation of general relativity is one of the most important geometric partial differential equations. Over the past decade, the mathematical research on Einstein equation has made spectacular progress on many fronts, including the Cauchy problem, cosmic censorship, and asymptotic behavior. These developments have brought into focus the deep connections between the Einstein equation and other important geometric partial differential equations, including the wave map equation, Yang-Mills equation, Yamabe equation, as well as Hamilton’s Ricci flow. The field is of growing interest for mathematicians and of intense current activity, as is illustrated by major recent breakthroughs concerning the uniqueness and stability of black hole models, the formation of trapped surfaces, and the bounded L2 curvature problem. The themes of mathematical interest that will be particularly developed in the present Program include the formation of trapped surfaces and the nonlinear interaction of gravitational waves. The new results are based on a vast extension of the earlier technique by Christodoulou and Klainerman establishing the nonlinear stability of the Minkowski space. This Program will be an excellent place in order to present the recent breakthrough on the bounded L2 curvature problem for the Einstein equation, which currently provides the lower regularity theory for the initial value problem, as well as the recently developed theory of weakly regular Einstein spacetimes with distributional curvature.

This workshop is a part of the Spring 2015 program, Mathematical Problems in General Relativity, which is organized by Philippe LeFloch, Mike Anderson, Sergiu Klainerman, and Jared Speck. This program takes place from January 5 – February 6, 2015.

First day of the workshop (January 19th, 2015) is the U.S. holiday of Martin Luther King Day. This will be an informal day during the workshop.

Workshop Application is now closed.

 

Mathematical Problems in General Relativity Workshop Schedule


Time Title Presenters Video
9:30am Linear instability of the Cauchy horizon in subextremal Reissner-Nordström spacetime under scalar perturbations Sung-Jin Oh video
10:30am Coffee Break
11:00am Stationarity of Time-Periodic Vacuum Spacetimes Volker Schlue video
12:00pm Lunch
1:30pm The Euler–Maxwell system for electrons: global solutions in 2D Alexandru Ionescu video
3:00pm Concentration Compactness for the Critical Maxwell Klein Gordon Equation Joachim Krieger video
slides
5:00pm Della Pietra Lecture Series and Reception, “The Story of Flat Surfaces” Etienne Ghys video

Time Title Presenters Video
9:30am Two Results on Formation of Trapped Surfaces Xinliang An video
slides
10:30am Coffee Break
11:00am The Dirac electron and the Kerr-Newman spacetime A. Shadi Tahvildar-Zadeh video
slides
12:00pm Lunch
1:30pm Lecture Mihalis Dafermos video
slides
3:00pm Asymptotically Hyperbolic Shear-Free Solutions of the Einstein Constraint Equations James Isenberg video

Time Title Presenters Video
9:30am Stability in exponential time of Minkowski Cécile Huneau video
10:30am Coffee Break
11:00am Vector field methods for transport equations with applications to the
Vlasov-Poisson system.
Jacques Smulevici video
12:00pm Lunch
1:30pm Quasi-local angular momentum and the limit at infinity Mu-Tao Wang video
3:00pm The Penrose inequality for perturbations of the Schwarzschild exterior Spyros Alexakis video
6:00pm Workshop Banquet Dinner

Time Title Presenters Video
9:30am Pointwise decay for the Maxwell system on black holes Mihai Tohaneanu video
10:30am Coffee Break
11:00am Lecture Qian Wang video
12:00pm Lunch
1:30pm Revisiting decay of fields outside a Schwarzschild black hole Peter Blue video
3:00pm Weak solutions to the Einstein equations in spherical or T2 symmetry Phillipe LeFloch video


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