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BIMSA General Relativity Seminar
Stability of Minkowski space-time governed by the Einstein-Yang-Mills equations
Stability of Minkowski space-time governed by the Einstein-Yang-Mills equations
Organizers
Speaker
Time
Monday, April 29, 2024 3:30 PM - 5:00 PM
Venue
A3-4-101
Online
Zoom 559 700 6085
(BIMSA)
Abstract
I shall start by presenting the Einstein-Yang-Mills system and by writing it in the Lorenz gauge and in wave coordinates as a coupled system of non-linear hyperbolic partial differential equations, and I will then show how one constructs the initial data for a Cauchy hyperbolic formulation of the problem. Thereafter, I will present the idea behind the proof of the non-linear stability of the Minkowski space-time, solution to the Einstein-Yang-Mills equations, in the Lorenz gauge and in wave coordinates, in all space dimensions greater or equal to three, based on a continuity argument for a higher order weighted energy norm. In the critical case of three space-dimensions, we use a null frame decomposition, that was first used by Lindblad and Rodnianski for the Einstein vacuum equations. We then deal with new difficulties that do not exist for Einstein vacuum nor for Einstein-Maxwell fields. In particular, we treat new terms that have a different structure in the non-linearities, and we derive a more refined formula to estimate the commutator term. This provides a new independent proof of the result by Mondal and Yau, that I posted on arXiv in a series of three papers that build up on each other, which cover all space dimensions greater or equal to three.
Speaker Intro
Sari Ghanem had his undergraduate education at Classe Préparatoire in Toulouse and completed his Master degree in Paris, and a second Master in the USA. Thereafter, he obtained his PhD in 2014 from University of Paris VII (Institut de Mathématiques de Jussieu) under the supervision of Frédéric Hélein (Jussieu) and Vincent Moncrief (Yale University). He then worked as a postdoctoral fellow at the Albert Einstein Institute (Max-Planck Institute for Gravitational Physics), and at the University of Grenoble in France. Thereafter, he founded the Al-Khwarizmi-Noether Institute for mathematics (https://akn-institute.org/the-institute/about/) of which he was the creator and chair on a voluntary basis, and worked at the Universities of Hamburg and of Lübeck in Germany. Now, he is a research Visiting Assistant Professor at BIMSA in China.