Yvonne Choquet-Bruhat: a Mathematician in Einstein’s Universe

• Thibault Damour (IHES)

Room: Centre de conférences Marilyn et James Simons Yvonne Choquet-Bruhat has made fundamental contributions to both the mathematical and the physical understanding of Einstein's theory of gravitation. I will briefly summarize some of her achievements including: 1. The first proof of the existence of general (non-analytic) solutions of Einstein's theory, including the first rigorous proof that they involve propagation phenomena at the velocity of light, i.e. gravitational waves; 2. Studies of relativistic fluids and of relativistic magneto-hydrodynamics; 3. A study of the exceptional properties of strong high-frequency gravitational waves; 4. Positivity of mass in a neighborhood of Minkowski space; 5. Causality of supergravity and study of Gauss-Bonnet gravity; 6. Existence proofs for classes of cosmological spacetimes; and 7. New formulations of Einstein's equations proved crucial to the possibility of numerically simulating the motion and gravitational radiation of coalescing binary black holes.

On the Canonical Geometric Structure of Initial Data for the Einstein Equations

• Michael Eichmair (University of Vienna)

Room: Centre de conférences Marilyn et James Simons I will start my talk with an overview of recent results on canonical geometric foliations of asymptotically flat Riemannian manifolds that complete a program initiated by G. Huisken and S.-T. Yau in the early nineties. I will explain how these results are closely tied to what I call effective versions of the positive mass theorem. In the second half of my talk, I will focus on a related conjecture due to R. Schoen on the minimal surface proof of the positive mass theorem, its solution in three space dimensions in my joint work with O. Chodosh, as well as the proof of an important special case of the conjecture and counterexamples to the general conjecture in higher dimensions in joint work with T. Koerber.

High Frequency Gravitationnal Waves and Einstein Equations with U(1) Symmetry

• Cécile Huneau (École polytechnique)

Room: Centre de conférences Marilyn et James Simons In this talk, I will present two works of Yvonne Choquet-Bruhat. The first one, written in 1969, concerns the behaviour of high-frequency gravitationnal waves, and enlighten the beautiful structure of Einstein equations. She has subsequently generalized this work to Einstein equations coupled with other fields (electromagnetic, fluid...). The second more recent work I will speek about concerns the global existence of cosmological solutions with U(1) symmetry, with the introduction of the elliptic gauge. I will then present a work in collaboration with Jonathan Luk, about high-frequency solutions of Einstein equations with U(1) symmetry, in which the elliptic gauge is a very nice setting to study the superposition of waves.

Mathematical GR Seventy Two Years after Yvonne's Foundational Acta Paper

• Sergiu Klainerman (Princeton University)

Room: Centre de conférences Marilyn et James Simons I will try to review some of the main achievements in mathematical general relativity, field which has its origin in Y.C. Bruhat's foundational Acta paper: "Théorème d’existence pour certains systèmes d’equations aux dérivées partielles non-linéaires."