Day in Honor of Yvonne Choquet-Bruhat's 100th Birthday

vendredi 8 déc. 2023, 10:30 → 18:30 Europe/Paris

Centre de conférences Marilyn et James Simons (Le Bois-Marie)

December 2023 marks Yvonne Choquet-Bruhat's 100th birthday. For this special occasion, IHES organizes a day in her honor on December 8, 2023.

Registration is free but mandatory.

Yvonne Choquet-Bruhat's work has had a long-lasting impact on the field of mathematical relativity starting with her seminal 1952 paper on the local well-posedness of Einstein equations. Her numerous contributions, both to constraint equations and to the evolution problem in general relativity, have deeply influenced several generations of researchers. This special day in her honor will be the occasion to present some of the latest developments in the field.

Invited Speakers:

• Thibault Damour, IHES  
• Michael Eichmair, University of Vienna  
• Cécile Huneau, École polytechnique
• Sergiu Klainerman, Princeton University   

Organizers: Laure Saint-Raymond (IHES) & Jérémie Szeftel (Laboratoire Jacques-Louis Lions)

10:30 Registration and Welcome Coffee

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

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.

Orateur: Prof. Thibault Damour (IHES)

Vidéo

12:00 Lunch Break

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

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.

Orateur: Prof. Michael Eichmair (University of Vienna)

Vidéo

15:00 Coffee Break

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

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.

Orateur: Prof. Cécile Huneau (École polytechnique)

Vidéo

16:30 Coffee break

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

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."

Orateur: Prof. Sergiu Klainerman (Princeton University)

Vidéo