Du 18 au 20 septembre 2014
IRMA
La 94ème rencontre entre mathématiciens et physiciens théoriciens aura pour thème : Riemann, Einstein, et la géométrie.
The 94th Encounter between Mathematicians and Theoretical Physicists will take place at Institut de Recherche Mathématique Avancée (University of Strasbourg and CNRS) on September 18-20, 2014. The theme will be : "Riemann, Einstein and geometry".
Organizers : Athanase Papadopoulos (Strasbourg) and Sumio Yamada (Tokyo)
The invited speakers include :
- Jean-Pierre Bourguignon (Paris)
- Mihalis Dafermos (Princeton)
- Erwann Delay (Avignon)
- Jacques Franchi (Strasbourg)
- Hubert Goenner (Göttingen)
- Eric Gourgoulhon (Observatoire de Paris)
- Oussama Hijazi (Nancy)
- Gerhard Huisken (Tübingen)
- Emmanuel Humbert (Tours)
- Marc Mars (Salamanca)
- Andre Neves (Imperial College, London)
- Jean-Philippe Nicolas (Brest)
- Jean-Marc Schlenker (Luxembourg)
- Richard Schoen (UC Irvine)
- Tetsuya Shiromizu (Kyoto)
The content of this conference has been published by Springer here and is also avalaible on ArXiv.
Graduate students and young mathematicians are welcome. Registration is required (and free of charge) at this link. Hotel booking can be asked for through the registration link.
List of participants (see here)
For practical and other questions please contact the organizers :
- Athanase Papadopoulos : athanase.papadopoulos@math.unistra.fr
- Sumio Yamada : yamada@math.gakushuin.ac.jp
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Jeudi 18 septembre 2014
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09:00
Richard Schoen, UC Irvine
The impact of General Relativity on Riemannian Geometry
Abstract.--- While it is true that the ideas of Riemann were put to use by Einstein in the formulation of the theory of General Relativity, there have also been important applications of ideas originating in General Relativity to Riemannian Geometry. These include much of our understanding of the behavior of scalar curvature. In this survey talk we will describe this interaction for a general audience. -
10:00
Pause -
10:30
Marc Mars, Salamanca
Marginally outer trapped surfaces: properties, propagation and equilibrium configurations
Abstract.--- Marginally outer trapped surfaces (MOTS) are expected to be suitable quasi-local replacements of black holes. In this talk I will discuss a number of results where this expectation is analyzed in detail. I will introduce the notion of stability of MOTS and discuss some of its consequences, in particular, for the propagation of MOTS given a 3+1 decomposition of the spacetime. I will also analyze the interplay between MOTS and event horizons in stationary/static situations. -
11:30
Emmanuel Humbert, Tours
Mass of a compact manifold
Abstract.--- General relativity is a geometric theory: it is therefore not surprising that many problems of general relativity can be solved by geometric tools. But it is much more surprising that a famous problem in geometric analysis/PDEs - the Yamabe problem -was solved by Schoen using the positive mass theorem, which comes from the general relativity. Schoen's argument lead to the definition of the mass of a compact manifold. In this talk, we will present this object for a non-specialist audience and will finish by stating our recent results obtained together with Andreas Hermann. -
14:00
Eric Gourgoulhon, Observatoire de Paris
Some aspects of differential geometry in black hole spacetimes
Abstract.--- Black hole solutions of Einstein equations will be reviewed, putting forward their geometrical properties. Both exact solutions and numerical ones will be discussed, as well as the quasi-local approach, based on trapping horizons. Some focus will be put on the (null and timelike) geodesic curves. Free softwares for investigating these spacetimes will also be presented: Gyoto [1] for computing geodesics and SageManifolds [2] for symbolic tensor calculus. [1] http://gyoto.obspm.fr/ ; [2] http://sagemanifolds.obspm.fr/ -
15:00
Pause -
15:30
Hubert Goenner, Goettingen
Albert Einstein and mathematics
Abstract.--- Albert Einstein's relation to mathematics will be reviewed. The mathematical methods applied by him and the question whether he has made a genuine contribution to mathematics will be discussed. Also included is a look at his philosophical and emotional position with regard to mathematics. This talk is intended for a general audience. -
16:30
Michalis Dafermos, Princeton
TBA
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19:30
Conference Dinner Restaurant Le Petit Bois Vert
Everybody is invited
Address: 2 quai de la Bruche (quartier petite France); a map will be provided. -
Vendredi 19 septembre 2014
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09:00
Andre Neves, Imperial College (London)
Min-max theory in Geometry
Abstract.--- The first use of min-max theory in geometry was found by Birkhoff around 100 years ago. In the last years, the theory has made a comeback and has been used to solve some long standing open questions. I will survey some of its applications. This is joint work with Fernando Marques. -
10:00
Pause -
10:30
Erwann Delay, Avignon
A study of some curvature operators near the euclidean metric
Abstract.--- We first review the prescribed Ricci curvature type problem on a riemannian manifold. In the second part we will focus on the case of Rn. We will then show that some curvature operators of Ricci (or Einstein) type, are locally invertible near the euclidian metric. In the smooth case, we then deduce that the image of some Riemann-Christoffel type operators are smooth submanifolds in the neighbourhood of the euclidean metric. -
11:30
Oussama Hijazi, Nancy
On a Liu-Yau type Inequality for Surfaces
Abstract.--- We report on a recent joint work with S. Raulot and S. Montiel regarding an application of the use of the Dirac operator and its conformal covariance for surfaces in the Minkowski spacetime. -
14:30
Jean-Pierre Bourguignon, Bruxelles
TBA
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15:30
Pause -
16:00
Jean-Marc Schlenker, Luxembourg
Anti-de Sitter geometry and its connections to Teichmüller theory
Abstract.--- Anti-de Sitter (AdS) geometry is the constant curvature (-1) Lorentzian geometry, it can be considered as the Lorentzian analog of hyperbolic geometry. AdS was introduced as a solution of Einstein's equations with negative cosmological constant. There are deep connections between Teichmüller theory, the study of the space of complex structures on a surface, and 3-dimensional hyperbolic geometry. We will describe other deep connections, discovered more recently, between 3-dimensional AdS manifolds and Teichmüller theory. This talk is part of the monthly colloquium talk series at IRMA. -
Samedi 20 septembre 2014
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09:00
Jacques Franchi, Strasbourg
From Riemannian to relativistic diffusions
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10:00
Pause -
10:30
Tetsuya Shiromizu, Kyoto
Positive mass as a principle?
Abstract.--- According to recent observations, our universe is in the phase of accelerating expansion. To explain this, cosmologists are seriously thinking of introduction of dark energy models and/or modifications of gravitational theory. I will discuss the role of positive mass in such theories and see that the form of a certain theory compatible with positive mass is strongly limited. Therefore, as imposed in linearized theory, one may be able to adopt the positive mass as a new additional principle to construct the theory for dark energy/modified gravity. For such theories, stability will be automatically guaranteed in kinematical sense. -
11:30
Jean-Pierre Nicolas, Brest
The conformal approach to asymptotic analysis
Abstract.--- This talk, based on joint works with Lionel Mason, will be devoted to Roger Penrose's introduction of conformal geometric methods in general relativity in the mid 1960's and how they changed asymptotic analysis in that framework. We shall focus on two closely related aspects: scattering theory and peeling. The conformal compactification was introduced by Penrose in order to provide a natural reformulation of the notion of peeling that was initially due to Sachs. His work was interpreted as claiming that the asymptotic behaviour of test fields in flat spacetime provides a model for generic asymptotically flat situations, which triggered a long controversy. It also inspired Friedlander to propose a re-interpretation of the Lax-Phillips scattering in conformal geometric terms and alternative geometric tools for developing scattering theories. The use of conformal geometry for analyzing the asymptotic behaviour of test fields in general relativity provides flexible techniques that allow the treatment of time dependent situations. Penrose's initial formulation can be recast, using geometrical energy estimates, into an analytically robust framework ensuring optimal results. We shall explain the notion of peeling as described by Penrose, its reformulation using energy estimates and how a complete understanding of the peeling of test fields in the Schwarzschild metric can be obtained. Then we shall explain the principles of conformal scattering as developed by Friedlander and their extension to non stationary spacetimes and black hole geometries.