Tri :
Date
Editeur
Auteur
Titre


Giovanni Alberti  Introduction to minimal surfaces and finite perimeter sets (Part 4)
/ Giovanni Alberti
/ 18062015
/ Canalu.fr
Bastien Fanny
Voir le résumé
Voir le résumé
In these lectures I will first
recall the basic notions and results that are needed to study minimal
surfaces in the smooth setting (above all the area formula and the first
variation of the area), give a short review of the main (classical)
techniques for existence results, and then outline the theory of Finite
Perimeter Sets, including the
main results of the theory (compactness, structure of distributional
derivative, rectifiability). If time allows, I will conclude with a few
applications. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

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Thomas Backdahl  Symmetry operators, conserved currents and energy momentum tensors
/ Fanny Bastien
/ 04072014
/ Canalu.fr
Backdahl Thomas
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Voir le résumé
Conserved quantities, for example energy and momentum, play a fundamental role in the analysis of dynamics of particles and fields. For field equations, one manifestation of conserved quantities in a broad sense is the existence of symmetry operators, i.e. linear differential operators which take solutions to solutions. A well known example of a symmetry operator for the scalar wave equation is provided by the Lie derivative along a Killing vector field. It is important to note that other kinds of objects can generate symmetry operators. For waves in the Kerr spacetime there is a symmetry operator associated with Carter's constant. This symmetry, which is "hidden" in the sense that it arises from a Killing spinor, satisfying a generalization of the Killing vector equation, rather than a Killing vector, was an essential ingredient in a proof of decay of scalar waves on the Kerr background by Andersson and Blue. In this talk we will consider what conditions on a spacetime are necessary for existence of symmetry operators for the conformal wave equation, the Dirac Weyl equation, and the Maxwell equation, i.e. for massless test fields of spins 0, 1/2 and 1. We will investigate how the conditions for the symmetry operators for the different field equations are related, and how they are related to existence of conserved currents. Furthermore, these tools lead to the construction of a new energy momentum tensor for a Maxwell field on a Kerr background. This will provide a powerful tool for the study of decay of Maxwell fields on the Kerr spacetime. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

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Alain Bachelot  Waves in the Antide Sitter spacetime Ads
/ Fanny Bastien
/ 04072014
/ Canalu.fr
Bachelot Alain
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In this talk we address some issues concerning the wave propagation in the 4D+1 anti de Sitter space time : the role of the conformal boundary, the representation of the fields in term of Kaluza Klein tower, the existence of new dynamics associated with a family of novel boundary conditions, the linear stability of a De Sitter brane. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

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Lars Andersson  Symmetry operators and energies
/ 02072014
/ Canalu.fr
Andersson Lars
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Voir le résumé
Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity.
Following a brief introduction to the evolution problem for the
Einstein equations, I will give some background on geometry of the Kerr spacetime. The
analysis of fields on the exterior of the Kerr black hole serve as important model problems for the black hole stability problem. I will discuss some of the difficulties one encounters in analyzing waves in the Kerr exterior
and how they can be overcome. A fundamentally important as
pect of geometry and analysis in the Kerr spacetime is the fact that it is algebraically special, of Petrov type D, and therefore admits a Killing spinor of valence 2. I will introduce the 2 spinor and related formalisms which can be used to see how this structure leads to the Carter constant and the Teukolsky system. If there is
time, I will discuss in this context some new conservation laws for fields of non zero spin. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

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Lars Andersson  Geometry and analysis in black hole spacetimes (Part 3)
/ 18062014
/ Canalu.fr
Andersson Lars
Voir le résumé
Voir le résumé
Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity.
Following a brief introduction to the evolution problem for the
Einstein equations, I will give some background on geometry of the Kerr spacetime. The
analysis of fields on the exterior of the Kerr black hole serve as important model problems for the black hole stability problem. I will discuss some of the difficulties one encounters in analyzing waves in the Kerr exterior
and how they can be overcome. A fundamentally important as
pect of geometry and analysis in the Kerr spacetime is the fact that it is algebraically special, of Petrov type D, and therefore admits a Killing spinor of valence 2. I will introduce the 2 spinor and related formalisms which can be used to see how this structure leads to the Carter constant and the Teukolsky system. If there is
time, I will discuss in this context some new conservation laws for fields of non zero spin. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

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Lars Andersson  Geometry and analysis in black hole spacetimes (Part 2)
/ Fanny Bastien
/ 17062014
/ Canalu.fr
Andersson Lars
Voir le résumé
Voir le résumé
Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity.
Following a brief introduction to the evolution problem for the
Einstein equations, I will give some background on geometry of the Kerr spacetime. The
analysis of fields on the exterior of the Kerr black hole serve as important model problems for the black hole stability problem. I will discuss some of the difficulties one encounters in analyzing waves in the Kerr exterior
and how they can be overcome. A fundamentally important as
pect of geometry and analysis in the Kerr spacetime is the fact that it is algebraically special, of Petrov type D, and therefore admits a Killing spinor of valence 2. I will introduce the 2 spinor and related formalisms which can be used to see how this structure leads to the Carter constant and the Teukolsky system. If there is
time, I will discuss in this context some new conservation laws for fields of non zero spin. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

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Lars Andersson  Geometry and analysis in black hole spacetimes (Part 1)
/ Fanny Bastien
/ 16062014
/ Canalu.fr
Andersson Lars
Voir le résumé
Voir le résumé
Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity.
Following a brief introduction to the evolution problem for the
Einstein equations, I will give some background on geometry of the Kerr spacetime. The
analysis of fields on the exterior of the Kerr black hole serve as important model problems for the black hole stability problem. I will discuss some of the difficulties one encounters in analyzing waves in the Kerr exterior
and how they can be overcome. A fundamentally important as
pect of geometry and analysis in the Kerr spacetime is the fact that it is algebraically special, of Petrov type D, and therefore admits a Killing spinor of valence 2. I will introduce the 2 spinor and related formalisms which can be used to see how this structure leads to the Carter constant and the Teukolsky system. If there is
time, I will discuss in this context some new conservation laws for fields of non zero spin. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, General Relativity, institut fourier, summer school, asymptotic analysis

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Nicholas Alikakos  On the structure of phase transition maps : density estimates and applications
/ Fanny Bastien
/ 02072015
/ Canalu.fr
Alikakos Nicholas
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Voir le résumé
indisponible Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

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Giovanni Alberti  Introduction to minimal surfaces and finite perimeter sets (Part 5)
/ Fanny Bastien
/ 18062015
/ Canalu.fr
Alberti Giovanni
Voir le résumé
Voir le résumé
In these lectures I will first
recall the basic notions and results that are needed to study minimal
surfaces in the smooth setting (above all the area formula and the first
variation of the area), give a short review of the main (classical)
techniques for existence results, and then outline the theory of Finite
Perimeter Sets, including the
main results of the theory (compactness, structure of distributional
derivative, rectifiability). If time allows, I will conclude with a few
applications. Mot(s) clés libre(s) : mathématiques, Grenoble, école d'été, institut fourier, summer school, geometric measure theory, calculus of variation

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Giovanni Alberti  Introduction to minimal surfaces and finite perimeter sets (Part 1)
/ Fanny Bastien
/ 15062015
/ Canalu.fr
Alberti Giovanni
Voir le résumé
Voir le résumé
In
these lectures I will first recall the basic notions and results that
are needed to study minimal surfaces in the smooth setting (above all
the area formula and the first variation of the area), give a short
review of the main (classical) techniques for existence results, and
then outline the theory of Finite Perimeter Sets, including
the main results of the theory (compactness, structure
of distributional derivative, rectifiability). If time allows, I
will conclude with a few applications.
Mot(s) clés libre(s) : Grenoble, école d'été, mathématique, institut fourier, summer school, geometric measure theory, calculus of variation

Accéder à la ressource

