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Lars Andersson - Geometry and analysis in black hole spacetimes (Part 1)


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Lars Andersson - Geometry and analysis in black hole spacetimes (Part 1)

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.
 

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 Lars Andersson - Geometry and analysis in black hole spacetimes (Part 3)
 Lars Andersson - Geometry and analysis in black hole spacetimes (Part 4)
 Lars Andersson - Symmetry operators and energies
 Alessandro Giacomini - Free discontinuity problems and Robin boundary conditions
 Bernd Kirchheim - Equidimensional isometric maps
 Gian Paolo Leonardi - Towards a unified theory of surface discretization
 Bruno Lévy - A numerical algorithm for L2 semi-discrete optimal transport in 3D
 Xiangyu Liang - An example of proving Almgrem's minimality by product of paired calibrations
 Andrew Lorent - The Aviles-Giga functional: past and present
 Francesco Maggi - A quantitative description of almost constant mean curvature hypersurfaces
 Matteo Novaga - Nonlocal isoperimetric problems
 Guy David - Minimal sets (Part 2)
 Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 1)
 Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 2)
 Guy David - Minimal sets (Part 3)
 Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 3)
 Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 4)
 Camillo De Lellis - Center manifolds and regularity of area-minimizing currents (Part 5)
 Joseph Fu - Integral geometric regularity (Part 1)
 Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 1)
 Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 2)
 Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 3)
 Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 4)
 Yoshihiro Tonegawa - Analysis on the mean curvature flow and the reaction-diffusion approximation (Part 5)
 Tatiana Toro - Geometry of measures and applications (Part 1)
 Tatiana Toro - Geometry of measures and applications (Part 2)
 Tatiana Toro - Geometry of measures and applications (Part 3)
 Tatiana Toro - Geometry of measures and applications (Part 4)
 Tatiana Toro - Geometry of measures and applications (Part 5)
 Joseph Fu - Integral geometric regularity (Part 2)
 Joseph Fu - Integral geometric regularity (Part 3)
 Joseph Fu - Integral geometric regularity (Part 4)
 Joseph Fu - Integral geometric regularity (Part 5)
 Andrea Braides - Geometric measure theory issues from discrete energies
 Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 2)
 Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 3)
 Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 4)
 Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 5)
 Nicholas Alikakos - On the structure of phase transition maps : density estimates and applications
 Elie Bretin - About phase field method to approximate the willmore flow
 Guy David - Minimal sets (Part 1)
 Giovanni Alberti - Introduction to minimal surfaces and finite perimeter sets (Part 1)
FMSH
 
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