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# Résultats de recherche

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## Joseph Fu - Integral geometric regularity (Part 5)

In the original form given by Blaschke in the 1930s, the famous Principal Kinematic Formula expresses the Euler characteristic of the intersection of two sufficiently regular objects in euclidean space, integrated over the space of all possible relative positions, in terms of geometric invariants associated to each of them individually. It is natural to wonder about the precise regularity needed for this to work. The question turns on the existence of the normal cycle of such an object A, i.e. an integral current that stands ... Voir la vidéole (2h2m57s)

## 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 ... Voir la vidéole (2h56s)

## Lars Andersson - Geometry and analysis in black hole spacetimes (Part 2)

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 theEinstein equations, I will give some background on geometry of the Kerr spacetime. Theanalysis 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 ... Voir la vidéole (2h13m24s)

## Lars Andersson - Geometry and analysis in black hole spacetimes (Part 3)

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 theEinstein equations, I will give some background on geometry of the Kerr spacetime. Theanalysis 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 ... Voir la vidéole (1h55m56s)

## Lars Andersson - Geometry and analysis in black hole spacetimes (Part 4)

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 theEinstein equations, I will give some background on geometry of the Kerr spacetime. Theanalysis 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 ... Voir la vidéole (59m58s)

## Lars Andersson - Symmetry operators and energies

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 theEinstein equations, I will give some background on geometry of the Kerr spacetime. Theanalysis 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 ... Voir la vidéole (1h55m38s)

## Rod Gover - An introduction to conformal geometry and tractor calculus (Part 1)

After recalling some features (and the value of) the invariant ``Ricci calculus'' of pseudo-‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal ... Voir la vidéole (2h4m58s)

## Rod Gover - An introduction to conformal geometry and tractor calculus (Part 2)

After recalling some features (and the value of) the invariant ``Ricci calculus'' of pseudo-‐Riemannian geometry, we look at conformal rescaling from an elementary perspective. The idea of conformal covariance is visited and some covariant/invariant equations from physics are recovered in this framework. Motivated by the need to develop a more effective approach to such problems we are led into the idea of conformal geometry and a conformally invariant calculus; this``tractor calculus'' is then developed explicitly. We will discuss how to calculate using this, and touch on applications to the construction of conformal invariants and conformally invariant differential operators. The second ... Voir la vidéole (1h58m33s)