Prochainement




Jeudi 7 mai 11:00-12:00 Olivier Graf (Laboratoire Jacques-Louis Lions)
The spacelike-characteristic Cauchy problem with bounded L2 curvature in general relativity

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Lieu : Salle 3L8

Résumé : In this talk I will review the classical Cauchy problem for
Einstein equations. I will explain some of its geometric features and
recast the equations as a system of coupled quasilinear
transport-elliptic-Maxwell equations. I will present the global-in-time
existence conjecture (aka the conjecture of weak cosmic censorship) and
how low regularity local existence results (as the celebrated bounded L2
curvature theorem) can be used to get insight on the formation of
singularities. I will then review the classical bounded L2 curvature
theorem of Klainerman-Rodnianski-Szeftel and present a version
generalised to initial data posed on an initial spacelike and an initial
characteristic hypersurface that I obtained jointly with Stefan Czimek.
The talk will be in English and presented purely from a PDEist perspective.

The spacelike-characteristic Cauchy problem with bounded L2 curvature in general relativity  Version PDF


Jeudi 18 juin 11:00-12:00 Jose Palacios Armesto (Université de Tours)
Séminaire des doctorants ANH et ANEDP (T.B.A)

Passés


Vendredi 13 mars 14:00-15:00 Jiao He 
[Reporté]

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Lieu : Salle 3L8

Résumé : Les équations de Saint-Venant sont largement utilisées en géophysique pour décrire les courants de marées par example, et plus récemment pour décrire les interactions vague-structure. Cet exposé commencera par rappeler la dérivation des équations de Saint-Venant et leurs propriétés. Je présenterai ensuite l’interaction des vagues décrite par les équations de Saint-Venant avec deux obstacles : le premier obstacle est un topographe et le deuxième obstacle est un object flottant sur la surface. Nous monterons que ce problème peut être réduit à deux problèmes de transmission. Nous aborderons par ailleurs la résolution numérique de ces équations.
Modelling and simulation of fluid-structure interaction :
Nonlinear shallow water equations are widely used for applications in coastal oceanography and more recently for the description of wave-structure interactions. This talk will begin by recalling the derivation of the shallow water water equations and the properties of their solutions. Then, I will present the interaction of wave described by the nonlinear shallow water equations with two obstacles : the first obstacle is a step in the topography while the second obstacle is a floating object. We show that the problem can be reduced to two simple transmission problems, and we show how to solve it numerically.

[Reporté]  Version PDF

Mardi 10 mars 11:00-12:00 Nir Schwartz  (LMO)
The fractal uncertainty principle and applications

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Lieu : Salle 3L8

Résumé : In 1927 Heisenberg has introduced a fundamental result in quantum mechanics — the uncertainty principle. Heisenberg’s result tells that a wave function cannot be localized simultaneously both in position and in momentum. We introduce a recent extension of the result due to Dyatlov and Bourgain adapted to the settings of « fractal » sets. We survey briefly their result and present several applications of it to problems in quantum chaos and to semi-classical analysis.

The fractal uncertainty principle and applications  Version PDF

Jeudi 27 février 11:00-12:00 The Anh Ta  (LMO)
Rigid equivalence of Levi degenerate hypersurfaces in complex dimension 3

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Lieu : Salle 3L8

Résumé : Poincaré observed that general analytic hypersurfaces in complex space of dimension at least 2 are not equivalent under biholomorphisms.
This raises the question of finding biholomorphic invariants and constructing normal forms for hypersurfaces in complex spaces.
After the works of E. Cartan and of Chern-Moser, a fully developed theory is now available for Levi nondegenerate hypersurfaces,
while the class of Levi degenerate hypersurfaces is still the subject of current researches.
In this talk, we review the developments of the subject and outline recent results in our joint works with Z. Chen, W.-G. Foo and J. Merker.

Rigid equivalence of Levi degenerate hypersurfaces in complex dimension 3  Version PDF