11 janvier 2018

Sara Maloni (University of Virginia)
The geometry of quasi-Hitchin symplectic Anosov representations

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Lieu : IMO, salle 2L8

Résumé : In this talk we will focus on our joint work in progress with Daniele Alessandrini and Anna Wienhard about quasi-Hitchin representations in Sp(4,C), which are deformations of Fuchsian representations which remain Anosov. These representations acts on the space Lag(C^4) of complex lagrangian subspaces of C^4. We will show that the quotient of the domain of discontinuity for this action is a fiber bundle over the surface and we will describe the fiber. In particular, we will describe how the projection map comes from an interesting parametrization of Lag(C^4) as the space of regular ideal hyperbolic tetrahedra and their degenerations.

Notes de dernières minutes : Café culturel assuré à 13h par Daniel Monclair

The geometry of quasi-Hitchin symplectic Anosov representations  Version PDF

Quentin Berger (LPMA)
Localisation pour un polymère dirigé dans un environnement aléatoire

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Lieu : salle 3L15

Résumé : Le modèle de polymère dirigé en environment aléatoire, introduit il y a plus de 30 ans et intensément étudié depuis, est utilisé pour décrire un polymère interagissant avec les impuretés d’un milieu hétérogène. On présentera dans cet exposé une brève histoire de ce modèle, et on s’intéressera plus particulièrement au phénomène de localisation des trajectoires, le polymère ‘’s’étirant’’ pour atteindre des régions plus favorables de l’environnement. La question de décrire de manière précise les trajectoires localisées (exposant de super-diffusivité, limite d’échelle, etc...) est en grande partie ouverte. On considérera cependant le cas d’un environnement à queue de distribution lourde, où ces résultats s’avèrent accessibles. (Travail en collaboration avec Niccolò Torri.)

Localisation pour un polymère dirigé dans un environnement aléatoire  Version PDF

Luca Calatroni (Ecole Polytechnique)
Anisotropic image osmosis models for visual computing

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Résumé : We consider a drift-diffusion PDE modelling the non-symmetric physical phenomenon of osmosis (Weickert, ’13) and apply it to solve efficiently several imaging tasks such as image cloning, image compression and shadow removal. For the latter problem, in order to overcome the smearing artefacts on the shadow boundary due to the action of the Laplace operator, we extend the linear model by means of directional diffusion weights allowing for a combined osmosis and non-linear inpainting procedure. In particular, analogies with the second order diffusion inpainting equations (e.g. Harmonic, Absolutely Minimising Lipschitz Extensions, Total Variation) and connections with Grushin operators are shown. Numerical details on the efficient implementation of the model via appropriate stencils mimicking the anisotropy at a discrete level are presented and applications to camera and cultural heritage conservation images are also presented.

Anisotropic image osmosis models for visual computing  Version PDF

Simão Correia (Université de Strasbourg)
Some new local and global well-posedness results for the nonlinear Schrödinger equation

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Lieu : IMO, Salle 3L8

Résumé : In this presentation, we shall consider the nonlinear Schrödinger equation on \mathbb{R}^d,

iu_t + \Delta u + \lambda |u|^\sigma u = 0

with an initial condition at t=0. This is already a classical equation, with a vast literature regarding the behaviour of the solutions to this problem. We discuss the extension of the H^1 local well-posedness theory to some larger spaces which, in particular, do not lie inside L^2. As a byproduct, we develop the theory for the plane wave transform, which is of independent mathematical interest. If time allows, we present some global existence results, which either rely on a small data theory or on the concept of finite speed of disturbance.

Some new local and global well-posedness results for the nonlinear Schrödinger equation  Version PDF