14 février 2019

Philippe Gravejat (Université de Cergy-Pontoise)
Dérivation de régimes asymptotiques pour l’équation de Landau-Lifshitz

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Lieu : IMO, Salle 3L8

Résumé : L’équation de Landau-Lifshitz rend compte de la dynamique de l’aimantation dans les matériaux ferromagnétiques. L’objectif de cet exposé est de présenter la dérivation rigoureuse de deux régimes asymptotiques de cette équation : l’un vers l’équation de Sine-Gordon, l’autre vers celle de Schrödinger cubique. Il s’agit de deux travaux en collaboration avec André de Laire (Université de Lille)

Dérivation de régimes asymptotiques pour l’équation de Landau-Lifshitz  Version PDF

Kate Vokes (IHES)
Hierarchical hyperbolicity of graphs associated to surfaces

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Lieu : Salle 2L8 (IMO, bâtiment 307)

Résumé : In the study of mapping class groups of surfaces, an important tool is the action of the mapping class group on various infinite diameter graphs associated to the surface. A key example of such a graph is the curve graph, shown by Masur and Minsky to be Gromov hyperbolic. Further work of Masur and Minsky described properties of the large scale geometry of mapping class groups in terms of projections to curve graphs of subsurfaces, later inspiring the definition by Behrstock, Hagen and Sisto of hierarchically hyperbolic spaces, which have an analogous structure. I will give some background on these concepts and present a result showing that many graphs whose vertices represent multicurves in a surface are hierarchically hyperbolic.

Notes de dernières minutes : Le café culturel sera assuré à 13h par Camille Horbez.

Hierarchical hyperbolicity of graphs associated to surfaces  Version PDF

Pascal Maillard (LMO)
The algorithmic hardness threshold for continuous random energy models

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Résumé : I will report on recent work with Louigi Addario-Berry on algorithmic hardness for finding low-energy states in the continuous random energy model of Bovier and Kurkova. This model can be regarded as a toy model for strongly correlated random energy landscapes such as the Sherrington—Kirkpatrick model. We exhibit a precise and explicit hardness threshold : finding states of energy above the threshold can be done in linear time, while below the threshold this takes exponential time for any algorithm with high probability. If time permits, I further discuss what insights this yields for understanding algorithmic hardness thresholds for random instances of combinatorial optimization problems.

The algorithmic hardness threshold for continuous random energy models  Version PDF

Clément Cosco (Université Paris Diderot, LPSM. )
Gaussian Fluctuations and Rate of Convergence of the Kardar-Parisi-Zhang equation in Weak Disorder in d ≥ 3

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Lieu : 3L15

Résumé : Trying to give a proper definition of the KPZ (Kardar-Parisi-Zhang) equation in dimension d ≥ 3 is a challenging question. A plan to do so, is to first consider the well-defined KPZ equation when the white noise is smoothed in space. For d ≥ 3 and small noise intensity, the solution is known to converge to some random variable as the smoothing is removed. It is also known that the limiting random variable can be related to the free energy of a Brownian polymer, in a smoothed white noise environment. In this talk, we will state some recent results about the fluctuations of the convergence of the solution. In particular, we will show that the fluctuation of the solution, around the rescaled free energy of the polymer, converges pointwise towards a Gaussian limit.
(joint work with Francis Comets and Chiranjib Mukherjee).

Gaussian Fluctuations and Rate of Convergence of the Kardar-Parisi-Zhang equation in Weak Disorder in d ≥ 3  Version PDF