Le groupe de Brauer d'une surface d'Enriques S (quotient d'une surface K3 X par une involution)a un seul élément non trivial. Cet élément devient-il trivial sur X ? Je caractériserai les surfacespour lesquelles cela se produit, et montrerai qu'elles forment une réunion dénombrabled'hypersurfaces dans l'espace des modules.
Since the basic work of Peierls it is common consensus thatweakly nonlinear wave equations with random initial data can be wellapproximated by a kinetic equation. I will explain the precise conjecture.I will also discuss my recent joint work with J. Lukkarinen, where wecontrol the kinetic limit in special cases for the lattice nonlinearSchroedinger equation.
We describe recent theoretical and experimental progress on making objects invisible to detection by electromagnetic waves, acoustic waves and matter waves. For the case of electromagnetic waves, Maxwell's equations have transformation laws that allow for design of electromagnetic materials that steer light around a hidden region, returning it to its original path on the far side. Not only would observers be unaware of the contents of the hidden region, they would not even be aware that something was being hidden. The object, which would have no shadow, is said to […]
Inverse transport consists of reconstructing the optical parameters in a transportequation from knowledge of a measurement operator. We review several uniqueness andstability results obtained in the context of various boundary measurements as they arisee.g. in optical tomography, a medical imaging modality. Accurate numerical reconstructionsobtained by carefully capturing the singularities of the measurement operator are also brieflypresented.In many practical settings, the typical boundary measurements available in inversetransport do not allow us to reconstruct the optical parameters with sufficient resolution.In the second part of the talk, I present recent results obtained for […]
K-theoretic Gromov-Witten invariants are holomorphic Euler characteristicsof various interesting vector bundles over Kontsevich's moduli spaces ofstable maps.The problem of computing these invariants is well-motivated by examples offlag manifolds, where quantum K-theory turned out to be related toquantum groups and finite-difference versions of Toda lattices (prettymuch the same way as quantum cohomology theory of flag manifolds isrelated to semisimple Lie groups and differential Toda lattices).Although it seems natural to express K-theoretic Gromov-Witten invariantsin terms of the usual (cohomological) ones by means of the formula ofRiemann-Roch-Hirzebruch, there has been little success in […]
C'est le fameux théorème d'Assouad sur le plongement dans l'espace euclidien d'espaces de dimension d'Assouad finie.
Travail joint avec Damien Lamberton. Nous avons revisité de très anciennes familles d'algorithmes d'apprentissage, issues de la psychologie mathématique et des automates d'apprentissage et connues en approximation stochatique récursive pour leur comportement atypique et longtemps mal élucidé. Dans leur forme historique, la problématique est plutôt ici de détecter on line le meilleur des bras d'un bandit, plutôt que de maximiser le gain que l'on retire à les actionner. Nous analyserons le comportement de ces procédures en termes de convergence et de vitesse. Diverses extensions (en cours) seront aussi évoquées si […]
Difféomorphismes du cercle, de Poincaré à aujourd'hui
