3 février 2021

Antoine Meddane (Nantes)
Théorème des variétés stables

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Lieu : https://bbb.imo.universite-paris-saclay.fr/b/nic-jog-f24-z6j

Résumé : La dynamique hyperbolique désigne un cas particulier de dynamique non-linéaire où de puissants outils (théorème de Hadamard-Perron, théorème de Hartman-Grobman) permettent d’étudier le comportement qualitatif des solutions. Dans un cadre simplifié, je présenterai une démonstration du théorème des variétés stables tirée des « notes on hyperbolic dynamics » de Semyon Dyatlov. Je ferai également quelques liens avec la topologie.

Théorème des variétés stables  Version PDF

Othmane Jerhaoui (UMA, Ensta.)
Optimal control and Hamilton Jacobi Bellman equations on stratified domains

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Lieu : Salle 2L8

Résumé : In this talk, we are interested in some control problems on stratified domains. In such problems, the state variable space is partitioned in different open sets separated by an interface, that is a collection of lower dimensional manifolds. Each open region is associated with a compact control set, a controlled dynamics and a cost function. The simplest example of such structures (in dimension 2) is two open and disjoint half planes with a common boundary which is a line. We are interested in characterizing the value function of the optimal control problem as the solution to an adequate Hamilton-Jacobi equation. More precisely, we prove that an essential Hamiltonian characterizes both the sub and super solutions. Finally, we show that a strong comparison principle holds even when the solution in the viscosity sense (the value function) is only lower semicontinuous.

Notes de dernières minutes : Replay : https://scalelite.lal.cloud.math.cnrs.fr/playback/presentation/2.0/playback.html++cs_INTERRO++meetingId=07328e5495597cd77347ced584539447d62e46a3-1612362802230

Optimal control and Hamilton Jacobi Bellman equations on stratified domains  Version PDF

Valentino Tosatti (McGill)
Smooth asymptotics for collapsing Ricci-flat metrics

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Lieu : Demander le lien Zoom à jean-michel.bismut@universite-paris-saclay.fr

Résumé : I will discuss the problem of understanding the collapsing behavior of Ricci-flat Kahler metrics on a Calabi-Yau manifold that admits a holomorphic fibration structure, when the Kahler class degenerates to the pullback of a Kahler class from the base. I will present new work with Hans-Joachim Hein where we obtain a priori estimates of all orders for the Ricci-flat metrics away from the singular fibers, as a corollary of a complete asymptotic expansion.

Smooth asymptotics for collapsing Ricci-flat metrics  Version PDF