Vendredi 28 Janvier
Heure: 
10:30  12:00 
Lieu: 
Salle B407, bâtiment B, LAGA, Institut Galilée, Université Paris 13 
Résumé: 
Géométrie Arithmétique et Motivique  On locally analytic vectors of the completed cohomology of Shimura varieties; a generalization of Lue Pan's work  
Description: 
Juan Esteban Rodriguez CamargoIn this talk we discuss a natural generalization of Pan's work on locally analytic vectors of completed cohomology. We will sketch how Sen theory provides the bridge between Dmodules over the flag variety and the HodgeTate cohomology of Shimura varieties via the HodgeTate period map. We will prove that the same method apply for the cohomology with compact supports and their duals, obtaining a description of all different completed cohomologies as the analytic cohomology of certain (locally analytic) sheaves over the infinite level Shimura variety. &nbsp;We shall mention how the understanding of Dmodules over the flag variety can be helpful to describe the Lie algebra action over the locally analytic completed cohomology. &nbsp; 
Heure: 
13:00  14:00 
Lieu: 
Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13 
Résumé: 
Modélisation et Calcul Scientifique  Existence of traveling wave solutions for the Diffusion Poisson Coupled Model: a computerassisted proof  
Description: 
Antoine Zureck In France one option under study for the storage of highlevel radioactive waste is based on an underground repository. More precisely, the waste shall be confined in a glass matrix and then placed into cylindrical steel canisters. These containers shall be placed into microtunnels in the highly impermeable CallovoOxfordian claystone layer at a depth of several hundred meters. The Diffusion Poisson Coupled Model (DPCM) aims to investigate the safety of such long term repository concept by describing the corrosion processes appearing at the surface of carbon steel canisters in contact with a claystone formation. It involves driftdiffusion equations on the density of species (electrons, ferric cations and oxygen vacancies), coupled with a Poisson equation on the electrostatic potential and with moving boundary equations. So far, no theoretical results giving a precise description of the solutions, or at least under which conditions the solutions may exist, are avalaible in the literature. However, a finite volume scheme has been developed to approximate the equations of the DPCM model. In particular, it was observed numerically the existence of traveling wave solutions for the DPCM model. These solutions are defined by stationary profiles on a fixed size domain with interfaces moving at the same velocity. The main objective of this talk is to present how we apply a computerassisted method in order to prove the existence of such traveling wave solutions for the system. This approach allows us to obtain for the first time a precise and certified description of some solutions. This work is in collaboration with Maxime Breden and Claire ChainaisHillairet. 

