Applied Mathematics Seminar

See the Google Agenda of the seminar, and add the iCal url to your calendar.


Titus van Erp (Norwegian University of Science and Technology)

Thursday, December 19th, 10h — Salle de séminaire du CERMICS

Replica Exchange Transition Interface Sampling

Nearly 20 years ago, transition path sampling (TPS) emerged as an alternative method to free energy based approaches for the study of rare events such as nucleation, protein folding, chemical reactions, and phase transitions. TPS effectively performs Monte Carlo simulations with relatively short molecular dynamics trajectories, with the advantage of not having to alter the actual potential energy surface nor the underlying physical dynamics. Although the TPS approach also introduced a methodology to compute reaction rates, the efficiency got considerably improved by the transition interface sampling (TIS) and the replica exchange TIS (RETIS) algorithms. In this talk, I will discuss the principles of the RETIS approach and show a recent application of the method for the study of water dissociation. I will also present a method for the analyses of the path data which allows the identification of reaction triggers at an early stage of the reaction.


Nicolas Bouleau (École des Ponts)

Thursday, January 16th, 10h — Salle de séminaire du CERMICS

Théorie des erreurs

En calcul des structures, en automatique, en traitement du signal, en statistiques, en mathématiques financières, dans le guidage par satellites ou la prévision du climat, ou encore en mécanique quantique, il était devenu nécessaire d’élaborer de nouvelles méthodes de calcul d’erreur, fondées sur des bases mathématiques rigoureuses. Ces outils nouveaux sont adaptés au célèbre calcul d’Ito et aux processus aléatoires qu’on peut construire à partir du mouvement brownien – c’est avec les mêmes idées que Paul Malliavin est parvenu à améliorer le théorème de Hörmander sur les équations elliptiques.


Max Fathi (Toulouse)

Thursday, January 23rd, 10h — Salle de séminaire du CERMICS

TBA


Laure Dumaz (CEREMADE)

Thursday, February 6th, 10h — Salle de séminaire du CERMICS

Localization of the continuous Anderson hamiltonian in 1-d and its transition

We consider the continuous Schrödinger operator – d^2/d^x^2 + B’(x) on the interval [0,L] where the potential B’ is a white noise. We study the spectrum of this operator in the large L limit. We show the convergence of the smallest eigenvalues as well as the eigenvalues in the bulk towards a Poisson point process, and the localization of the associated eigenvectors in a precise sense. We also find that the transition towards delocalization holds for large eigenvalues of order L, where the limiting law of the point process corresponds to Sch_tau, a process introduced by Kritchevski, Valko and Virag for discrete Schrodinger operators. In this case, the eigenvectors behave like the exponential Brownian motion plus a drift, which proves a conjecture of Rifkind Virag. Joint works with Cyril Labbé.


Archive of past seminars: here

Organizers: Antoine Levitt, Julien Reygner.