Séminaires : Séminaire de Systèmes Dynamiques

Equipe(s) : gd,
Responsables :H. Eliasson, B. Fayad, R. Krikorian, P. Le Calvez
Email des responsables :
Salle : 15-25-502
Adresse :Campus Pierre et Marie Curie

Archive avant 2015

Hébergé par le projet Géométrie et Dynamique de l’IMJ

Orateur(s) Giovanni Forni (Maryland) - Sur la vitesse de mélange pour les reparamétrages des flots d'Heisenberg,
Titre ATTENTION : SEANCE ANNULEE --Effective ergodicity of higher step nilflows and bounds on Weyl sums
Horaire14:00 à 16:00
The best known upper bound on Weyl sums for higher degree polynomials were derived by Bourgain, 
Demeter and Guth from their proof (2015) of Vinogradov  ''Main Conjecture''   (on the number of integral solutions 
of certain Diophantine equations). A similar, slightly weaker, bound follows from T. Wooley's series of results 
(in the 2010's) on the ''Main Conjecture''.   
In joint work with L. Flaminio we gave a direct proof (2014) of a similar bound for Weyl sums based on ideas  from
dynamical systems (cohomological equations for nilflows, renormalization), but only for a full measure set of lower 
degree coefficients (vs. for all of them). We will outline our approach and a recent improvement which allows us
to eliminate this shortcoming and to give a new proof of the Bourgain-Demeter-Guth bound. In fact, our proof works 
under a new multidimensional Diophantine condition which appears to be weaker than classical one-dimensional 
conditions in the above mentioned works.  This is joint work, in progress, with L. Flaminio.
AdresseCampus Pierre et Marie Curie