Description
Le Colloquium a lieu en général une fois par mois, le jeudi à 17h. Il est donné par un invité qui doit proposer un thème de son choix en mathématiques en s’efforçant de s’adresser à l’ensemble des mathématiciens du Département de Mathématiques de l’Université de Nantes (doctorants.es, postdoctorants.es, enseignants.es, chercheurs.ses).
Le Colloquium invite Emanuel Carneiro (IMPA et Trieste) :
Some problems in the interface of analysis and number theory.
Résumé :
This will be a broad talk on some interesting problems in Fourier analysis that appear when bounding some central objects in number theory. The problems in analysis that we consider can be seen as « Fourier optimization problems », in whichone prescribes some information (constraints) about a function and its Fouriertransform, with the aim of optimizing some quantity of interest.
Band limited approximations, sharp test functions for sphere packings, and Fourier uncertainty principles are just a few examples of problems within this scope. The applications we have in mind are related to the Riemann zeta-function : we look for bounds of its modulus and argument on the critical line, and also of the gaps between consecutive prime numbers.
Very little background in analysis and number theory is required.
Lieu du Colloquium :
Université de Nantes,Campus de la Lombarderie, Laboratoire de mathématiques Jean Leray, bâtiment 10, Salle des séminaires.
