Séminaires : Séminaire d'Algèbres d'Opérateurs

Equipe(s) : ao,
Responsables :Pierre Fima, François Le Maître, Romain Tessera
Email des responsables :
Salle : 1013
Adresse :Sophie Germain

Orateur(s) Marek Kaluba - Karlsruhe Institute of Technology,
Titre Introduction to property (T) and sums of squares
Horaire10:00 à 11:00
RésumeWe will start by looking into Cayley graphs of a group and build some geometric understanding of group Laplacians. Then we will look at their algebraic description in the group rings. This description allows to bridge Kazhdan property (T) and algebraic positivity of a certain operator in the group ring. We will explain how such positivity statements can be reformulated to a sum of squares decomposition problems. These in turn can be relaxed to problems of semidefinite optimization which can be effectively solved a computer. Finally I will say a few words on how such (imprecise) solution could be certified to form a mathematical proof of property (T). The talk will be based on 1312.5431 by N.Ozawa and 1703.09680 by P.Nowak and myself.
AdresseSophie Germain