Séminaires : Séminaire Théorie des Nombres

Equipe(s) : tn,
Responsables :Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos
Email des responsables : ziyang.gao@imj-prg.fr
Salle :
Adresse :



Orateur(s) Mehmet Haluk Sengun - ,
Titre Cohomology of Bianchi groups and Arithmetic
Horaire14:00 à 16:00
RésumeBianchi groups are groups of the form $\mathrm{SL}(2,R)$ where $R$ is the ring of an imaginaryquadratic field. They arise naturally in the study of hyperbolic 3-manifolds and ofcertain generalizations of the classical modular forms (called Bianchi modular forms)for which they assume the role of the classical modular group $\mathrm{SL}(2,\mathbb Z)$.In this talk, I will put the cohomology of Bianchi groups in the center and willdiscuss its connections with abelian varieties of $\mathrm{GL}_2$ type and Galoisrepresentations. I will continue with a discussion of the size of the cohomology andthe amount of the torsion, which will bring me to the latest work of N.Bergeron andA.Venkatesh on the torsion homology of arithmetic groups. I will expose some of mytheoretical/computational investigations along the way.