|Location:||MSRI: Simons Auditorium|
Speaker: Haluk Sengun
Title: Cohomology of Bianchi Groups and Arithmetic
Bianchi groups are groups of the form SL(2,R) where R is
the ring of an imaginary quadratic field. They arise naturally in the
study of hyperbolic 3-manifolds and of certain generalizations of the
classical modular forms (called Bianchi modular forms) for which they
assume the role of the classical modular group SL(2,ℤ).
In this talk, I will put the cohomology of Bianchi groups in the center
and will discuss its connections with abelian varieties of GL(2)-type and
Galois representations. I will continue with a discussion of the size of the
cohomology and the amount of the torsion, which will bring me to the
latest work of N.Bergeron and A.Venkatesh on the torsion homology of
arithmetic groups. I will expose some of my theoretical/computational
investigations along the way.