Cohomology of Bianchi Groups and Arithmetic
Speaker: Dr. Mehmet Haluk Sengun (Warwick)
Time: 4.00 PM
Date: Thursday April 18th 2013
Location: Seminar Room, Ag. 1.01
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). After giving the necessary background, I will start with a discussion of the problem of understanding the behavior of the dimensions of the cohomology of Bianchi groups and their congruence subgroups. Next, I will focus on the amount of the torsion that one encounters in the cohomology . Finally, I will discuss the arithmetic significance of these torsion classes.