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Thursday, October 17, 2013

**Abstract:** Bianchi groups are groups of the form SL(2,R) where R is the ring of integers of an imaginary quadratic field. They form an important class of arithmetic Kleinian groups and moreover they hold a key role for the development of the Langlands program for GL(2) beyond totally real fields. In this talk, I will discuss several interesting questions related to the torsion in the homology of Bianchi groups. After discussing the importance of torsion from the perspective of number theory, I will talk on the recent results on the asymptotic behavior of the size of torsion, including joint work with N.Bergeron and A.Venkatesh on the cycle complexity of arithmetic manifolds and torsion growth.