On the growth of torsion in the cohomology of arithmetic groups

In this talk I will discuss various aspects of the growth of torsion in the cohomology of locally symmetric
spaces of finite volume, associated to arithmetic groups.  Here "growth" means that we consider either
towers of coverings  or special sequences of local systems of growing rank associated to algebraic
representations of the underlying reductive group. The method is analytic and is based on the study
of the Ray-Singer analytic torsion of the locally symmetric spaces. I will review some of the recent
results and discuss some open problems.