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Homology torsion growth of higher rank lattices

Presented by: 
Nikolay Nikolov
Wednesday 10th May 2017 - 10:00 to 11:00
INI Seminar Room 1
The asymptotic behaviour of Betti numbers and more generally, representation multiplicities associated to lattices in Lie groups have been extensively studied. In this talk I will discuss the asymptotic behaviour of two related invariants: rank and homology torsion in higher rank lattices. In the nonuniform case this is well understood due to the validity of the Congruence subgroup property but the uniform (cocompact) case is wide open. With M. Abert and T. Gelander we resolved this for right angled lattices. A group is right angled if it can be generated by a sequence of elements of infinite order each of which commutes with the previous one. However not all lattices are right angled and I will survey the many open questions in this area.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons