Tue, 10 Oct 2006
17:00
17:00
L1
Forthcoming events in this series
conjecture is still true (again for "most" groups) if one restricts to counting non-uniform lattices. A crucial ingredient of the argument in [2] is the existence of towers of field extensions with bounded root discriminant which follows from the seminal work of Golod and Shafarevich on class field towers.
I plan to give an overview of these recent results and discuss some ideas beyond the proofs.
[1] M. Belolipetsky (with an appendix by J. Ellenberg and A.
Venkatesh), Counting maximal arithmetic subgroups, arXiv:
math.GR/0501198.
[2] M. Belolipetsky, A. Lubotzky, Class field towers and subgroup
growth, work in progress.