# Past Algebra Seminar

22 November 2005
17:00
Dr Peter Neumann
Abstract
• Algebra Seminar
15 November 2005
17:00
Dr Simon Goodwin
Abstract
• Algebra Seminar
8 November 2005
17:00
Dr Mikhail Belolipetsky
Abstract
My lecture is based on results of [1] and [2]. In [1] we use an extension of the method due to Borel and Prasad to determine the growth rate of the number of maximal arithmetic subgroups of bounded covolumes in a semi-simple Lie group. In [2] the results of [1] are combined with the previously known asymptotic of the number of subgroups in a given lattice in order to study the general lattice growth. We show that for many high-rank simple Lie groups (and conjecturally for all) the rate of growth of lattices of covolume at most $x$ is like $x^{\log x}$ and not $x^{\log x/ \log\log x}$ as it was conjectured before. We also prove that the 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.
• Algebra Seminar
1 November 2005
17:00
Prof. Peter Kropholler
Abstract
• Algebra Seminar
25 October 2005
17:00
Dr Mario Nardone
Abstract
• Algebra Seminar
18 October 2005
17:00
Dr Michael Bate
Abstract
• Algebra Seminar
11 October 2005
17:00
• Algebra Seminar
7 June 2005
17:00
Dr. R.G. Moller
Abstract
• Algebra Seminar
31 May 2005
17:00
Prof. Boris Zilber
Abstract
• Algebra Seminar
24 May 2005
17:00
Prof. Yuri Bahturin
Abstract
• Algebra Seminar