Forthcoming events in this series

Tue, 10 Oct 2006
17:00
L1

### Odd Characterisations of simple groups

Prof. C.W. Parker
(University of Birmingham)
Tue, 30 May 2006
17:00
L1

### Graded Hecke algebras and deformations of crossed products

Dr. Sarah Witherspoon
(Texas A&M / Munich)
Tue, 23 May 2006
17:00
L1

### Primitive groups and the Leech lattice

Dr. Michael Collins
(Oxford)
Tue, 16 May 2006
17:00
L1

### Finite simple groups as expanders

Dr. Nikolay Nikolov
(Oxford)
Tue, 09 May 2006
17:00
L1

### Moonshine in finite groups, and sunshine in finite geometry

Prof. Mark Ronan
(University of Illinois, Chicago)
Tue, 02 May 2006
17:00
L1

### Solubility for finite groups

Prof. J.S. Wilson
(Oxford)
Tue, 25 Apr 2006
17:00
L1

### GSO Groups

Prof. Michael Vaughan-Lee
(Oxford)
Tue, 07 Mar 2006
17:00
L1

### (3,4) - transpositions, II

Professor Bernd Fischer
(Bielefeld)
Tue, 28 Feb 2006
17:00
L1

### Testing polycyclicity of rational matrix groups

Dr. Bjoern Assmann
(St. Andrews / Oxford)
Tue, 21 Feb 2006
17:00
L1

### Smoothness of positive integers, permutations, polynomials and other paraphernalia

Dr. Peter Neumann
(Oxford)
Tue, 14 Feb 2006
17:00
L1

### Classification of Finite Simple Groups. Some aspects of the Generation-2 Proof

Dr. Inna Korchagina
(Birmingham)
Tue, 31 Jan 2006
17:00
L1

### A non-commutative Waring type theorem

Professor Aner Shalev
(Jerusalem)
Tue, 24 Jan 2006
17:00
L1

### Small presentations of finite simple groups

Dr. Martin Kassabov
(Cornell)
Tue, 17 Jan 2006
17:00
L1

### Complexes of injective kG-modules

Prof. Dave Benson
(Aberdeen)
Tue, 29 Nov 2005
17:00
L1

### Skew linear unipotent groups

Dr Jamshid Derakhshan
Tue, 22 Nov 2005
17:00
L1

Dr Peter Neumann
(Oxford)
Tue, 15 Nov 2005
17:00
L1

Dr Simon Goodwin
(Oxford)
Tue, 08 Nov 2005
17:00
L1

### Counting lattices in semi-simple Lie groups

Dr Mikhail Belolipetsky
(Durham)
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.

Tue, 01 Nov 2005
17:00
L1

### When is group cohomology continuous?

Prof. Peter Kropholler
(Glasgow)
Tue, 25 Oct 2005
17:00
L1

Dr Mario Nardone
(Oxford)
Tue, 18 Oct 2005
17:00
L1

Dr Michael Bate
(Oxford)
Tue, 11 Oct 2005
17:00
L1

Dr Simon Goodwin
(Oxford)
Tue, 07 Jun 2005
17:00
L1

Dr. R.G. Moller
(Reykjavik)
Tue, 31 May 2005
17:00
L1

### Zariski geometries : from classical to quantum

Prof. Boris Zilber
(Oxford)
Tue, 24 May 2005
17:00
L1

### TBA

Prof. Yuri Bahturin