15. John von Neumann-Lecture: Prof. Dr. Yves Benoist (Université Paris-Sud): Arithmeticity of discrete groups
Thursday, 18.04.2019 16:30 im Raum M5
In 1905, Minkowski proved that the discrete group
SL(n,Z) is a lattice in the Lie group SL(n,R).
This means that a fundamental domain has finite volume.
More generally, by a theorem of Borel and Harish-Chandra,
an arithmetic group in a simple Lie group is always a lattice.
Conversely, by a celebrated theorem of Margulis,
in a higher rank simple Lie group G
any lattice is an arithmetic group.
The aim of this lecture is to survey
other arithmeticity criteria for discrete groups
which are not assumed to be lattices.
Generalizing work of Selberg and Hee Oh
and solving with Miquel a conjecture of Margulis,
we will see that a discrete subgroup
in G is a non-cocompact arithmetic group
if and only if it is Zariski dense and
intersects cocompactly at least one
horospherical subgroup U of G.