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Colloquium
Seminar information archive ～04/23｜Next seminar｜Future seminars 04/24～
| Organizer(s) | ASUKE Taro, TERADA Itaru, HASEGAWA Ryu, MIYAMOTO Yasuhito (chair) |
|---|---|
| URL | https://www.ms.u-tokyo.ac.jp/seminar/colloquium/index_e.html |
2019/10/25
15:30-16:30 Room #123 (Graduate School of Math. Sci. Bldg.)
Yves Benoist ( CNRS, Paris-Sud)
Arithmeticity of discrete subgroups (英語)
Yves Benoist ( CNRS, Paris-Sud)
Arithmeticity of discrete subgroups (英語)
[ Abstract ]
By a theorem of Borel and Harish-Chandra,
an arithmetic group in a semisimple Lie group is a lattice.
Conversely, by a celebrated theorem of Margulis,
in a higher rank semisimple Lie group G
any irreducible lattice is an arithmetic group.
The aim of this lecture is to survey an
arithmeticity criterium for discrete subgroups
which are not assumed to be lattices.
This criterium, obtained with Miquel,
generalizes works of Selberg and Hee Oh
and solves a conjecture of Margulis. It says:
a discrete irreducible Zariski-dense subgroup
of G that intersects cocompactly at least one
horospherical subgroup of G is an arithmetic group.
By a theorem of Borel and Harish-Chandra,
an arithmetic group in a semisimple Lie group is a lattice.
Conversely, by a celebrated theorem of Margulis,
in a higher rank semisimple Lie group G
any irreducible lattice is an arithmetic group.
The aim of this lecture is to survey an
arithmeticity criterium for discrete subgroups
which are not assumed to be lattices.
This criterium, obtained with Miquel,
generalizes works of Selberg and Hee Oh
and solves a conjecture of Margulis. It says:
a discrete irreducible Zariski-dense subgroup
of G that intersects cocompactly at least one
horospherical subgroup of G is an arithmetic group.
