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| 集中講義 intensive lectures (数理科学特論VIII) |
| Date: |
Oct 3, 10, 17, 24, 31, Nov 7, 14, 21, 28, 2019, 13:00-14:45 |
| Place: |
Room 128, Graduate School of Mathematical Sciences, the University of Tokyo |
| Speaker: |
Yves Benoist (CNRS, Université Paris-Sud) |
| Title: |
Kleinian groups |
Abstract:
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Kleinian groups are discrete groups of isometries of the hyperbolic
space.
We will study both subgroups of finite and infinite covolume.
Here are a few aspects that we will discuss:
- The hyperbolic space, its boundary and its isometries.
- Construction of discrete subgroups and lattices.
- Limit set, convex cocompact subgroups and autosimilar fractal sets.
- Hausdorff dimension, critical exponent and spectrum of the Laplacian.
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| 談話会 Colloquium |
| Date: |
Oct 25, 2019, 15:30-16:30 |
| Place: |
Room 123, Graduate School of Mathematical Sciences, the University of Tokyo |
| Speaker: |
Yves Benoist (CNRS, Université Paris-Sud) |
| Title: |
Arithmeticity of discrete subgroups |
Abstract:
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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.
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