Nicolas Tholozan: The existence problem for compact quotients of homogeneous spaces

Let X be a homogeneous space under the action of a Lie group G. Can we find a discrete subgroup of $G$ acting properly discontinuously and cocompactly on X? While the answer is essentially known when G preserves a distance on X (thanks to a famous theorem of Borel and Harish-Chandra), the general question remains mostly open. In this talk I will review the few known constructions of such compact quotients and the various known obstructions to their existence, the most recent of which is a work in progress with Fanny Kassel and Yosuke Morita.

Schedule

• 14:00 - Pretalk with Nicolas Tholozan and PhD Students
• 14:30 - Coffee Break
• 15:00 - Colloquium Talk: Simplicial volume of one-relator groups