**SMS scnews item created by Haotian Wu at Fri 18 Aug 2017 1728**

Type: Seminar

Distribution: World

Expiry: 17 Feb 2018

**Calendar1: 24 Aug 2017 1200-1300**

**CalLoc1: Carslaw 535A**

CalTitle1: Geometry & Topology Seminar: Wolfgang Globke -- Compact pseudo-Riemannian homogeneous spaces

Auth: haotianw@como.maths.usyd.edu.au

### Geometry & Topology Seminar

# Compact pseudo-Riemannian homogeneous spaces

### Wolfgang Globke (Adelaide)

**Thursday 24 August 12:00–13:00 in Carslaw 535A.**

Please join us for lunch after the talk!

**Abstract:**

A pseudo-Riemannian homogeneous space \(M\) of finite volume can be presented as \(M=G/H\), where \(G\) is a Lie group acting transitively and isometrically on \(M\), and \(H\) is a closed subgroup of \(G\).

The condition that \(G\) acts isometrically and thus preserves a finite measure on \(M\) leads to strong algebraic restrictions on \(G\). In the special case where \(G\) has no compact semisimple normal subgroups, it turns out that the isotropy subgroup \(H\) is a lattice, and that the metric on \(M\) comes from a bi-invariant metric on \(G\).

This result allows us to recover Zeghib’s classification of Lorentzian compact homogeneous spaces, and to move towards a classification for metric index \(2\).

As an application we can investigate which pseudo-Riemannian homogeneous spaces of finite volume are Einstein spaces. Through the existence questions for lattice subgroups, this leads to an interesting connection with the theory of transcendental numbers, which allows us to characterize the Einstein cases in low dimensions.

This talk is based on joint works with Oliver Baues, Yuri Nikolayevsky and Abdelghani Zeghib.