Discrete approximate subgroups of Lie groups

We study generalisations of a theorem of Yves Meyer concerning the structure of approximate lattices. An approximate lattice is a discrete approximate subgroup of a locally compact group - i.e. a subset that is closed under multiplication up to an error controlled by a finite set - that has finite co-volume. We study, successively, generalisations of Meyer's theorem in soluble Lie groups, in amenable locally compact groups and in higher-rank semi-simple algebraic groups. Along the way, we investigate properties of closed and discrete approximate subgroups of locally compact groups in general.

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2022

Author dc:creator

• Machado, Simon

Advisor dc:contributor.advisor

• Breuillard, Emmanuel

• Mathematics

Licence

• https://www.rioxx.net/licenses/all-rights-reserved/

Language dc:language

eng

Author Identifier

0000-0002-1787-6864

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/339030