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Discrete approximate subgroups of Lie groups 10.17863/CAM.86438 Machado, Simon 0000000217876864 Breuillard, Emmanuel 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. University of Cambridge 2022-04-11 Thesis Doctoral eng https://www.repository.cam.ac.uk/handle/1810/339030 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/595793c8-df9d-42b2-864a-19f3b6fb1b03/download 37931e000dac85cc918d7b75fc85b662 https://www.rioxx.net/licenses/all-rights-reserved/ Mathematics