Séminaires : Séminaire de Logique Lyon-Paris

Equipe(s) : lm,
Responsables :S. Anscombe, O. Finkel, A. Khélif, S. Rideau, T. Tsankov, A. Vignati
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Orateur(s) Simon Machado - Cambridge University,
Titre Theorems of Meyer-type for approximate lattices
Horaire16:00 à 17:15
Diffusion https://u-paris.zoom.us/rec/share/-bmfbjmz8LRLj8z6L4aTWTNDhAEvLRqTcfUNq-o9rj8BCphAEUD0cph7AG_nVPj2.Cy3n6sLSnfhuzpkG
RésumeBjörklund and Hartnick recently introduced a type of approximate subgroups called approximate lattices: discrete approximate subgroups of locally compact groups with finite co-volume. Their motivation was to define a non-commutative generalisation of Meyer’s mathematical quasi-crystals (certain aperiodic subsets of Euclidean spaces with long range order). A key question asks whether Meyer’s main theorem, that asserts that quasi-crystals are projections of certain subsets of higher-dimensional lattices, holds true for all approximate lattices. I will discuss how to relate Meyer’s theorem to a consequence of Hrushovski’s stabilizer theorem and how this idea can be utilised to obtain both an extension of Meyer’s theorem to amenable groups, and a decomposition theorem à la Auslander for approximate lattices in Lie groups. The latter result will then naturally lead us to take a look at approximate lattices in semi-simple groups. While an amenable Meyer-type theorem can be proved by drawing parallels between Meyer’s and Hrushovski’s point of view, we will see how ergodic-theoretic tools from Margulis’ proof of arithmeticity and Zimmer’s proof of cocycle superrigidity lead to a partial solution in the semi-simple case.
SalleContacter Silvain Rideau ou Alessandro Vignati