Orateur(s)  Simon Machado  Cambridge University,

Titre  Theorems of Meyertype for approximate lattices 
Date  13/01/2021 
Horaire  16:00 à 17:15 

Diffusion  https://uparis.zoom.us/rec/share/bmfbjmz8LRLj8z6L4aTWTNDhAEvLRqTcfUNqo9rj8BCphAEUD0cph7AG_nVPj2.Cy3n6sLSnfhuzpkG 
Résume  Björklund and Hartnick recently introduced a type of approximate subgroups called approximate lattices: discrete approximate subgroups of locally compact groups with finite covolume. Their motivation was to define a noncommutative generalisation of Meyer’s mathematical quasicrystals (certain aperiodic subsets of Euclidean spaces with long range order). A key question asks whether Meyer’s main theorem, that asserts that quasicrystals are projections of certain subsets of higherdimensional 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 semisimple groups. While an amenable Meyertype theorem can be proved by drawing parallels between Meyer’s and Hrushovski’s point of view, we will see how ergodictheoretic tools from Margulis’ proof of arithmeticity and Zimmer’s proof of cocycle superrigidity lead to a partial solution in the semisimple case. 
Salle  Contacter Silvain Rideau ou Alessandro Vignati 
Adresse  