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SUMMARY:The Structure of Approximate Lattices in Linear Groups
DTSTART:20231113T150000Z
DTEND:20231113T161500Z
DTSTAMP:20260504T085000Z
UID:indico-event-10821@indico.math.cnrs.fr
CONTACT:cecile@ihes.fr
DESCRIPTION:Speakers: Simon Machado (ETH Zürich)\n\nApproximate lattices 
 are discrete subsets of locally compact groups that are an aperiodic gener
 alisation of lattices. They are defined as approximate subgroups (i.e. sub
 sets that are closed under multiplication up to a finite multiplicative er
 ror) that are discrete and have finite co-volume. They were first studied 
 by Yves Meyer who classified them in locally compact abelian groups by mea
 ns of the so-called "cut-and-project schemes". Approximate lattices were s
 ubsequently used to model a diversity of objects such as aperiodic tilings
  (Penrose and the "hat")\, Pisot numbers\, and quasi-crystals.In non-abeli
 an groups\, however\, their structure remained mysterious. I will explain 
 how the structure of approximate lattices in linear algebraic groups can b
 e understood thanks to a notion of cohomology that sits halfway between bo
 unded cohomology and the usual cohomology\, thus generalising Meyer's theo
 rem. Along the way\, we will talk about Pisot numbers\, extending a theore
 m of Lubotzky\, Mozes and Raghunathan\, amenability and (some) model theor
 y.\n\nhttps://indico.math.cnrs.fr/event/10821/
LOCATION:Amphithéâtre Léon Motchane (IHES)
URL:https://indico.math.cnrs.fr/event/10821/
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