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SUMMARY:The Structure of Approximate Lattices in Linear Groups
DTSTART:20231113T150000Z
DTEND:20231113T161500Z
DTSTAMP:20240222T015000Z
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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