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SUMMARY:Approximate lattices in amenable groups - Simon Machado (Universit
 y of Cambridge)
DTSTART:20200131T134500Z
DTEND:20200131T144500Z
UID:TALK134272@talks.cam.ac.uk
CONTACT:76015
DESCRIPTION:Approximate lattices are approximate subgroups of locally comp
 act groups\nthat generalise lattices (discrete subgroups of finite co-volu
 me). A\ntheorem due to Yves Meyer asserts that approximate lattices in Euc
 lidean\nspaces are projections of certain subsets of lattices in\nhigher-d
 imensional spaces. This raises the following question: does\nMeyer's theor
 em hold for approximate lattices in non-commutative locally\ncompact group
 s?\n\nI will prove that Meyer's theorem holds for approximate lattices in\
 namenable locally compact subgroups. To do so I will define "good models"\
 nthat relate approximate subgroups to compact neighbourhoods of the\nident
 ity in locally compact groups. I will also explain how similar\nmethods yi
 eld a generalisation of Auslander's theorem about the\nintersection of a l
 attice in a Lie group and the amenable radical.\n
LOCATION:CMS\, MR13
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