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SUMMARY:Samuel Mellick: "Fixed price one for higher rank Lie groups and so
 me products of groups"
DTSTART:20231010T083000Z
DTEND:20231010T093000Z
DTSTAMP:20260423T145300Z
UID:indico-event-10419@indico.math.cnrs.fr
DESCRIPTION:In recent joint work with Mikolaj Fraczyk and Amanda Wilkens\,
  it was shown that higher rank Lie groups and products of automorphism gro
 ups of regular trees have fixed price one. This immediately implies that a
 ll lattices in such groups have fixed price one (this was known for non-un
 iform lattices\, due to Gaboriau). Additionally\, by applying a theorem of
  Abert-M. or a theorem of Carderi (independently proved) we get uniform va
 nishing of rank gradient for any sequence of lattices in higher rank Lie g
 roups\, resolving a conjecture of Abert-Gelander-Nikolov. In a follow up 
 paper\, I prove a generalisation of a criterion of Gaboriau for showing th
 at a group has fixed price one. This gives an alternative proof for fixed 
 price one for higher rank Lie groups (but not products of trees). It also 
 applies to certain products of groups\, which yields as a corollary fixed 
 price one for SL(2\,Q). In this talk I will explain how the generalistaio
 n of Gaboriau's criterion is proved. No prior knowledge of cost for topolo
 gical groups will be assumed. \n\nhttps://indico.math.cnrs.fr/event/10419
 /
URL:https://indico.math.cnrs.fr/event/10419/
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