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SUMMARY:On coarse fixed point properties - Romain Tessera (Université Par
 is Saclay)
DTSTART:20251006T130000Z
DTEND:20251006T140000Z
UID:TALK236272@talks.cam.ac.uk
DESCRIPTION:We investigate fixed point properties for isometric actions of
  topological groups on a wide class of metric spaces\, with a particular e
 mphasis on Hilbert spaces. Instead of requiring the action to be continuou
 s\, we assume that it is ``controlled"\, i.e. compatible with respect to s
 ome natural left-invariant coarse structure. For locally compact groups\, 
 we prove that these coarse fixed point properties are equivalent to the us
 ual ones\, defined for continuous actions. We deduce generalisations of tw
 o results of Gromov originally stated for discrete groups. For Polish grou
 ps with bounded geometry (in the sense of Rosendal)\, we prove a version o
 f Serre's theorem on the stability of coarse property FH under central ext
 ensions\, and apply it to the group of homeomorphisms of the line commutin
 g with integral translations. Finally\, we characterise geometric property
  (T) for sequences of finite Cayley graphs in terms of coarse property FH 
 of a certain ``large'' group. This is a joint work with Jeroen Winkel.
LOCATION:Seminar Room 1\, Newton Institute
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