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SUMMARY:All countable groups are full quasi-isometry groups - Joseph MacMa
 nus (University of Bristol)
DTSTART:20251105T150000Z
DTEND:20251105T160000Z
UID:TALK239356@talks.cam.ac.uk
DESCRIPTION:Given a metric space X\, we denote by QI(X) the set of all qua
 si-isometries f : X -> X\, modulo finite sup-distance. This set admits a n
 atural group structure via composition\, and is called the full quasi-isom
 etry group of X.\nThese groups are\, in general\, incredibly wild and hard
  to compute\, even for very natural spaces\, and very few explicit example
 s are known. One source of explicit examples comes from certain families o
 f symmetric spaces\, due to a strong rigidity theorem of Pansu.&nbsp\;\nIn
  this talk I will discuss how\, given any countable group G\, one can appl
 y Pansu&rsquo\;s rigidity theorem together with the classical Frucht&rsquo
 \;s theorem from graph theory\, and construct uncountably many quasi-isome
 try classes of metric spaces X such that QI(X) = G. I will also advertise 
 some interesting open problems related to QI groups.\nThis talk is based o
 n joint work with Paula Heim and Lawk Mineh.&nbsp\;
LOCATION:Seminar Room 2\, Newton Institute
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