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SUMMARY:Alistair Miller (University of Southern Denmark)
DTSTART:20241009T190000Z
DTEND:20241009T200000Z
DTSTAMP:20260420T053237Z
UID:NYC-NCG/170
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NYC-NCG/170/
 ">Homology and K-theory for self-similar group actions</a>\nby Alistair Mi
 ller (University of Southern Denmark) as part of Noncommutative geometry i
 n NYC\n\n\nAbstract\nSelf-similar groups are groups of automorphisms of in
 finite rooted trees obeying a simple but powerful rule. Under this rule\, 
 groups with exotic properties can be generated from very basic starting da
 ta\, most famously the Grigorchuk group which was the first example of a g
 roup with intermediate growth.\n\nNekrashevych introduced a groupoid and a
  $C^*$-algebra for a self-similar group action on a tree as models for som
 e underlying noncommutative space for the system. Our goal is to compute t
 he K-theory of the $C^*$-algebra and the homology of the groupoid. Our mai
 n theorem provides long exact sequences which reduce the problems to group
  theory. I will demonstrate how to apply this theorem to fully compute hom
 ology and K-theory through the example of the Grigorchuk group.\n\nThis is
  joint work with Benjamin Steinberg.\n
LOCATION:https://researchseminars.org/talk/NYC-NCG/170/
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