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SUMMARY:Atticus Stonestrom - Approximate groups in NIP structures
DTSTART:20260528T130000Z
DTEND:20260528T140000Z
DTSTAMP:20260610T213600Z
UID:indico-event-16621@indico.math.cnrs.fr
DESCRIPTION:Recall that a subset X of a group is said to be an approximate
  group if the product set XX:=\\{ab:a\,b\\in X\\} can be covered by finite
 ly many translates of X. I will discuss a work-in-progress which attempts 
 to give a structure theory for approximate groups definable in NIP theorie
 s. First I will present an example of an approximate group definable in th
 e universal cover of SL(2\,R) that has no "locally compact model"\; this g
 ives a NIP counterexample to a conjecture of Massicot-Wagner\, first dispr
 oved by Hrushovski\, Krupiński\, and Pillay. I will then discuss some ten
 tative positive structural results\, some of which are of interest even in
  the case of definable groups. Among other things I will discuss the shape
  of Hrushovski’s “generalized locally compact models” in the NIP set
 ting.\n\nhttps://indico.math.cnrs.fr/event/16621/
LOCATION:112 (ICJ)
URL:https://indico.math.cnrs.fr/event/16621/
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