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SUMMARY:Kaleidoscopic groups and the generic point property
DTSTART:20221219T160000
DTEND:20221219T170000
DTSTAMP:20260408T083849Z
UID:4407554a583c9442da3272fc64b05ffd5d08e9b684e4b6c8c017728f
CATEGORIES:Conferences - Seminars
DESCRIPTION:Gianluca Basso (Lyon)\nDuchesne\, Monod and Wesolek described 
 how to associate a group acting on a certain one-dimensional space to each
  permutation group of countable degree. This is called its kaleidoscopic g
 roup. We study such groups under the lens of their continuous actions on c
 ompact spaces\, and determine which dynamical properties of are preserved 
 in the kaleidoscopic construction. Doing so requires a novel structural Ra
 msey theorem and produces a new class of examples exhibiting a poorly unde
 rstood phenomenon. Indeed\, a Polish group has the generic point property 
 if every minimal flow has a comeager orbit. It has been shown that any Pol
 ish group with metrizable universal minimal flow has the generic point pro
 perty\, but the converse does not hold\, as shown by Kwiatkowska. Until re
 cently\, Kwiatkowska’s counterexample was the only known instance of thi
 s phenomenon\, but we find a large class of new counterexamples among kale
 idoscopic groups.\nThis is joint work with Todor Tsankov.
LOCATION:MA A1 10 https://plan.epfl.ch/?room==MA%20A1%2010
STATUS:CONFIRMED
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