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SUMMARY:Means on groups and degrees of commutativity [Geometric Group Theo
 ry Oberseminar]
DTSTART:20251105T100000Z
DTEND:20251105T110000Z
DTSTAMP:20260308T050200Z
UID:indico-event-673@math-events.uni-bonn.de
DESCRIPTION:Speakers: Motiejus Valiunas (University of Wrocław)\n\nGiven 
 a finite group G\, one can count the proportion of pairs of elements in G 
 that commute -- giving a number\, denoted dc(G)\, behaviour of which has b
 een studied since the 1960s.  Such a notion has straightforward generalis
 ations to residually finite or amenable groups.  To make sense of this fo
 r other infinite groups G\, one needs to define some sort of a nice measur
 e or a mean on G.  In this talk\, I will explain how such means -- more s
 pecifically\, finitely additive probability means that give the "correct" 
 answer for cosets of subgroups -- can be constructed.  As an application 
 of these methods\, one can define dc(G) for any group G\, and show that dc
 (G) > 0 if and only if G is finite-by-abelian-by-finite.This is joint work
  with Armando Martino.\n\nhttps://math-events.uni-bonn.de/event/673/
LOCATION:Endenicher Allee 60/0-008 (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/673/
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