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SUMMARY:Matteo Vannacci (University of the Basque Country)
DTSTART:20240516T103000Z
DTEND:20240516T112000Z
DTSTAMP:20260416T215341Z
UID:GiG2024/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GiG2024/2/">
 Profinite groups of finite probabilistic virtual rank</a>\nby Matteo Vanna
 cci (University of the Basque Country) as part of Groups in Galway 2024\n\
 nLecture held in McMunn lecture theatre.\n\nAbstract\nA profinite group $G
 $ carries naturally the structure of a probability space\, namely with res
 pect to its normalised Haar measure. We study the probability $Q(G\,k)$ th
 at $k$ Haar-random elements generate an open subgroup in the profinite gro
 up $G$. In particular\, in this talk I will introduce the probabilistic vi
 rtual rank $\\mathrm{pvr}(G)$ of $G$\; that is\, the smallest $k$ such tha
 t $Q(G\,k)=1$.  We will discuss some key theorems and open problems about 
 random generation in profinite groups\, with a view toward finite direct p
 roducts of hereditarily just infinite profinite groups. Classic examples o
 f the latter type of groups are semisimple algebraic groups over non-archi
 medean local fields. This is joint work with Benjamin Klopsch and Davide V
 eronelli.\n
LOCATION:https://researchseminars.org/talk/GiG2024/2/
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