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SUMMARY:Poisson--Voronoi percolation in higher rank [MPIM]
DTSTART:20260528T143000Z
DTEND:20260528T160000Z
DTSTAMP:20260719T030900Z
UID:indico-event-1344@math-events.uni-bonn.de
DESCRIPTION:Speakers: Konstantin Recke (Oxford)\n\nOberseminar Differentia
 lgeometrie\nThe Poisson--Voronoi percolation model can be defined on any m
 etric measured space as follows. \nSample a random discrete set of points
  according to a Poisson point process of intensity $\\lambda>0$\, divide t
 he space into the corresponding\nVoronoi cells\, color the cells black in
 dependently with probability $p\\in(0\,1)$ and consider the union of blac
 k cells. This model has been widely studied in Euclidean space and also be
 yond\, notably in the hyperbolic plane by Benjamini and Schramm (2001). 
 In this talk\, we will discuss a new phenomenon for higher rank symmetric 
 spaces. We will show an application of this result to a question of Hutchc
 roft and Pete (2020) and Pete and Rokob (2025)\, and its close connectio
 n to Gaboriau's fixed price problem. In the final part of the talk\, we w
 ill explain the strategy of proof and in particular the way in which our a
 pproach builds on recent results about ideal Poisson--Voronoi tessellatio
 ns and a breakthrough of Frączyk\, Mellick and Wilkens (2025). Based o
 n joint works with Jan Grebík and with Matteo D'Achille\, Jan Grebík\, 
 Ali Khezeli\, Amanda Wilkens.\n\nhttps://math-events.uni-bonn.de/event/134
 4/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1344/
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