BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tom Hutchcroft (University of Cambridge) DTSTART:20200427T130000Z DTEND:20200427T133000Z DTSTAMP:20260423T035625Z UID:LPDD/1 DESCRIPTION:Title: Per colation on hyperbolic groups\nby Tom Hutchcroft (University of Cambri dge) as part of Les probabilités de demain webinar\n\n\nAbstract\nMany qu estions in probability theory concern the way the geometry of a space infl uences the behaviour of random processes on that space\, and in particular how the geometry of a space is affected by random perturbations. One of t he simplest models of such a random perturbation is percolation\, in which the edges of a graph are either deleted or retained independently at rand om with retention probability p. We are particularly interested in phase t ransitions\, in which the geometry of the percolated subgraph undergoes a qualitative change as p is varied through some special value. Although per colation has traditionally been studied primarily in the context of Euclid ean lattices\, the behaviour of percolation in more exotic settings has re cently attracted a great deal of attention. In this talk\, I will discuss conjectures and results concerning percolation on the Cayley graphs of non amenable groups and hyperbolic spaces\, and give a taste of the proof of o ur recent result that percolation in any hyperbolic graph has a non-trivia l phase in which there are infinitely many infinite clusters.\n LOCATION:https://researchseminars.org/talk/LPDD/1/ END:VEVENT END:VCALENDAR