BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gábor Pete (Budapest) DTSTART:20210212T140000Z DTEND:20210212T150000Z DTSTAMP:20260423T020954Z UID:WCS/18 DESCRIPTION:Title: The Free Uniform Spanning Forest is disconnected in some virtually free group s\, depending on the generating set\nby Gábor Pete (Budapest) as part of Warwick Combinatorics Seminar\n\n\nAbstract\nThe uniform random spanni ng tree of a finite graph is a classical object in probability and combina torics. In an infinite graph\, one can take any exhaustion by finite subgr aphs\, with some boundary conditions\, and take the limit measure. The Fre e Uniform Spanning Forest (FUSF) is one of the natural limits\, but it is less understood than the wired version\, the WUSF. Taking a finitely gener ated group\, several properties of WUSF and FUSF have been known to be ind ependent of the chosen Cayley graph of the group: the average degree in WU SF and in FUSF\; the number of ends in the components of the WUSF and of t he FUSF\; the number of trees in the WUSF. Lyons and Peres asked if this l atter should also be the case for the FUSF.\n\nIn joint work with Ádám T imár\, we give two different Cayley graphs of the same group such that th e FUSF is connected in one of them but has infinitely many trees in the ot her. Since our example is a virtually free group\, this is also a countere xample to the general expectation that such "tree-like" graphs would have connected FUSF. Many open questions are inspired by the results.\n LOCATION:https://researchseminars.org/talk/WCS/18/ END:VEVENT END:VCALENDAR