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CATEGORIES:Probability
SUMMARY:Continuity and stability of the cut locus of the B
rownian map - Brett Kolesnik (UBC)
DTSTART;TZID=Europe/London:20150224T160000
DTEND;TZID=Europe/London:20150224T170000
UID:TALK58198AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/58198
DESCRIPTION:A prototype for pure quantum gravity is the Browni
an map\, a random geodesic metric space which is h
omeomorphic to the sphere\, of Hausdorff dimension
4\, and the scaling limit of a wide variety of pl
anar maps.\nWe strengthen the so-called confluence
of geodesics phenomenon observed at the root of t
he map\, and with this\, reveal several properties
of its rich geodesic structure.\nOur main result
is the continuity of the cut locus on an open\, de
nse subset of the Brownian map. Moreover\, the cut
locus is uniformly stable in the sense that any t
wo cut loci coincide outside a nowhere dense set.\
nOther consequences include the classification of
geodesic networks which are dense. For each j\,k i
n {1\,2\,3}\, there is a dense set of Hausdorff di
mension 2(6-j-k) of pairs of points which are join
ed by networks of exactly jk geodesics and of a sp
ecific topological form. All other networks are no
where dense.\n\nJoint work with Omer Angel (UBC) a
nd Gregory Miermont (ENS Lyon and IUF)
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:John Shimmon
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