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SUMMARY:Continuity and stability of the cut locus of the Brownian map - Br
 ett Kolesnik (UBC)
DTSTART:20150224T160000Z
DTEND:20150224T170000Z
UID:TALK58198@talks.cam.ac.uk
CONTACT:John Shimmon
DESCRIPTION:A prototype for pure quantum gravity is the Brownian map\, a r
 andom geodesic metric space which is homeomorphic to the sphere\, of Hausd
 orff dimension 4\, and the scaling limit of a wide variety of planar maps.
 \nWe strengthen the so-called confluence of geodesics phenomenon observed 
 at the root of the map\, and with this\, reveal several properties of its 
 rich geodesic structure.\nOur main result is the continuity of the cut loc
 us on an open\, dense subset of the Brownian map. Moreover\, the cut locus
  is uniformly stable in the sense that any two cut loci coincide outside a
  nowhere dense set.\nOther consequences include the classification of geod
 esic networks which are dense. For each j\,k in {1\,2\,3}\, there is a den
 se set of Hausdorff dimension 2(6-j-k) of pairs of points which are joined
  by networks of exactly jk geodesics and of a specific topological form. A
 ll other networks are nowhere dense.\n\nJoint work with Omer Angel (UBC) a
 nd Gregory Miermont (ENS Lyon and IUF)
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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