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SUMMARY:Tangles and the Mona Lisa - Reinhard Diestel (University of Hambur
 g)
DTSTART:20170316T143000Z
DTEND:20170316T153000Z
UID:TALK70311@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:Tangles\, first introduced by Robertson and Seymour in their w
 ork on graph minors\, are a radically new way to define regions of high co
 nnectivity in a graph. The idea is that\, whatever that highly connected r
 egion might `be'\,\nlow-order separations of the graph cannot cut through 
 it\, and so it will orient them: towards the side of the separation on whi
 ch it lies. A tangle\, thus\, is simply a consistent way of orienting all 
 the low-order separations in a graph.\n\nThe new paradigm this brings to c
 onnectivity theory is that such consistent orientations of all the low-ord
 er separations may\, in themselves\, be thought of as highly connected reg
 ions: rather than asking exactly which vertices or edges belong to such a 
 region\, we only ask where it is\, collecting pointers to it from all side
 s.\n\nPixellated images share this property: we cannot tell exactly which 
 pixels belong to the Mona Lisa's nose\, rather than her cheek\, but we can
  identify `low-order' separations of the picture that do not cut right thr
 ough such features\, and which can therefore be used collectively to delin
 eate them.\n\nThis talk will outline a general theory of tangles that appl
 ies not only to graphs and matroids but to a broad range of discrete struc
 tures. Including\, perhaps\, the pixellated Mona Lisa.\n
LOCATION:MR12
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