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SUMMARY:Isoperimetry in integer lattices - Ben Barber (University of Brist
 ol)
DTSTART:20171116T143000Z
DTEND:20171116T153000Z
UID:TALK88961@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:The edge isoperimetric problem for a graph G is to find\, for 
 each n\, the minimum number of edges leaving any set of n vertices. Exact 
 solutions are known only in very special cases\, for example when G is the
  usual cubic lattice on Z^d\, with edges between pairs of vertices\nat l_1
  distance 1. The most attractive open problem was to answer this question 
 for the "strong lattice" on Z^d\, with edges between pairs of vertices at 
 l_infty distance 1. Whilst studying this question we in fact solved the ed
 ge isoperimetric problem asymptotically for every\nCayley graph on Z^d. I'
 ll talk about how to go from the specification of a lattice to a correspon
 ding near-optimal shape\, for both this and the related vertex isoperimetr
 ic problem\, and sketch the key ideas of\nthe proof. Joint work with Joshu
 a Erde.\n
LOCATION:MR12
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