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PRODID:-//Columba Systems Ltd//NONSGML CPNG/SpringViewer/ICal Output/3.3-
M3//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20200205T185921Z
DTSTART:20200211T150000Z
SUMMARY:Ben Barber (Manchester) - Stable isoperimetry in lattice-like gr
aphs
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}cgb-k69oejl
6-by6fce
DESCRIPTION:Abstract : In a graph G\, the edge boundary of a set of vert
ices S is the set of edges leaving S\; the vertex boundary of S is the s
et of vertices you can get to by following those edges. The edge or ve
rtex isoperimetric problem for G is to determine how small the edge or v
ertex boundary of S can be\, given |S|. Solving these problems for arbi
trary G is\, unsurprisingly\, NP-hard.\n\nIn the 90s\, Imre Ruzsa used a
combination of techniques from geometry and additive number theory to s
olve the vertex isoperimetric problem asymptotically for “lattice-like”
graphs (Cayley graphs of Z^d). In 2017\, Joshua Erde and I solved the e
dge isoperimetric problem asymptotically for these graphs.\n\nEach of th
ese results has the slightly stronger form “this particular configuratio
n of n points has close to the smallest possible boundary”. Must every s
et of n points with close to the smallest possible boundary be similar t
o one of these configurations? That is\, is the solution to the isoperi
metric problem stable? We show that the answer is yes\, in a strong qua
ntitative form. We also extend these results to Cayley graphs of arbitr
ary finitely generated abelian groups with a free part.\n\nJoint work wi
th Joshua Erde.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams 1\, Alan Turing Building\, Manchester
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