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Isoperimetry in integer lattices

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  • UserBen Barber (University of Bristol)
  • ClockThursday 16 November 2017, 14:30-15:30
  • HouseMR12.

If you have a question about this talk, please contact Andrew Thomason.

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 Zd, with edges between pairs of vertices at l_1 distance 1. The most attractive open problem was to answer this question for the “strong lattice” on Zd, with edges between pairs of vertices at l_infty distance 1. Whilst studying this question we in fact solved the edge isoperimetric problem asymptotically for every Cayley graph on Z^d. I’ll talk about how to go from the specification of a lattice to a corresponding near-optimal shape, for both this and the related vertex isoperimetric problem, and sketch the key ideas of the proof. Joint work with Joshua Erde.

This talk is part of the Combinatorics Seminar series.

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