This week's seminars
Pure Maths Colloquium: Optimal partition problems and the honeycomb conjecture
21 May 2018 16:00 in CM301
In 2005-2007 Burdzy, Caffarelli and Lin, Van den Berg
conjectured in different contexts that the sum (or the maximum) of the
first eigenvalues of the Dirichlet-Laplacian associated to arbitrary
cells partitioning a given domain of the plane, is asymptomatically
minimal on honeycomb structures, when the number of cells goes to
infinity. I will discuss the history of this conjecture, giving the
arguments of Toth and Hales on the classical honeycomb problem, and I
will prove the conjecture (of the maximum) for the Robin-Laplacian
eigenvalues. The results have been obtained with I. Fragala, B.
Velichkov and G. Verzini.
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