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Optimal honeycomb structures

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DNM - The mathematical design of new materials

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 and Cheeger constants. The results have been obtained in joint works with I. Fragala, G. Verzini and B. Velichkov

This talk is part of the Isaac Newton Institute Seminar Series series.

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