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Optimal honeycomb structures

Presented by: 
Dorin Bucur Université de Savoie
Wednesday 20th February 2019 - 17:00 to 18:00
INI Seminar Room 2
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
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons