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SUMMARY:Neumann convex partitions and fundamental spectral gaps - Dorin Bu
 cur (Université de Savoie)
DTSTART:20260326T101500Z
DTEND:20260326T111500Z
UID:TALK241150@talks.cam.ac.uk
DESCRIPTION:The fundamental gap conjecture proved by Andrews and Clutterbu
 ck in 2011 provides the sharp lower bound for the difference between the f
 irst two Dirichlet Laplacian eigenvalues in terms of the diameter of a con
 vex set in ℝ^N. The result presented in this talk strengthens Andrews-Cl
 utterbuck inequality by quantifying geometrically the excess of the gap co
 mpared to the diameter in terms of flatness. The proof relies on a variati
 onal interpretation of the fundamental gap and the analysis of convex part
 itions &agrave\; la Payne-Weinberger. This is a joint work with Vincenzo A
 mato and Ilaria Fragal&agrave\;.
LOCATION:Seminar Room 1\, Newton Institute
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