# A metric approach to the spectrum of hypersurfaces of the Euclidean space

by Bruno Colbois (Université de Neuchâtel)

In this talk I will present (without going into details of the proofs) a metric approach to study the spectrum of the Laplacian of hypersurfaces of the Euclidean space. The goal is to obtain estimates that do not depend on the curvature, but on more global geometric ingredients. For example, one of these results, obtained with E. Dryden and A. El Soufi, allows, as a corollary, to estimate the spectrum of algebraic hypersurfaces according to their degree. Another, obtained with A. El Soufi and A. Girouard, provides estimates based on the isoperimetric ratio associated with the hypersurface. Given enough time, I will conclude with some open questions.