A Sharp Lower Bound on the Small Eigenvalues of Surfaces

by Renan Gross (Cambridge)

Friday Oct 11, 2024, 2:00 PM → 4:00 PM Europe/Paris

Amphithéâtre Léon Motchane (IHES)

Probability and analysis informal seminar

The Laplacian is a central operator in the analysis of surfaces (and life in general). In this talk, we investigate how small its small eigenvalues can be, giving a sharp, quadratic bound on the k-th eigenvalue of a surface in terms of k, the surface's genus g, and its global geometry via the injectivity radius. The techniques involve extremal length, spectral embedding, and volume arguments.

Joint work with Guy Lachman and Asaf Nachmias, based on the paper: https://arxiv.org/abs/2407.21780
For an exposition and overview of the paper, see here:

https://sarcasticresonance.wordpress.com/2024/08/02/new-paper-on-arxiv-a-sharp-lower-bound-on-the-eigenvalues-of-surfaces/

 

 

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