In this talk, I will describe results obtained in the last decade on the first eigenvalues of the Neumann magnetic Laplacian in the semi-classical limit, more particularly, I will show how the geometry of the situation (singularities of the boundary, curvature) influences the first order asymptotics, and also the spectral gap, under suitable assumptions. Then I will present recent results about eigenvalues of Robin Laplacian with strong Dirichlet boundary condition and show the analogies between these two operators.

Slides

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