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Inverse localization properties of high-energy eigenfunctions of the Laplacian

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GSTW01 - High energy spectral theory: geometry and dynamics

We consider the question of when the high-energy Laplace eigenfunctions are flexible enough to approximate, over the natural length scale, an arbitrary solution of the Helmholtz equation. The validity of this inverse localization property is analyzed in various settings, including flat tori and polygonal domains whose associated classical billiard dynamics are integrable. A surprising connection with Berry’s random wave conjecture is also discussed.

This talk is part of the Isaac Newton Institute Seminar Series series.

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