Lp-restriction of eigenfunctions to random Cantor type sets

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• Suresh Eswarathasan, Cardiff
• Wednesday 07 March 2018, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

Let (M,g) be a compact Riemannian surface without boundary. Consider the corresponding L2-normalized Laplace-Beltrami eigenfunctions. Eigenfunctions of this type arise in physics as modes of periodic vibration of drums and membranes. They also represent stationary states of a free quantum particle on a Riemannian manifold. In the first part of the lecture, I will give a survey of results which demonstrate how the geometry of M affects the behaviour of these special functions, particularly their size which can be quantified by estimating Lp norms.

In the second part, I will present joint results with Pramanik (UBC) on the Lp restrictions of these eigenfunctions to random Cantor-type subsets of M. Our method includes concentration inequalities from probability theory in addition to the analysis of singular Fourier integral operators on fractals.

This talk is part of the Differential Geometry and Topology Seminar series.

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