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The semiclassical limit for eigenfunctions of the laplacian : a survey

Presented by: 
N Anantharaman [Paris-Sud]
Date: 
Tuesday 29th March 2011 - 16:30 to 17:30
Venue: 
INI Seminar Room 1
Abstract: 
This will be a (non exhaustive) survey talk about the behaviour of eigenfunctions of the laplacian on a compact manifold, in the asymptotic regime where the eigenvalue goes to infinity. The issue of ``quantum ergodicity'' is to understand the places where the eigenfunctions can concentrate. Recently, there has been increasing interest about possible analogues for the discrete laplacian on finite graphs (for instance, with the work of Brooks and Lindenstrauss). According to the physics literature, the interesting asymptotic regime to look at is the case of families of graphs whose size goes to infinity. As far as graphs are concerned, the talk will contain more open questions than results.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons