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Lower bounds on eigenfunctions on hyperbolic surfaces. Dyatlov, Semyon Mar 21, 2018

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Title Lower bounds on eigenfunctions on hyperbolic surfaces.
Creator Dyatlov, Semyon
Publisher Banff International Research Station for Mathematical Innovation and Discovery
Date Issued 2018-03-21T19:33
Description I show that on a compact hyperbolic surface, the mass of an L2- normalized eigenfunction of the Laplacian on any nonempty open set is bounded below by a positive constant depending on the set, but not on the eigenvalue. This statement, more precisely its stronger semiclassi- cal version, has many applications including control for the Schrdinger equation and the full support property for semiclassical defect mea- sures. The key new ingredient of the proof is a fractal uncertainty principle, stating that no function can be localized close to a porous set in both position and frequency. This talk is based on joint works with Long Jin and with Jean Bourgain.
Extent 48 minutes
Subject Mathematics
Dynamical systems and ergodic theory
Probability theory and stochastic processes
Dynamical systems
Geographic Location Banff (Alta.)
Type Moving Image
FileFormat video/mp4
Language eng
Notes Author affiliation: Massachusetts Institute of Technology
Series BIRS Workshop Lecture Videos (Banff, Alta)
Date Available 2018-09-18
Provider Vancouver : University of British Columbia Library
Rights Attribution-NonCommercial-NoDerivatives 4.0 International
DOI 10.14288/1.0372065
URI http://hdl.handle.net/2429/67196
Affiliation Non UBC
Peer Review Status Unreviewed
Scholarly Level Faculty
Rights URI http://creativecommons.org/licenses/by-nc-nd/4.0/
AggregatedSourceRepository DSpace

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