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SUMMARY:Lp-restriction of eigenfunctions to random Cantor type sets - Sure
 sh Eswarathasan\, Cardiff
DTSTART:20180307T160000Z
DTEND:20180307T170000Z
UID:TALK94654@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION: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 vibrati
 on of drums and membranes. They also represent stationary states of a free
  quantum particle on a Riemannian manifold. In the first part of the lectu
 re\, I will give a survey of results which demonstrate how the geometry of
  M affects the behaviour of these special functions\, particularly their s
 ize which can be quantified by estimating Lp norms.\n\nIn 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 in
 cludes concentration inequalities from probability theory in addition to t
 he analysis of singular Fourier integral operators on fractals.\n
LOCATION:MR13
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