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SUMMARY:New Directions in the Fractalization\, Quantization\, and Revival 
 of Dispersive Systems - Peter Olver (University of Minnesota)
DTSTART:20230425T160000Z
DTEND:20230425T170000Z
UID:TALK196684@talks.cam.ac.uk
CONTACT:Professor Maciej Dunajski
DESCRIPTION:The Talbot effect describes the remarkable evolution\, through
  spatially periodic linear dispersion\, of rough initial data\, producing 
 fractal\, non-differentiable profiles at irrational times and\, for asympt
 otically polynomial dispersion relations\, quantized structures and reviva
 ls at rational times.  Such phenomena have been observed in dispersive wav
 es\, optics\, and quantum mechanics\, and have intriguing connections with
  number theoretic exponential sums.   I will present some recent developme
 nts in the study of these fascinating phenomena\, including the effects of
  boundary conditions\, coupling dispersive systems to Lamb oscillators\, n
 ew manifestations in integro-differential equations modeling interface dyn
 amics\, and a study of the Fermi-Pasta-Ulam-Tsingou problem for coupled no
 nlinear oscillators.
LOCATION:MR11
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