New Directions in the Fractalization, Quantization, and Revival of Dispersive Systems

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• Peter Olver (University of Minnesota)
• Tuesday 25 April 2023, 17:00-18:00
• MR11.

If you have a question about this talk, please contact Professor Maciej Dunajski.

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 asymptotically polynomial dispersion relations, quantized structures and revivals at rational times. Such phenomena have been observed in dispersive waves, optics, and quantum mechanics, and have intriguing connections with number theoretic exponential sums. I will present some recent developments in the study of these fascinating phenomena, including the effects of boundary conditions, coupling dispersive systems to Lamb oscillators, new manifestations in integro-differential equations modeling interface dynamics, and a study of the Fermi-Pasta-Ulam-Tsingou problem for coupled nonlinear oscillators.

This talk is part of the Mathematical Physics Seminar series.

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