Dispersive Quantization of Linear and Nonlinear Waves

The evolution, through spatially periodic linear dispersion, of rough initial data leads to surprising quantized structures at rational times, and fractal, non-differentiable profiles at irrational times. The Talbot effect, named after an optical experiment by one of the founders of photography, was first observed in optics and quantum mechanics, and leads to intriguing connections with exponential sums arising in number theory. Ramifications of these phenomena and recent progress on the analysis, numerics, and extensions to nonlinear wave models will be discussed.

• Speaker: Peter Olver (University of Minnesota)
• Tuesday 16 January 2018, 16:00–17:00
• Venue: MR12, Centre for Mathematical Sciences.
• Series: Applied and Computational Analysis; organiser: ai10.