Event Detail Information
Peter Olver (University of Minnesota) will present "Dispersive Quantization -- the Talbot Effect." The evolution, through linear dispersion, of piecewise constant periodic initial data leads to surprising quantized structures at rational times, and fractal, non-differentiable profiles at irrational times. Similar phenomena have been observed in optics and quantum mechanics, where it is known as the Talbot effect after an optical experiment by one of the founders of photography, and lead to intriguing connections with exponential sums arising in number theory. Ramifications of these observations for numerics and nonlinear wave models will be discussed.