Peter Olver (University of Minnesota)

Math & Stats Department Colloquium

Friday, March 25th, 2022

Time: 2:30 p.m.  Place: Online (via Zoom)

Speaker: Peter Olver (University of Minnesota)

Title: Fractalization and Quantization in Dispersive Systems

Abstract: The evolution, through spatially periodic linear dispersion, of rough initial data produces fractal, non-differentiable profiles at irrational times and, for asymptotically polynomial dispersion relations, quantized structures at rational times. Such phenomena have been observed in dispersive wave models, optics, and quantum mechanics, and lead to intriguing connections with exponential sums arising in number theory. Ramifications and recent progress on the analysis, numerics, and extensions to nonlinear wave models, both integrable and non-integrable, will be presented. Time permitting, recent related results for the Fermi-Pasta-Ulam problem will also be discussed.

Peter Olver is a Full Professor in the School of Mathematics at the University of Minnesota since 1985. He served as the Head of the Department from 2008 to 2020. He is a Fellow of the American Mathematical Society, the Society for Industrial and Applied Mathematics (SIAM), and the Institute of Physics, UK. His research interests revolve around the applications of symmetry and Lie groups to differential equations. Over the years, he has contributed to a wide range of fields, including mathematical physics, fluid mechanics, elasticity, quantum mechanics, Hamiltonian mechanics, the calculus of variations, differential geometry, classical invariant theory, computer vision, geometric numerical methods.