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Speaker: Mark Hoefer, Professor & Chair, Department of Applied Mathematics, University of Colorado, Boulder
Title: A Wave Theory of Waves
Abstract: Hydrodynamic theories describe long wave propagation in a continuum, such as a fluid where the microscopic constituents are interacting fluid particles. When the constituents are interacting waves rather than particles, we arrive at a macroscopic wave theory of waves called dispersive hydrodynamics. A canonical example is the dispersive shock wave or DSW, which consists of an unsteady (expanding) collection of nonlinear oscillations terminating with zero amplitude (harmonic limit) at one end and zero wavenumber (soliton limit) at the other. Scale separation leads to the mathematical framework of nonlinear wave modulation theory, originally developed by G. B. Whitham in 1965. Applications include geophysics (internal and surface ocean or atmospheric waves), fluid dynamics (interfacial waves), condensed matter (ultracold atomic gases, magnetic materials), and nonlinear photonics (fiber and spatial optics). This talk will present a variety of developments and results in dispersive hydrodynamics utilizing Whitham modulation theory, numerical simulations, and experiment.
Short bio: Mark Hoefer is Professor and Chair of the Department of Applied Mathematics at the University of Colorado, Boulder, drawn back to the Rockies in 2014 after obtaining his PhD from the same department in 2006. In between, he held National Research Council and National Science Foundation postdoc positions at NIST and Columbia University before becoming an Assistant Professor in the Mathematics Department of North Carolina State University. Mark's research encompasses the mathematics and physics, including in-house experiments, of multiscale nonlinear waves. He received the National Science Foundation's Career award in 2013 and the T. Brooke Benjamin Prize in Nonlinear Waves from SIAM in 2020. In 2022, he was the principal organizer for a six-month research program on Dispersive Hydrodynamics at the Isaac Newton Institute in Cambridge, UK. He is deputy editor of the recently established Journal of Nonlinear Waves, published by Cambridge University Press.