The APDE seminar on Monday, 4/5, will be given by Maciej Zworski online via Zoom from 4:10 to 5:00pm. To participate, email Georgios Moschidis (firstname.lastname@example.org) or Federico Pasqualotto (email@example.com).
Title: Internal waves and homeomorphism of the circle.
Abstract: The connection between the formation of internal waves in fluids and
the dynamics of homeomorphisms of the circle was investigated by
oceanographers in the 90s and resulted in novel experimental
observations (Maas et al, 1997). The specific homeomorphism is given
by a chess billiard” and has been considered by many authors (John
1941, Arnold 1957, Ralston 1973, … , Lenci et al 2021). The relation
between the nonlinear dynamics of this homeomorphism and linearized
internal waves provides a striking example of classical/quantum
correspondence (in a classical and surprising setting of fluids!) and,
using a model of tori and of zeroth order pseudodifferential
operators, it has been a subject of recent research, first by Colin de
Verdière-Saint Raymond 2020 and then by Dyatlov, Galkowski, Wang and
the speaker. In these works, many facets of the relationship between
hyperbolic sources and sinks for the classical dynamics and internal
waves in fluids were explained. I will present some of these results
as well as some numerical discoveries (including those of
Almonacid-Nigam 2020). I will also describe various open problems.