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 (gmoschidis@berkeley.edu) or Federico Pasqualotto (fpasqualotto@berkeley.edu).

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.