The HADES seminar on Tuesday, February 25th, will be at 3:30pm in Room 740.

Speaker: Jason Zhao

Abstract: It has been observed both experimentally and mathematically that solutions to linear dispersive equations, such as the Schrodinger and Airy equations, posed on the torus exhibit dramatically different behaviors between rational and irrational times. For example, the evolution of piecewise constant data remains so at rational times, while it becomes continuous and fractalised at irrational times. A natural question to ask is whether this Talbot effect, as it broadly known, persists under non-linear dispersive flows. Focusing on the KdV equation, we will present two perspectives which follow in the spirit of the seminal works of Bourgain (1993) and Babin-Ilyin-Titi (2011): the first is the non-linear smoothing effect observed by Erdogan-Tzirakis (2013), and the second is the numerical work of Hofmanova-Schratz (2017) and Rousset-Schratz (2022}.