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SUMMARY:Recent advances on the Carleson convergence problem for the Schrö
 dinger equation
DTSTART:20261016T114500Z
DTEND:20261016T133000Z
DTSTAMP:20261012T004400Z
UID:indico-event-17426@indico.math.cnrs.fr
DESCRIPTION:Speakers: Daniel Eceizabarrena (Basque Center for Applied Math
 ematics (BCAM))\n\nLet $u = u(t\,x)$ be the solution to the free Schrödin
 ger equation with initial data $f$. One would expect to recover the data w
 hen the time $t$ goes to zero\, even pointwise. It of course holds if $f$ 
 is Schwartz\, but it may fail for $f$ in $L^2$. In this setting\, what is
  the minimal regularity for $f$ such that $u(t\,x)$ tends to $f(x)$ pointw
 ise\, when $t$ goes to zero? This is popularly known as Carleson's conver
 gence problem for the Schrödinger equation. \nIn the first part of the ta
 lk\, I will introduce the problem and discuss the main results\, like th
 e solution to the Euclidean problem obtained in 2019\, as well as the une
 xpected solution to the periodic problem given a few weeks ago with the he
 lp of AI (except in dimension 1 which remains open). I will also discuss 
 some other interesting variations of the problem. \nIn the second part\, I
  will introduce a probabilistic element that allows to dramatically decrea
 se the regularity of the data\, and I will share my latest work for the 2
 D quintic periodic NLS (https://arxiv.org/abs/2608.17100) in collaboration
  with Pablo Merino. \n\nhttps://indico.math.cnrs.fr/event/17426/
LOCATION:Salle de séminaire (Orléans institut Denis Poisson)
URL:https://indico.math.cnrs.fr/event/17426/
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