Welcome to the website of the APDE group in Bilbao (at BCAM and EHU) working in mathematical analysis, partial differential equations, inverse problems, mathematical physics, and related topics.
BCAM, October 22nd, 2026, 17:00 - 18:00
A nonlinear and probabilistic approach to the periodic Carleson convergence problem
Daniel Eceizabarrena - BCAM
Given the solution $u = u(x,t)$ to the Schrodinger equation with initial data $f$, when can we say that $\lim_{t \to 0} u(x,t) = f(x)$ pointwise in $x$? More precisely, what Sobolev regularity do we require for $f$ for this property to hold? This is known as Carleson's convergence problem.
I will discuss recent results in the periodic setting, both for the linear and non-linear Schrödinger equations, and how a probabilistic approach can dramatically decrease the Sobolev regularity required for the initial data.
This talk is in the context of the recent work https://arxiv.org/abs/2608.17100 in collaboration with Pablo Merino (BCAM).
Current organizers: Daniel Eceizabarrena (BCAM), Mikel Florez (EHU), Arnab Roy (BCAM).