Pointwise convergence for single-particle Schrödinger equation and Schrödinger equation with infinitely many particles on the torus and waveguide manifolds

In 1980, Carleson posed a question about the least regularity required for initial data in a Sobolev space $H^s$ to ensure pointwise convergence of the solution to the single particle linear Schrodinger equation. In this paper, we study Carleson problem on the $d$-dimensional waveguide manifold $\ma