Jia-Hao Tan

Maximal estimates for perturbations of the Schr\"odinger operator on $\mathbb{T}^d$

We study $L^p_x L^\infty_t$ maximal estimates for exponential sums associated to $C^2$ graph hypersurfaces, motivated by Schr\"odinger maximal estimates on $\mathbb{T}^d$. We show that the conjectured maximal estimate for the periodic Schr\"odinger equation fails when one allows small perturbations of the paraboloid, w...