We prove Strichartz estimates with fractional loss of derivatives for the Schrödinger equation
on any Riemannian compact manifold. As a consequence we infer low regularity local well …

We study the local existence of strong solutions for the cubic nonlinear wave equation with
data in H s (M), s< 1/2, where M is a three dimensional compact Riemannian manifold. This …

The last fifteen years have seen a flurry of exciting developments in Fourier restriction
theory, leading to significant new applications in diverse fields. This timely text brings the …

3. Construction of Z: A (GL (2)) x A (GL (2))-+ A (GL (4)) 3.1. Relevant objects and the
strategy 3.2. Weak to strong lifting, and the cuspidality criterion 3.3. Triple product L …

In practice, encoding invariances into models improves sample complexity. In this work, we
study this phenomenon from a theoretical perspective. In particular, we provide minimax …

1. INTRODUCTION The purpose of this paper is twofold. First, if Y and Z are smooth
paracompact manifolds of dimensions n> 2 and n+ 1, respectively, we shall prove local …

In 1903 Voronoi [42] postulated the existence of explicit formulas for sums of the form
(ii)??>!*?/(*). for any" arithmetically interesting" sequence of coefficients (an) n> i and …

We study the cubic non linear Schrödinger equation (NLS) on compact surfaces. On the
sphere S^2 and more generally on Zoll surfaces, we prove that, for s> 1/4, NLS is uniformly …

Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins
University, this book introduces eigenfunctions on Riemannian manifolds. Christopher …

We give an overview of some new and old results on geometric properties of eigenfunctions
of Laplacians on Riemannian manifolds. We discuss properties of nodal sets and critical …