Explore the mathematical connections between restriction theory and projection theorems in this 57-minute lecture delivered at the Centre de recherches mathématiques. Delve into restriction theory, which examines functions whose Fourier transforms are supported on curved manifolds in R^n, including solutions to linear Schrödinger and wave equations. Investigate projection theorems that analyze the Hausdorff dimension of fractal sets under orthogonal projections from R^n to its subspaces. Survey recent developments in both mathematical fields while discovering their fascinating interactions and applications. Gain insights into advanced harmonic analysis concepts through this accessible presentation designed for a general mathematical audience, part of the CRM Nirenberg Lectures in Geometric Analysis series.