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RestrictionÌýtheory studies functions whose Fourier transforms are supported on some curved manifold in R^n (for example, solutions to the linear Schrodinger equation or to the wave equation).ÌýÌýProjectionÌýtheorems study the Hausdorff dimension of fractal sets under orthogonalÌýprojectionsÌýfrom R^n to its subspaces. We will survey some recent works in both fields and discuss their interactions.Ìý This talk is intended for a general mathematical audience.Ìý