Title: Restriction estimates for fractal sets
Abstract: Restriction estimates for surface-carried measures on smooth manifolds have been studied extensively in harmonic analysis. In this setting, the range of exponents for which restriction estimates are available depends primarily on the dimension and curvature of the manifold. It turns out that a similar theory can also be developed for fractal sets, including sets of dimension less than one on the line. Generally, additive structure plays the role of curvature, so that "random" (in a quantifiable sense) fractals play toe role of curved manifolds and "additively structured" fractals behave like flat surfaces; however, the situation for fractals turns out to be more complicated, with additional types of behaviour present that cannot occur for smooth manifolds. We will survey the recent developments in the area and discuss some open questions.