Analysis and Mathematical Physics

We obtain new bounds on the additive energy of (Ahlfors-David type) regular measures in both one and higher dimensions, which implies expansion results for sums and products of the associated regular sets, as well as more general nonlinear functions of these sets. As a corollary of the higher-dimensional results we obtains some new cases of the fractal uncertainty principle in odd dimensions. This is joint work with Terence Tao.