The numerical computation of spectral properties (Green functions, densities of states...) of periodic crystals relies on singular integrals in Fourier space. I will describe new algorithms to compute these integrals, with applications to solid state physics and connections to spectral

In this talk, I will present some results on unique continuation for semilinear wave and Schrödinger equations with analytic nonlinearities. After recalling some motivation and classical results on the topic, I will describe a new method, introduced in a joint