**Prelectura de tesis**

**Doctorando: Giuseppe Negro (UAM-ICMAT & Université Paris 13). **

**Directores de tesis: Keith Rogers (ICMAT), Thomas Duyckaerts (UP13). **

**Título: Sharp estimates for linear and nonlinear wave equations via the Penrose **

**transform. **

**Jueves 13 de diciembre**

**15:30 hr, Módulo 17, aula 520**

**Resumen: In 2006, Damiano Foschi found the sharp constant in the Strichartz estimate for the wave equation in $R^{3+1}$ and conjectured what the maximizers should be in other dimensions. On the one hand, we will see how his inequality can be sharpened further, adding a term which is zero on the maximizers, and on the other hand we will disprove his conjecture in even dimensions. For this we will take advantage of a conformal transformation which compactifies the space-time. We will also present a sharp estimate for the scattering norm of the cubic wave equation on Minkowski space with data in the critical $L ^{^2}$-Sobolev space. **