The HADES seminar on Tuesday, **January 24th** will be at **3:30 pm** in **Room 740**.

**Speaker:** Marsden Katie Sabrina Catherine Rosie

**Abstract:** In this talk we will discuss the Cauchy problem for the energy-critical nonlinear Schrodinger equation in high dimensions. It is well-known that this problem is well-posed for data in Sobolev spaces with regularity $s>1$. The critical case $s=1$ was also shown to be globally well-posed with scattering by Ryckman-Vişan in the mid-2000s. In this talk we will show that even for some super-critical regularities, $s<1$, the equation is “almost-surely” globally well-posed with respect to a certain randomisation of the initial data and exhibits scattering.