Carlos Kenig, The University of Chicago:
Global well-posedness and scattering for critical non-linear
Schrodinger and wave equations

We will discuss recent works with Frank Merle in which we show, for the energy critical focusing Schrodinger and wave equations, that for data with energy smaller than that of the standing wave (the ground state for the corresponding nonlinear elliptic equation) that a sharp alternative holds: we either have global existence and scattering or finite time blow-up. The dividing surface is the sphere in H1 whose radius is the norm of the standing wave. The methods combine variational ideas, elliptic and parabolic theory with oscillatory integrals.