Diff. Geom, Math. Phys., PDE Seminar: Kenji Nakanishi

This is a survey on the joint works with Wilhelm Schlag, Joachim Krieger and Tristan Roy. We classify global behavior of all solutions with energy up to slightly more than the ground state for the nonlinear Klein-Gordon, Schrodinger, and wave equations. The dynamics include scatteing (to 0), blow-up, and scatttering to solitons. The solutions scattering to solitons form threshold hypersurfaces in the energy space, giving a complete classification under the energy constraint. It also describes how a solution can disperse in the past and blow up in the future.