In this talk, we will discuss and motivate some fundamental nonlinear problems that involve fractional powers of the Laplacian. In particular, we will study nonlinear ground states, which play an essential role in theory of water waves (and related dispersive equations). Here, the uniqueness of ground states has been a central open problem in the field since the formulation of the Benjamin-Ono equation in 1970s. In this talk, I will present a recent general uniqueness result, which answers this question affirmatively. This is joint work with Rupert Frank (Princeton).
Attention -- change of location!! Now: HS 102, Building 10.50