Skip to content Skip to navigation

MIGSAA Mini Course in Bilinear Restriction Estimates and Applications

MIGSAA welcomes you to join a short course in Bilinear Restriction Estimates and Applications run by Tim Candy (Bielefeld)

TIme: 4-5pm on 19, 20 and 21 October, 2016

Venue: Teviot - 1.416 Teaching Room 9 -- Doorway 3


The bilinear restriction problem was originally developed to make progress on the question of linear Lp
estimates for the Fourier transform of compact hypersurfaces. The bilinear problem can also be stated in
terms of bilinear estimates for transverse waves, and thus is closely connected to problems in nonlinear
dispersive PDE.
In these lectures we will follow the argument of Tao [3], giving the essentially optimal bilinear restriction
estimates for the paraboloid, and explain some recent applications to controlling resonant interactions in
dispersive PDE developed in [1]. In particular we aim to cover the wave packet decomposition, the induction
on scales argument, extensions to V p spaces, and explain how these bilinear estimates can be applied to
obtain scattering for the Dirac-Klein-Gordon system.