Speaker: Prof. Christopher D.Sogge
Venue: Lecture Hall, 4th Floor, Run Run Shaw Business Administration Building
Abstract: Many problems in harmonic analysis involve the wave equation, and one can use Fourier analysis and Fourier integral operators to solve wave equations. We shall discuss several of these problems, including spherical maximal estimates, local smoothing bounds and Kakeya problems. We shall also go over recent decoupling estimates of Bourgain and Demeter that were inspired by the work of Wolff on regularity estimates for the wave equation. We shall also show how one can use Fourier analysis to solve critical nonlinear wave equations.