Title: Harmonic analysis (with a little taste of geometry)

Abstract: I will give a brief survey about some recent work I have done with
my collaborators. The main dishes will be from harmonic analysis, but we'll
see a little trace of geometry on the sides. Some ingredients we have are
pseudodifferential operators, Carleson operators and Gagliardo-Nirenberg
inequalities. Towards the end of the talk, we will discuss some nonlinear
wave equations that exhibit conformal invariance. These are joint work with
Elias Stein, Lillian Pierce, Yi Wang and Sagun Chanillo.