Joram Seminar: Larry Guth (MIT) - Introduction to decoupling

Thu, 10/01/201914:30-15:30
Manchester Building (Hall 2), Hebrew University Jerusalem
Decoupling is a recent development in Fourier analysis. In the late 90s, Tom Wolff proposed a decoupling conjecture and made the first progress on it. The full conjecture had seemed well out of reach until a breakthrough by Jean Bourgain and Ciprian Demeter about five years ago.
Decoupling has applications to problems in PDE and also to analytic number theory. One application involves exponential sums, sums of the form
$$\sum_j e^{2 pi i \omega_j x}.$$
Decoupling helps to relate geometric information about the way the frequencies $\omega_j$ are arranged with analytic information about the sum.
In this first talk, we will introduce decoupling inequalities and describe some applications.