Conference

We will cover the basic theory of the Fourier transform in Rn, the Wigner transform, X-ray and Radon transforms, fractional integration and the Kenig-Stein operator.

We will cover the Stein-Tomas theory and applications to PDE, discuss some of the tools used over the last 50 years to study the restriction conjecture and understand its connection to the Kakeya problems.

The plan for this lecture is to introduce Stein’s and Mizohata-Takeuchi’s conjectures, build our intuition through simple cases and cover the basics of spherical harmonics and Bessel functions that will be necessary for the next lecture.

The plan is to verify the Mizohata-Takeuchi conjecture for the sphere when whe underlying weight is radial. This will require the previously covered background on spherical harmonics and Bessel functions.

The plan is to present recent progress in our joint work with Bennett, Gutierrez and Nakamura on a Sobolev version of the Mizohata-Takeuchi problem. This is a weaker version of the conjecture that can be studied in connection with certain nonlinear variants of the Wigner transform and of the Kenig-Stein operator.

Itamar Oliveira (University of Birmingham)

Itamar is a research fellow at the University of Birmingham working in linear and multilinear harmonic analysis.

Link to webpage: https://sites.google.com/view/itamaroliveira/home