Conference Global Portuguese Mathematicians 

14/07/2017, 15:00 — 16:00 — Amphitheatre Pa1, Mathematics Building
Diogo Oliveira e Silva, University of Bonn

From Kakeya to Restriction, and how to make it sharp

What is the smallest area which is required to rotate a unit line segment by 180 degrees in the plane? How is the geometric notion of curvature related to the analytic notion of decay? What can be said about the convergence of Fourier series in higher dimensions? And, perhaps more interestingly, how are these apparently unrelated questions connected?

In this talk, we will provide a short introduction to the Kakeya problem, the Fourier restriction problem, and the Bochner-Riesz problem, highlighting the various interdependences. We will then focus on some recent progress on sharp Fourier restriction theory on spheres, hyperboloids and perturbed paraboloids, and describe some applications.

See also

DOS_s.pdf