Mathematical Sciences

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17 July 2019

Research Seminar: From Kakeya to Restriction, and how to make it sharp

Presented By Diogo Oliveira e Silva (Birmingham)
  • SCH.0.13 Schofield Building

About this event

Abstract: 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, and describe some applications.