Speaker
Itamar Oliveira, University of Birmingham
Abstract
Harmonic Analysis witnessed a remarkable number of breakthroughs in recent times, such as the solution of the Kakeya conjecture in R^3 and significant progress in Fourier restriction theory. A major modern challenge is to build bridges between oscillatory and non-oscillatory problems (like Restriction and Kakeya-type problems) by using tools of the latter kind to solve problems of the former. One such bridge, Stein’s conjecture for weighted L^2 Fourier extension estimates, combines in a single inequality a Kakeya-maximal-type operator and the Fourier extension operator. This conjecture was recently shown to be false in its global form by Hannah Cairo, which immediately raised concerns that it may be false even at the local level. We will see an alternative way of checking the failure of its global form by putting together the Schrödinger equation, counts of rectangles and isosceles triangles, and elementary number theory.