Upcoming events

Virtual harmonic analysis seminar: Diogo Oliveira e Silva (University of Birmingham)

Location: Zoom,

Description: https://sites.google.com/view/virtual-harmonic-analysis/homeTitle: Sign uncertainty principles: old and new  Abstract: Ten years ago, Bourgain, Clozel & Kahane established a surprising "sign uncertainty principle" (SUP), asserting that if a function and its Fourier transform are nonpositive at the origin and not identically zero, then they cannot both be nonnegative outside an arbitrarily small neighbourhood of the origin. In 2017, Gonçalves & Cohn solved the 12-dimensional SUP via connections to the sphere packing problem, and discovered a complementary SUP. This talk will focus on some new sign uncertainty principles which generalise the developments of Bourgain, Clozel & Kahane and Cohn & Gonçalves. In particular, we will discuss SUPs for Fourier series, the Hilbert transform, spherical harmonics, and Jacobi polynomials. As a by-product, we determine some sharp instances of the spherical SUP via connections to tight spherical designs. Time permitting, we will outline a possible path towards the sharp 1-dimensional SUP. This talk is based on recent joint work with Felipe Gonçalves and João Pedro Ramos.