PLEASE NOTE ROOM CHANGE FROM LAST TERM: SEMINAR WILL NOW BE HELD IN FINE 110. In recent times - particularly the last two decades - discrete analogues in harmonic analysis have gone through a period of considerable changes and developments.
$\ell^p(\mathbf Z^d)$ boundedness for discrete operators of Radon types: maximal and variational estimates
The restriction conjecture is an open problem in Fourier analysis first raised by Stein in the late 60’s. It is about the L^p estimates obeyed by an oscillatory integral operator. I will explain a recent approach to this problem, which gives a slightly better estimate in three dimensions.