A Carleson operator of Radon type

Must the Fourier series of an $L^2$ function converge pointwise almost everywhere? In the 1960’s, Carleson answered this question in the affirmative, by studying a certain maximal operator that is now generally referred to as the Carleson operator. In this talk we will introduce the Carleson operator, survey several of its generalizations, and then describe new joint work with Lillian Pierce that introduces curved structure to the setting of Carleson operators.