# Mathematics Colloquia and Seminars

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 give a general survey of the Carleson operator, and then describe recent joint work with Lillian Pierce that introduces curved structure to the setting of Carleson operators.