Mathematics Colloquia and Seminars

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This is intended to be a talk for a (more) general audience. The plan of it is as follows: we start by discussing several facts about the history and evolution of the time-frequency area (Fourier Series, Calderon-Zygmund theory, wave-packet theory) and then refer to the general approach/tools for solving a time-frequency problem. Next we present two fundamental topics in this eld: the pointwise convergence of the Fourier Series and the boundedness of the Bilinear Hilbert transform. We end by adressing several key aspects of our work including the following problems: -- the boundedness of the Bilinear Hilbert transform on smooth curves; -- the boundedness of the Polynomial Carleson operator; -- the pointwise convergence of Fourier Series near L1.