Title: Cancellation for the multilinear Hilbert and simplex transforms
Abstract: The Lp boundedness of the trilinear and higher Hilbert transforms (and more generally, the simplex transforms) are one of the main open problems in multilinear harmonic analysis. We present work by the author and by Zorin-Kranich establishing a small partial result towards this problem, namely that there is some cancellation in these operators allowing one to improve very slightly over the triangle inequality bound.