Seminar

Brascamp-Lieb inequality generalizes many inequalities in analysis, including the Hölder, Loomis-Whitney, and Young convolution inequalities.  Sharp constants for such inequalities have a long history and have only been determined in a few cases. We investigate the stability and regularity of the sharp constant as a function of the implicit parameters. The focus of the talk will be a continuity result with several applications including generalizations with connections to PDEs and Bourgain and Demeter's decoupling method.  The talk will be accessible to members of the Analytic number theory program, and maybe of interest, as the connection to Vinogradov's mean value theorem will be discussed. (joint with Jonathan Bennett, Neal Bez, Michael Cowling and Sanghyuk Lee.)