‘Continuity of the Brascamp–Lieb constant and applications’

Brascamp-Lieb inequality generalizes many inequalities in analysis, including the Hölder, Loomis-Whitney, and Young's 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 a sharp nonlinear Brascamp-Lieb inequality for so-called "simple data" and a mutlilinear Kakeya-type inequality with applications to Bourgain and Demeter's decoupling method. This is joint work with Jonathan Bennett, Neal Bez, Stefan Buschenhenke, Michael Cowling and Sanghyuk Lee.