Title: Behaviour of the Brascamp-Lieb constant and Applications
Abstract: The Brascamp-Lieb inequality generalizes many important 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 local-boundedness result with several applications including a nonlinear generalization arising in PDE. This is joint work with Jonathan Bennett, Neal Bez, Michael Cowling and Sanghyuk Lee.