Speaker: Taryn Flock (UNIVERSITY OF MASSACHUSETTS, AMHERST)
Title: A NONLINEAR BRASCAMP-LIEB INEQUALITY
Abstract: Inequalities play a central role in harmonic analysis. However, in many cases the fundamental question ”When and how can one achieve equality?” is left unanswered. Answering these questions opens the door to proving stronger or perturbed versions of the inequality. I will briefly discuss sharp inequalities in general, beginning with the classical isoperimetric inequality of Euclidean geometry, before focusing on a discussion of my recent work on the Brascamp–Lieb inequality. Time permitting, I will highlight connections to computer science, geometry, and number theory. In particular, this work is used in the proof of a longstanding conjecture in number theory, Vinogradov’s mean value theorem (works discussed will include joint work with Jon Bennett, Neal Bez, Stefan Buschenhenke, Michael Cowling, and Sanghyuk Lee).