Recorded 07 February 2022. Karoly Boroczky of the Renyi Institute of Mathematics presents "Equality in the Reverse Brascamp Lieb Inequality" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: The Reverse Brascamp Lieb inequality is a generalization of the Prekopa-Leindler inequality analogous to the Brascamp-Lieb inequality for functions defined on subspaces whose equality case has been clarified by Valdimarsson. Partially building on the work of Tao, Bennett, Carbery and Christ on the structure of "Brascamp-Lieb" data and Caffarelli's work related to his Contraction Principle, we characterize equality in the Reverse Brascamp Lieb inequality. (Joint work with Franck Barthe, Pavlos Kalanzopoulos, substantial input from Emanuel Milman)