Concavity principles for weighted marginals

Abstract. In this **technical** talk we shall explain how to derive a formula for the second derivative of marginals of functions defined on convex sets using the Bochner-Hörmander L2 method. This will allow us to prove some weighted concavity principles of Borell-Brascamp-Lieb type. This is the content of Sections 3 and 4 of our joint work https://arxiv.org/pdf/2506.16941 with Dario Cordero-Erausquin.