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Texas A&M University
Mathematics

Mathematical Physics and Harmonic Analysis Seminar

Date: October 23, 2020

Time: 1:50PM - 2:50PM

Location: Zoom

Speaker: Jun Kitagawa, Michigan State University

  

Title: On free discontinuities in optimal transport

Abstract: It is well known that regularity results for the optimal transport (Monge-Kantorovich) problem require rigid geometric restrictions. In this talk, we consider the structure of the set of ``free discontinuities'' which arise when transporting mass from a connected domain to a disconnected one, and show regularity of this set, along with a stability result under suitable perturbations of the target measure. These are based on a non-smooth implicit function theorem for convex functions, which is of independent interest. This talk is based on joint work with Robert McCann (Univ. of Toronto).