**Speaker:** Dr. Domynikas Norgilas from the University of Michigan (invited by Adriana Ocejo Monge)

**Title:** The Monge-Kantorovich mass transport with supermartingale constraints.

**Abstract:** Given two measures μ,ν on **R** with μ(**R**) ≤ ν(**R**), and such that μ is smaller than ν in positive convex-decreasing order (i.e., μ ≤_{pcd} ν), there exists a two-period supermartingale S = (S₁,S₂) that transports μ to ν. For each such supermartingale, S₁ ~ μ, but there are many possible choices for the law of S₂. In this talk we study two canonical choices (the minimal and the maximal measures) with respect to convex-decreasing order. We show how these measures give rise to the so-called *supermartingale shadow* couplings of S₁ and S₂.