**Title:** Optimal transportation and Sudakov’s type decomposition

**Abstract:**I will briefly present an introduction to optimal transportation problem. I will mainly focus on the definitions of potentials and c-monotonicity. These objects are linked to the optimality of a transference plans, in particular the existence of potentials allows to simplify the problem and to find solutions. Indeed, problems may arise when potentials do not exists.
In the last part I will sketch what is a Sudakov’s type decomposition of transference plans and i will show how to simplify a convex cost problem by means of this technique.
Moreover, in order to iterate this procedure and find a solution, I will show how to overcome the lack of potential throughout the existence of a preorder.

This seminar is part of the AJS series of seminars.