Talk Abstract: Z-mappings form a theory of non-variational problems initiated in the '70s but that has been for the most part overlooked by mathematicians.

In the first part of my talk I will show that although Z-mappings are not widely known, they can be found in a variety of contexts, such as:

- Hamilton-Jacobi-Bellman equations and their viscosity solutions,

- optimal transport,

- mean curvature flow,

- matching models in economics.

In the second part of the talk we will look at algorithms. Similar to how gradient descent is a natural algorithmic companion to convex problems, there exists a class of numerical methods naturally associated with Z-mappings. And it so happens that various well-established algorithms can be grouped under this point of view (Dijkstra's algorithm, MBO for interface dynamics, Bertsekas' naive auction, Sinkhorn, Gale-Shapley).

Bio: Flavien Léger is a French mathematician. Léger earned his PhD from the Courant Institute, New York University in 2017 under the supervision of Nader Masmoudi and Alfred Galichon. Since 2021 he is a permanent researcher at INRIA Paris. His research mainly revolves around theoretical and applied optimal transport, with a variety of connections to economics, geometry and optimization.