Z-mappings for mathematicians: Flavien Léger (INRIA Paris)

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).