Geometric measure theory and applications – GEOMETRYA

We shall address several problems within the framework of geometric measure theory, from both theoretical and numerical viewpoints. Our project is divided into 5 topics :
1) Geometric measure theory in singular metric spaces
2) Plateau problems
3) Around the Mumford-Shah functional
4) Irrigation and branched transport
5) Around the Willmore energy
The particularity of our project is to bring together pure and applied mathematicians, working in different areas: Geometric analysis, geometric measure theory, calculus of variations, numerical analysis, optimal transportation, scientific computing, and image processing. This diversity is a keypoint to tackle, with different but complementary approaches, the various issues raised in our project.