Project A8: Variational structures for evolution equations, optimal transport, and synthetic curvature

Summary:

One major focus of this project are gradient flows and other variational structures for evolutions in spaces of probability measures. We aim to identify such structures based on tailored geometries for large classes of PDEs and to exploit them in the analysis of singular limits and long-term behavior. Special emphasis will be put on optimal transport and evolutionary PDEs on networks. A second major focus is to push forward the analysis and geometry on singular spaces with synthetic bounds on the curvature.

Recent Preprints: