The goal of project B03 is to study diffusions and gradient flows on spaces of measures with methods from optimal transport. The diffusions under consideration will be versions of Brownian motions, e.g. with Gamma, Dirichlet-Ferguson, or entropic measure as invariant distributions. The project also aims to explore optimal transport techniques beyond the traditional scope of gradient flows for semiconvex functionals on Wasserstein spaces, addressing the challenges arising from singular, highly non-convex boundary conditions and interaction potentials.
DFG Programme
Collaborative Research Centres
