Abstract for the talk on 22.10.2019 (15:15 h)
Oberseminar ANALYSIS - PROBABILITYOliver Tse (Eindhoven University of Technology)
Dynamical-variational transport costs: Towards a framework for “generalised” gradient flows
Evolution equations in spaces of measures describe a wide variety of natural phenomena. The theory for such evolutions has seen tremendous growth in the last decades, of which resulted in general metric space theories for analysing variational evolutions—evolutions driven by one or more energies/entropies. On the other hand, physics and large-deviation theory suggest the study of generalised gradient flows—gradient flows with non-homogeneous dissipation potentials—which are not covered in metric space theories. In this talk, we introduce dynamical-variational transport costs (DVTs)—a large class of large-deviation inspired functionals that provide a variational generalisation of existing transport distances—to remedy this deficiency. The role in which these objects play in the theory of generalised gradient flows will be illustrated with an example on Markov jump processes. Finally, open questions and challenges will be mentioned.