I am developing a theory of intrinsic persistence. Three preprints are in preparation: on a Hopf type phenomenon; higher-dimensional persistence of metric graphs; and on approximations by complexes in topology.
With A. Akopyan, H. Edelsbrunner, and H. Wagner we are developing a TDA pipeline using Bregman divergences. Preprints are on the way.
With K. Austin we are working on generalizations of coarse dimension raising results and related problems. A preprint should be out soon.