Extension theory and
H. Edelsbrunner, Ž. Virk, and H. Wagner:
Topological data analysis in information space.
Manuscript, IST Austria, Klosterneuburg, Austria, 2018.
on IST repository
I am developing a theory of intrinsic persistence. A number of preprints are in preparation, including: on a Hopf type phenomenon; higher-dimensional persistence of metric graphs; and on approximations by complexes in topology.
With M. Čufar we are implementing computations of 1-dimensional intrinsic persistence.
With A. Akopyan, H. Edelsbrunner, and H. Wagner we are developing a TDA pipeline using Bregman divergences. Another preprint is 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.