Some current projects:

1. My PhD thesis Markov Fibrations. I am working on a "journal version" of the main contribution, the eponymous theory of Markov fibrations/stochastic module fibrations. This will probably also be the home for some minor contributions to Markov category theory, especially the theory of Slice Markov Categories.
2. Tangencies of commutative monoids. There should be a theory like this which interpolates between petri nets and DOTS-type dynamical systems (note that the state space of the dynamical system associated to a petri net is the free commutative monoid on the set of places). With Owen Lynch and David Jaz Myers.
3. Control theory/lyapunov functions for DOTS. There is a nice way to cook up a category of "systems equipped with invariant subspaces"/systems equipped with Lyapunov functions as an almost free enhancement to the theory of systems. Combining this idea with the triple category of "bisystems" has the potential to produce a very general approach to control theory. With Matteo Capucci.
4. Universal property of measure-theoretic probability theory. Nearly finished paper, The Universal Property of Measure-Theoretic Probability.
5. Lack's discrete or trivial model structure on a generic 2-category is self-dual (in the sense that the dual model structure on \mathcal {C}^\mathrm {op} is exactly the one associated to the 2-category \mathcal {C}^\mathrm {op}), something which simplifies a number of things in Lack's paper.
6. The tangency of martingale problems and representable dynamics for martingale problems. Almost done (written up on the safeguarded AI forest), should be made public soon.

Random crap:

1. Markov Fibrations
2. Lyapunov function
3. Slice Markov Categories
4. https://erischel.com/efr-ECP8/
5. Notions of prechart equivalence