I do research in higher categories and topological field theories, and I try to maintain a healthy interest in a variety of other subjects (mainly logic, manifold topology, and some parts of mathematical physics). Here are some questions I have thought about recently:

• Is there a simplicial space model for (∞,n)-categories that resembles n-complicial sets? The combinatorics of orientals, which dictates the lifting properties of complicial sets, is pretty complicated; can it be simplified so as to have one "Segal style" condition in every dimension?

• How do we freely add adjoints to k-morphisms in an n-category? The cobordism & tangle hypotheses provide an answer for very simple n-categories as long as we add all adjoints at once. What if we only want to add some adjoints? Do we still get cobordisms?

• Given a (complete) Segal space, its colimit computes the completion of the associated (∞,1)-category, i.e. the space obtained by inverting all of its morphisms. This space is initial with respect to maps out of the (∞,1)-category that land into the invertible part of the target. Since adjoints can be thought of as lax inverses, is there a context in which the process of freely adding adjoints to an (∞,1)-category can be expressed in terms of a (possibly lax) colimit?

About freely adding adjoints and connections to the cobordism category:

• Zigzags and free adjunctions - on some work done with Martina Rovelli, prepared for a seminar at Texas Tech University, November 2025

About the Rozansky-Witten 3-category:

• A step towards the Rozansky-Witten TFT - brief overview of my thesis project, prepared for "(∞,n)-Categories and Applications" in Utrecht, April 2024

• Longer overviews of my thesis project: an expository version (Rhind seminar, November 2024), a longer expository version (Vienna seminar, May-June 2024), a more categorical version (TUM seminar, September 2024)