In a discussion following a MathOverflow answer by Joel Hamkins, Timothy Chow and I got into a chat about what it means for a statement to “not have a definite truth value”. I need a break from writing the paper on countable reals (coming soon in a journal near you), so I thought it would be worth writing up my view of the matter in a blog post.

I gave a talk “Variations on Weihrauch degrees” at Computability in Europe 2023, which took place in Tbilisi, Georgia. The talk was a remote one, unfortunately. I spoke about generalizations of Weihrauch degrees, a largely unexplored territory that seems to offer many opportunities to explore new directions of research. I am unlikely to pursue them myself, but will gladly talk with anyone who is interested in doing so.

Slides: CiE-2023-slides.pdf.

On the occasion of Dieter Spreen's 75th birthday there will be a Festschrift in the Journal of Logic and Analysis. I have submitted a paper “Spreen spaces and the synthetic Kreisel-Lacombe-Shoenfield-Tseitin theorem”, available as a preprint arXiv:2307.07830, that develops a constructive account of Dieter's generalization of a famous theorem about continuity of computable functions. In this post I explain how the paper fits into the more general topic of continuity principles.

At TYPES 2023 I had the honor of giving an invited talk “On Isomorphism Invariance and Isomorphism Reflection in Type Theory” in which I discussed isomorphism reflection, which states that isomorphic types are judgementally equal. This strange principle is consistent, and it validates some fairly strange type-theoretic statements.

Here are the slides with speaker notes and the video recording of the talk.

I am at the Machine assisted proofs workshop at the UCLA Institute for Pure and Applied Mathematics, where I am about to give a talk on “Formalizing invisible mathematics”.

Here are the slides with speaker notes and the video recording of the talk.

On February 10, 2023, I gave my Levi L. Conant Lectur Series talk “Exploring strange new worlds of mathematics”, at the math department of Worcester Polytechnic Institute. Here are the slides with speaker notes and the video recording of the talk.