Yesterday I had a great conversation with Dmitri Tymoczko about groupoids in music theory. But at this Higgs Centre Colloquium, he preferred to downplay groupoids and talk in a way physicists would ...

How do you count rooted planar n n-ary trees with some number of leaves? For n = 2 n = 2 this puzzle leads to the Catalan numbers. These are so fascinating that the combinatorist Richard Stanley wrote ...

Despite the “2” in the title, you can follow this post without having read part 1. The whole point is to sneak up on the metricky, analysisy stuff about potential functions from a categorical angle, ...

I want to go back over something from Part 11, but in a more systematic and self-contained way. I’m stating these facts roughly now, to not get bogged down. But I’ll state them precisely, prove them, ...

In Part 1, I explained my hopes that classical statistical mechanics reduces to thermodynamics in the limit where Boltzmann’s constant k k approaches zero. In Part 2, I explained exactly what I mean ...

A physical framework often depends on some physical constants that we can imagine varying, and in some limit one framework may reduce to another. This suggests that we should study a ‘moduli space’ or ...

When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in category theory, and probability theory isn’t spared from this treatment. We’ve had a useful ...

The study of monoidal categories and their applications is an essential part of the research and applications of category theory. However, on occasion the coherence conditions of these categories ...

such that the following 5 5 diagrams commute: (for f: x 0 → x 1 f:x_0\to x_1 and y ∈ 풞 y\in\mathcal{C}, we write f ⊗ y f\otimes y to mean f ⊗ id y: x 0 ⊗ y → x 1 ⊗ y f\otimes\operatorname{id}_y: ...

This is part two of a three part series of expository posts on our paper Displayed Type Theory and Semi-Simplicial Types. In this part, we cover the main results of the paper.

I don’t really think mathematics is boring. I hope you don’t either. But I can’t count the number of times I’ve launched into reading a math paper, dewy-eyed and eager to learn, only to have my ...