Oct 6, 2025 I’m trying to better characterize two maximal subgroups of the group of automorphisms of the exceptional Jordan algebra, whose intersection is the Standard Model gauge group.

Earlier this month the Mathematics Institute at Uppsala University hosted a conference called Categorification in Algebra and Topology, clearly a theme close to our collective heart. As yet there are ...

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 ...

Back to modal HoTT. If what was considered last time were all, one would wonder what the fuss was about. Now, there’s much that needs to be said about type dependency, types as propositions, sets, ...

The discussion on Tom’s recent post about ETCS, and the subsequent followup blog post of Francois, have convinced me that it’s time to write a new introductory blog post about type theory. So if ...

Bless British trains. A two-hour delay with nothing to occupy me provided the perfect opportunity to figure out the relationships between some of the results that John, Tobias and I have come up with ...

I’m in Regensburg this week attending a workshop on Interactions of Proof Assistants and Mathematics. One of the lecture series is being given by John Harrison, a Senior Principal Applied Scientist in ...

Last summer my students Brendan Fong and Blake Pollard visited me at the Centre for Quantum Technologies, and we figured out how to understand open continuous-time Markov chains! I think this is a ...

These are notes for the talk I’m giving at the Edinburgh Category Theory Seminar this Wednesday, based on work with Joe Moeller and Todd Trimble. (No, the talk will not be recorded.) They still have ...

Example: suppose we have a data structure representing an abstract address. An address is, alternatively, an email address or a postal address like in the previous example. We can try to extract a ...

Many of you have heard murmurings about this book for several months now. I’m happy to report that it’s now out! Homotopy type theory: univalent foundations of mathematics, by the Univalent ...

A mathematician hands out a pack of cards to a group of five people. They repeatedly cut the deck and then take a card each. The mathematician tries to use telepathy to divine the cards that the ...