Jun 8, 2009 You can now see the introduction to a paper James Dolan is writing about algebraic geometry for category theorists. You can also see 5 lectures he gave on this topic.

I’ve just arXived my notes for Edinburgh’s undergraduate Galois theory course, which I taught from 2021 to 2023. I first shared the notes on my website some time ago. But it took me a while to arXiv ...

You’ve probably heard that there are a lot of deep conjectures about L L-functions. For example, there’s the Langlands program. And I guess the Riemann Hypothesis counts too, because the Riemann zeta ...

I’ve been talking about Grothendieck’s approach to Galois theory, but I haven’t yet touched on Brauer theory. Both of these involve separable algebras, but of different kinds. For Galois theory we ...

In the previous post I set the scene a little for enriched category theory by implying that by working ‘over’ the category of sets is a bit like working ‘over’ the integers in algebra and sometimes it ...

I was kindly invited to give an tutorial about my work with Tom Leinster and Tobias Fritz on Wednesday May 11, which I will give remotely to save carbon. Tai-Danae Bradley will also be giving a ...

Chris Heunen and Andre Kornell have found an axiomatic characterization of the category of Hilbert spaces! Chris Heunen and Andre Kornell, Axioms for the category of Hilbert spaces. arXiv:2109.07418, ...

The plan for this series is to talk about ever larger sets and ever stronger axioms. So far we’ve looked at weak limits, strong limits, and alephs. Today we’ll look at beths. The beths are the sets ...

We can think of the exceptional Jordan algebra as a funny sort of spacetime. This spacetime is 27-dimensional, with light rays through the origin moving on a lightcone given by a cubic equation ...