any generation of Standard Model fermions transforms as the direct sum of six irreducible representations: These correspond to the six types of left-handed fermion: q L, d R, u R, ℓ L, e R, ν R. Six ...

Jul 8, 2026 13:57 So you are disagreeing with Paul: you’re getting S(U(3)×U(2))\text{S}(\text{U}(3) \times \text{U}(2)) where he is getting SU(3)×SU(2)\text{SU}(3 ...

This looks rather like the characterization of determinant: det det is unique satisfying det (I) = 1 det(I) = 1, antisymmetry, and multilinearity. One difference is that we have symmetry rather than ...

Apr 29, 2026 In the last episode of my column in Notices of the American Mathematical Society, we looked at a particle moving in an attractive central force whose strength is proportional to the ...

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, ...

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 keep wanting to understand Bernoulli numbers more deeply, and people keep telling me stuff that’s fancy when I want to understand things simply. But let me try again.

Whether we grow up to become category theorists or applied mathematicians, one thing that I suspect unites us all is that we were once enchanted by prime numbers. It comes as no surprise then that a ...

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, ...

We start by introducing Petri nets and elementary Petri nets, which will be the focus of this post. In general, the weight of each condition can be an integer. In the case of elementary Petri nets, ...

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 ...

In this post I shall discuss the paper “On a Topological Topos” by Peter Johnstone. The basic problem is that algebraic topology needs a “convenient category of spaces” in which to work: the category ...