Define the Standard Model gauge group to be S ( U ( 2) × U ( 3)), the subgroup of SU ( 5) consisting of block diagonal matrices with a 2 × 2 block and then a 3 × 3 block. (This is isomorphic to the ...

is a more general antiderivative, for two arbitrary constants C and C +. (I’m writing ln for the natural logarithm function that Tom wrote as log, for reasons that will become clear later.) In the ...

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: ...

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 ...

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 ...

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 ...

Nine short stories about geometric higher categories. Today, I only want to focus on two basic questions about geometric higher categories: namely, what is the idea behind the connection of geometry ...

Are you interested in applying category-theoretic methods to problems outside of pure mathematics? Apply to the Adjoint School! Apply here. And do it soon. January 9, 2023. Application Due. February - ...

This is the homepage for the UT Geometry and Quantum Field Theory Seminar. At the organizational meeting we will flesh out the details of our plans for the semester. Below are some suggestions to get ...

I want to talk about some attempts to connect the Standard Model of particle physics to the octonions. I should start out by saying I don’t have any big agenda here. It’d be great if the octonions — ...