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 ...

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 ...

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 ...

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, ...

You may recall Greg Egan’s plea to save the magazine New Scientist from a rising tide of crackpottery after it published a glowing article about a propulsion system called the EmDrive. According to ...

It takes a while to explain the details. Actually, I’ve come to feel that in academia no project is ever really done. At least, not until you lose interest or die — which, come to think of it, is just ...

My friend the combinatorist Bill Schmitt breezed through Paris recently, taking a train back from Hopf-in-Lux with Paul-André Melliès, and spending a day here before going home to DC. We had some time ...

Hello [email protected]. So nice of you to stop by. I'm a member of the Theory Group here at UT. I've been at UT since September 1994. Before coming here, I was an Assistant Professor in the theory ...

I mentioned in my intro that as wonderful as n n-categories are, they’re really just one (important) part of the zoo of “higher categorical structures” out there. Today I want to tell you about ...

A few of us here at the Café decided that it would be good to have a short series of posts in which each of us (at least, each of us who wants to) says something about his overall take on higher ...

There’s been a bunch of discussion online recently (e.g. SBS, MathOverflow 1, 2, 3, etc.) about set-theoretic foundations for category theory, the role of universes, and so on. So I thought I would ...

A light mill is also known as a Crookes radiometer: It seems like a simple thing: an evacuated glass bulb with some vanes that can spin around, black on one side and white on the other. When you shine ...