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 ...

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 ...

Here is a comment about the bar construction which I wanted to mention, since John told me that his course is ending soon and he might not get around to mentioning it himself. I’d like to thank Urs ...

John Huerta’s paper on grand unified theories made some people eager to discuss aspects of group representation theory that this paper deliberately avoided. For example, in relativistic quantum ...

Part of what intrigues me about reading Terence Tao’s blog is that he displays there a different aesthetic to the one largely admired here. The best effort to capture this difference is, I believe, ...

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, ...

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 ...

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 ...

Over the last few years, I’ve been very slowly working up a short expository paper — requiring no knowledge of categories — on set theory done categorically. It’s now progressed to the stage where I’d ...

It’s an underappreciated fact that the interior of every simplex Δ n \Delta^n is a real vector space in a natural way. For instance, here’s the 2-simplex with twelve of its 1-dimensional linear ...

Mar 20, 2026 A large language model has very little self-awareness. But it is easy to give it some rudimentary but useful forms of self-awareness using the “plumbing” language.

Most recently, the Applied Category Theory Seminar took a step into linguistics by discussing the 2010 paper Mathematical Foundations for a Compositional Distributional Model of Meaning, by Bob Coecke ...