It was happenstance that I stumbled across these lectures on Youtube on Category Theory which were given by Steve Awodey, a professor of philosophy at Carnegie-Mellon. There are only a couple (I’ve watched the first one) and they were given during a short summer school on computer science (I still haven’t figured out how or why computer scientists use category theory). I watched the first one after reading the first couple sections of Maclane’s book and as it turns out Awodey was Maclane’s student! The lecture was quite good, well paced with good examples. I’m waiting to watch the next one as I try and pace myself on this topic. Simon and I are working the exercises at the end of the section on functors at the moment. No haste needed, we’re just taking our time.
Along these lines I’ve been starting my literature search on TQFTs and figuring out what order to read/work these. Baez has a couple of articles that are largely expository. I’ve read “Higher Dimensional Algebra and Plank scale physics” and it’s a fun read, not too taxing. I also came across an article by Atiyah entitled “Introduction to Topological Quantum Field Theories” and it’s also quite readable though I’ll need to spend a bit more time on it to work through a couple parts. His original article “Topological Quantum Field Theory” I’ve yet to read.
I’m still mulling over what I’ll say in my Pizza Pi talk at the end of February. The topic is certainly Penrose tiles but there are a number of ways of going after them. It’ll be light on proofs (sketches at best) and more of a story with highlighted results and properties that are surprising and novel. I would like to start with Wang and Logic and then work towards Penrose tiles, discuss some properties, and then finish off with a nod to noncommutative geometry. As a space or mathematical object it has a lot of surprises and links together some interesting characters like Wang, Penrose and Connes. I’ll post more as it becomes clearer to me. Martin Gardner has an excellent book “Penrose Tiles to Trapdoor Ciphers” which features Penrose tiles for the first couple of chapters.
I’m still getting the hang of this writing & posting business. Hopefully I’ll have something of substance to write soon.