There’s a new edition of John Baez’ This Week’s Finds in Mathematical Physics. He talks about places to read up on Felix Klein’s Erlangen Programme, which is a great application of group theory.
More interesting to me (and hopefully to readers here) is his continuing “Tale of Groupoidification”. He really fleshes out this extension of the notion of group actions, and ties it into the concept of spans. I hope it’s not gushing too much to say that spans are one of the most amazingly useful inventions ever, and I’ll be talking about them a lot more once i’ve laid down enough foundations to handle them properly. It’s not exaggerating to say that I owe the lion’s share of progress on my own research program to spans and their dual notion, cospans.
I’ve posted my notes for the first of Zuckerman’s lectures. Hopefully my handwriting isn’t too awful for you. I’ve never been very good with that pen-and-paper stuff.
I’m trying to explain this pretty comprehensibly, but I do have to use some terms most mathematicians know without defining them. I’ve got plans to get to them eventually in the main stream of my writings, but for now the exegesis sits at a middle level. Anyhow, there’s a lot to unpack here, so I’ll put it behind the jump.