At the annual departmental conference this week I will be giving yet another introduction to category theory for physicists! The talk is on Tuesday afternoon, and this time I’ll be focusing on how combinatorics associated to operads can be very useful. All welcome.
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Arcadian Functor 
CarlBrannen said,
September 1, 2007 @ 11:41 pm
Of course you will publish the slides here. But do have someone record the lecture as well.
I’m still trying to shake a cold. When I get better, I’m going to write a blog post about tripled Pauli statistics and the number of linearly indpendent massless chiral wave states.
Kea said,
September 1, 2007 @ 11:47 pm
Hi Carl. Hope the cold disappears soon. The slides won’t be worth worrying about, because I have to cater to an audience of astronomers, medical physicists, laser physicists etc. I lost count years ago of how many of these talks I’ve given. Physicists seem to appreciate the potential of category theory now, but they really don’t know anything about it. In fact, they really don’t know much mathematics at all, so I have to be very careful about the examples I choose. That’s why operads are nice to talk about: anybody can see that the combinatorics underlying the Standard Model might be useful.
kneemo said,
September 2, 2007 @ 2:23 am
Maybe you can give an operad picture of Carl’s mass matrix work. 🙂
Kea said,
September 2, 2007 @ 3:10 am
LOL, kneemo! Recall that my attempts to speak about the possible conjunction of Carl’s work with categories are usually met with extreme skepticism, somewhat beyond what might be termed healthy.
mendo said,
September 2, 2007 @ 7:03 pm
Hi Kea
As you note, physicists in general don’t have a formal maths background. I’d therefore second Carl’s request for you to post the slides as I think they’d be useful to many of your readers.
More generally, what areas of maths would you recommend physicists interested in getting started in category theory to study to build a grounding? I’m thinking (perhaps incorrectly I admit…) that jumping straight into category theory without that base might be rather difficult!
Cheers,
Mendo.
Kea said,
September 2, 2007 @ 7:59 pm
Hi Mendo, welcome. Like in most physics talks, my slides usually tell a colorful but sketchy story, and I focus on explaining what I really mean in the talk itself. But if you like I will post some slides here sometime soon.
More generally, what areas of maths would you recommend physicists interested in getting started in category theory to study to build a grounding?
Great question! After years of trying to introduce physicists to category theory, I realise that the abstraction on its own is fairly useless. Here are my recommendations for mathematics subjects, based on relative ease of self-study:
Must do:
1. Algebraic Topology (you can’t go wrong with Bott and Tu’s book) and homotopy theory
2. Representation Theory of Lie gr.
3. Quantum Groups (eg. Kassel’s book)
4. Knot theory and knots in dynamics (it is actually fairly easy to figure out the basics here)
And note that there are now some excellent basic textbooks on category theory itself.
If more keen on physical applications, maybe also include twistor theory, number theory, soliton theory and the ISM (I actually started with this many years ago), quantum computation (a la CompSci) and harmonic analysis and operator theory.
Kea said,
September 2, 2007 @ 8:17 pm
P.S. Oh, and don’t forget: Some good old fashioned geometry (eg. of complex curves).
mendo said,
September 3, 2007 @ 8:12 pm
Hi Kea,
Thank you for the recommendations! Have to admit I’m a real beginner here as I’ve only recently started looking at basic abstract and geometric algebras. Being on the experimental side of things it’s only as a postdoc I’ve had a little more to think about these things.
And note that there are now some excellent basic textbooks on category
theory itself.
Which ones would you particularly recommend? One other quick question (showing my ignorance again), what’s the ISM?
Oh, and hope your talk goes well!
Cheers,
Mendo.
Kea said,
September 3, 2007 @ 8:31 pm
Hi Mendo
The ISM just means ‘Inverse Scattering Method’ but I’m only recommending that if it happens to intersect with your interests – which it probably doesn’t if you are an experimenter – there is only so much one can take in!
Easiest Category Theory books:
Lawvere and Rosebrugh
Rydeheard and Burstall
a quantum diaries survivor said,
September 3, 2007 @ 11:17 pm
Hi Kea, good luck with your lecture, and make it just a bit harder than what they can fully understand 😉
Cheers,
T.
Kea said,
September 4, 2007 @ 12:12 am
Thanks, Tommaso, but given the wide research interests of the department it isn’t going to be a very serious talk. I only have to mention the word Theory and that scares most people away.