### Good News

#### Posted by John Baez

I’m in Sydney talking to Ross Street and other category theorists at Macquarie University. Once I’d expressed worries about the fate of Australian category theory now that Street has retired. I’m happy to say that we can put those worries to rest.

First of all, while Street has formally retired, he still comes to work every day and is very active. Second, Steve Lack has moved from Sydney University to Macquarie, so he can now have graduate students. On top of that, he’s gotten a 4-year grant that’ll let him spend most of his time on research! Richard Garner is here too, and has a 5-year research-only postdoc. Also in the math department are Michael Batanin, Alexei Davydov and Mark Weber. And if that weren’t enough, Dominic Verity has joined Mike Johnson over in Macquarie’s computing department.

So, it’s a great place to go if you want to talk to category theorists! I apologize to anyone whom I left out.

And on a more personal note…

… Jeffrey Morton has gotten a 2-year postdoc position in Christoph Schweigert’s group in Hamburg! As you may recall, this is Urs Schreiber’s old home. So, we can expect to see more interplay between string theory, TQFTs, and the study of categorified quantum theory using spans.

And there’s even more good news. Jeffrey Morton and Jamie Vicary are on the brink of releasing a paper that sheds new light on the quantum harmonic oscillator! They’ve both written about ways to *categorify* the harmonic oscillator, and now they’ve joined forces and figured out how to understand Khovanov’s categorified Heisenberg algebra using combinatorics!

You may recall how groupoidification lets us understand the canonical commutation relations

$a a^* - a^* a = 1$

in a very simple way, by making precise the fact that *‘there’s one more way to put a ball in a box and then take one out than to take one out and then put one in’*. Khovanov’s categorified Heisenberg algebra has some relations whose meaning is far less obvious.
They’re usually drawn using string diagrams, and they’re pretty, but what do they say about reality?

Jeffrey and Jamie have figured it out! The math is nontrivial—it involves bicategories, spans of groupoids, and the representation theory of symmetric groups, all working together. But the meaning of Khovanov’s relations can be understood in terms of balls in a box! This will, I think, add a whole new layer of depth to our understanding of a very basic item in physics: the quantum harmonic oscillator.

So, stay tuned.

## Re: Good News

Does this help in understanding what a categorified quantum harmonic oscillator might have to do with physics (apart from its decategorification being the ordinary quantum harmonic oscillator)?