The Unapologetic Mathematician

Mathematics for the interested outsider

Drafting a Paper

Long-time readers may remember that back in September I went to a conference at the University of Texas at Tyler. Well, it turns out that the AMS wants to publish a proceedings of the conference. So I’m trying to throw together a paper on the stuff I was talking about.

As I’m doing so, I’m recognizing that one part of my original talk — the whole business about anafunctors — isn’t quite ready for prime-time, and the whole thing hangs together better without it. And this brings up the design philosophy I talked about recently. In this case, writing the smaller paper first is being sort of forced on me by a short deadline.

Still, it’s crunch time, and I’m trying to crank this paper out while also teaching, applying for jobs, and dealing with car troubles you wouldn’t even believe. I don’t really feel like working up the next post in the calculus series today, and so I thought I’d toss up an alpha version of the paper. I’ll keep tweaking it, and replacing the version here as I finish more chunks, until I get to a beta version, which I’ll update here and post to the arXiv.

One particular note on the incompleteness: I haven’t even started writing the introductory section or the abstract yet. I’m finding that I tend to do better if I just dive into the mathematics and then come back later to say what I said.

And finally: it looks like I’ll be talking about this stuff at the University of Pennsylvania on March 19. Mark your calendars!

[UPDATE] 02/26: Still sans abstract and intro, but with all mathematical content there, I present a new version. Bibliography suggestions are particularly appreciated (thanks Scott).

[UPDATE] 03/04: Now with the abstract and introduction, a beta version. Bibliography suggestions would still be appreciated.

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February 22, 2008 - Posted by | Category theory, Knot theory

15 Comments »

  1. Cool! It’s not on the seminar schedule yet, which one are you talking in?

    Comment by Charles | February 22, 2008 | Reply

  2. Are you giving the colloquium, or some mysterious other talk that happens on Wednesdays? (Your talk isn’t on the departmental calendar yet.)

    And I didn’t realize “quandles” were a thing people actually studied; before now I’d only heard of them in Mark Dominus’ blog which is referring to the fictional journal Acta Quandalia.

    Comment by Isabel Lugo | February 22, 2008 | Reply

  3. It’s whatever one Jim Stasheff helps organize.. “deformation” something, I think. It’s a pretty recent development. Basically, “I’m going to be in MD.. I’ll bet I can borrow a car and drive to Philly, and Jim said there might be an opening. Let’s ask.” All arranged since.. Wednesday or Thursday.

    And Isabel: not only are quandles real, but they’re getting to be pretty big business lately. There’s a cohomology theory for them, and they’re actually tightly related to Lie algebras. But the reason you should know of them is that they were a major part of the Ph.D. thesis of David Joyce when he was a student of Peter Freyd’s at UPenn in 1979.

    Comment by John Armstrong | February 22, 2008 | Reply

  4. To be a bit clearer.. not just “were a major part of” but “were invented in”

    Comment by John Armstrong | February 22, 2008 | Reply

  5. You might or might not have heard about it yet, but I’ll be talking at UPenn, under basically the same circumstances, about a week later. Come listen?

    Comment by Mikael Vejdemo Johansson | February 22, 2008 | Reply

  6. A week later I’ll be back in New Orleans. Sorry.

    Comment by John Armstrong | February 22, 2008 | Reply

  7. Aw, man, there’s no way I could get down to UPenn on that date. Any chance of getting you to come speak at Union?

    Comment by musesusan | February 22, 2008 | Reply

  8. I’d be glad to, but I’d need an invitation. I’m going to be in MD anyway over my spring break, and I can do the driving myself, so it’s basically free for me. Visiting Schenectady again would require flying and lodging, and (given my wallet) would require the inviting institution to comp that for me.

    That said, if you’ve got a professor or three you’ve got some pull with…

    Comment by John Armstrong | February 22, 2008 | Reply

  9. Cool, I’ve been meaning to start going to the deformation theory seminar. I’ll most definitely be at your talk.

    Comment by Charles | February 22, 2008 | Reply

  10. “That said, if you’ve got a professor or three you’ve got some pull with…”
    That was what I was thinking, although I have no idea whether they’ve got speakers for the spring lined up already or not. But I’ll put the word in…

    Comment by musesusan | February 23, 2008 | Reply

  11. “… I haven’t even started writing the introductory section or the abstract yet….”

    My mentors taught me that the Abstract is the LAST thing to write, reverse engineered from what actually got done in the latest complete draft of the paper, or what you improvised while waving hands when the digital projector blacked out, which got heads nodding approvingly in the audience.

    Compare and contrast with the approach of writing the sexiest possible abstract, with the latest buzzwords and hot conjectures, and submitting that to journals and conferences, just before abstract submission deadline. Then, if and only if the abstract is accepted and your affiliated institution or significant other or budget-after-car-crisis allows you to go to the conference, you start to wonder: “is that that abstract the pre-image of some transformation I can do on what I said and what I know how to do or can coerce grad students to do for me, so as to get a paper that might be accepted, which I can always rewrite after the referees make constructive suggestions?”

    It’s nonlinear bottom-up versus top-down paper/abstract dynamics. And, of course, it is almost always chaotic.

    Comment by Jonathan Vos Post | February 24, 2008 | Reply

  12. Ahem… your bibliography looks a bit light. If you are going to talk about the 2-category of 2-tangles (it is not clear that you are), then Baez Langford and Fisher need mentioning. Also look at Lopes in JKTR. He (among others) looked at the coloring invariants. I KNOW, I KNOW, he wasn’t the first. Fox colorings (using the dihedral quandle before it was known as the dihedral quandle) came first, and near ’bout everyone who has thought about knot coloring has thought about quandle coloring and the coloring homom. Kauffman and Lopes have some nice explicit calculations on the arXiv as well. Oh yeah, there are some things like
    CJKLS and its successors that are related to the ideas in the draft.

    Comment by Scott Carter | February 24, 2008 | Reply

  13. That’s a good point, Scott. I may mention 2-tangles in passing, but I’m actually trying not to make this overbroad. And yes, there are probably other places the bibliography needs some shoring up. I just threw in what I noticed myself using along the way.

    Of course, if you’ve got specific line items to add, I’m glad to get an email with them.

    Comment by John Armstrong | February 24, 2008 | Reply

  14. Oh yes, and it’s the “dihedral” quandle, isn’t it.. Alexander is something else entirely. Bleh.

    Comment by John Armstrong | February 24, 2008 | Reply

  15. [...] While discussing the paper I’m working on, John Baez (from The n-Category Café) and I ended up discussing the use of web-based references in [...]

    Pingback by Bibliographies « The Unapologetic Mathematician | February 26, 2008 | Reply


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