The Unapologetic Mathematician

Mathematics for the interested outsider

Joint Meetings 2009 — day 1

Well, I made some good non-academic contacts already. I’d rather not go into details, since being too talky might be a problem when prospective employers look to Google and find me as the top hit for my name and subject. But I’m feeling good about my prospects, even without looking at the wilds of federal government and contracting jobs.

Anyhow, as for mathematics there were a number of good talks, but most of them were either what was expected from the speaker, or felt pretty technical. One, though, really grabbed me. Kerry Luse, formerly a student of Yongwu Rong’s at George Washington, spoke about “A transition polynomial for signed Feynman diagrams”. She started with the chord diagram of a knot and added a sign to each chord. If you read the signs as orientations, you get Feynman diagrams for a single species of noninteracting, non-self-dual particles. Alternately, you can interpret the diagrams as arising from RNA secondary structures, as she did. Either way, she was looking for a polynomial invariant to be calculated from such a diagram, and she came up with some really interesting results from her choice. One property in particular was the fact that the resulting polynomial (as applied to chord diagrams arising from knots) is multiplicative under connected sums of links. This makes me think it’s got something to do with the Alexander polynomial.

She also mentioned chord diagrams for links, with more than one loop, which I don’t think I’ve ever considered as such. Immediately this made me think of extending to tangles (naturally), and then that these chord diagrams may themselves form a category of their own. Is there some sort of duality here? If so it might turn connected sum on one side into disjoint union on the other side, which could provide a fascinating connection between classical and quantum topology…

See, I’m not going to be stopping research, and definitely not stopping this project here (thanks, btw, for the comments), but I just need to get out of the academic game I’ve been playing the last few years.

Anyhow, since it’s been weeks since I’ve been at home cooking for myself (thanks to Dad insisting on doing it all), I figured I’d have a bonus “I (Didn’t) Made It!”:

Eating at the Afghan Grill

Eating at the Afghan Grill

At the Afghan Grill, just around the corner from the Marriott, I’m having the mantoo, and across the table from me is the lamb qabili palao. So who ordered the Afghan equivalent of biryani?

Mikael Vejdemo Johansson

This guy! I also ran into Jesse Johnson this morning. Oh, and if Sarah from John Hopkins is reading this and is at the meetings, she really needs to drop me an email so she can join the fun.

January 6, 2009 Posted by | Uncategorized | 1 Comment