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.

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January 6, 2009 - Posted by | Uncategorized

1 Comment »

  1. Well, there are all kinds of teaching opportunities outside, as you say, academia. Here’s one (somewhat glorified, but still…) view of direct instruction like you do on this blog. Practically, I guess teaching on the interwebs you can be as independent as you like or as cheaply as you can live–or as generous as your students are via paypal (donations). From

    “There are many scary things about today’s world. But one that is truly thrilling is that the means of spreading both knowledge and inspiration have never been greater. Five years ago, an amazing teacher or professor with the ability to truly catalyze the lives of his or her students could realistically hope to impact maybe 100 people each year. Today that same teacher can have their words spread on video to millions of eager students. There are already numerous examples of powerful talks that have spread virally to massive Internet audiences.

    Driving this unexpected phenomenon is the fact that the physical cost of distributing a recorded talk or lecture anywhere in the world via the internet has fallen effectively to zero. This has happened with breathtaking speed and its implications are not yet widely understood. But it is surely capable of transforming global education.

    For one thing, the realization that today’s best teachers can become global celebrities is going to boost the caliber of those who teach. For the first time in many years it’s possible to imagine ambitious, brilliant 18-year-olds putting ‘teacher’ at the top of their career choice list. Indeed the very definition of “great teacher” will expand, as numerous others outside the profession with the ability to communicate important ideas find a new incentive to make that talent available to the world. Additionally every existing teacher can greatly amplify their own abilities by inviting into their classroom, on video, the world’s greatest scientists, visionaries and tutors. (Can a teacher inspire over video? Absolutely. We hear jaw-dropping stories of this every day.)”

    Comment by poverty of freedom | January 6, 2009 | Reply

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