Conference report: “Arithmetic harmonic analysis on character and quiver varieties”

So, let’s start off with some conference blogging. Last week, I was at a workshop at the American Institute of Mathematics in sunny Palo Alto, CA, with the somewhat excessive name of “Arithmetic harmonic analysis on character and quiver varieties.”

This was my second time at AIM in a little over two months (having also attended the lovely workshop on “Representations of surface groups” in March), and I was just struck again at what a great environment it is to do mathematics. I really recommend it strongly to any one who has a chance to go. There are a lot of little things they get right, such as keeping the conference well-supplied with snacks and coffee and having a pretty nice space specifically dedicated to math workshops (the only problem is the lack of windows), tucked into the side of the Fry’s Electronics in Palo Alto (I never cease to find this funny). One particularly good feature for conferences is that since the main lectures are in one corner of a larger room, it’s much easier for people to come and go from talks without being rude.

But on a larger level, the good people at AIM are really making an effort to start a different model for math conferences, one which makes for a good change. Most conferences seem a little too focused on people presenting their own bleeding edge research, without a lot of regard for whether the audience is interested or will benefit for hearing it. Of course, individual speakers (myself included) will often put in a lot of effort to tailor a talk to the audience, but conferences tend not to encourage it institutionally. The workshops at AIM focus much more on the audience learning what they want to know, or what they would need to know to work on certain problems, without much regard to whether the speaker did the research. For example, the last time I was at AIM, there were a number of essentially expository talks on Higgs bundles (in part because of demands from the audience), and Francois Labourie and I gave one on the work of Fock and Goncharov.

I will admit, however, that this past week showed some of the weaknesses of this approach. The topic of this workshop can be roughly described as “the appearance of MacDonald polynomials in nonabelian Hodge theory” (they have been conjectured by the organizers to give a description of Hodge numbers of the character varieties), and so included a lot of MacDonald polynomials people (Mark Haiman, Francosi Bergeron, Arun Ram, Sarah Mason, etc.), hyperkähler geometry and quiver variety people (David Ben-Zvi, Hiraku Nakajima, Bill Crawley-Boevey, etc.), and people who do representation theory of finite Lie groups (Emmanuel Lettelier, Jean Michel, Gus Lehrer), because that’s the method by which this connection was discovered. Not that these people are totally ignorant of each other’s fields, but still it would have taken more than a week to get everyone even roughly up to speed, and the organizers didn’t do a very good job of explaining why they thought all these people should be in the same place at once, at least for the first few days.

That said, I still had a lot of interesting conversations, especially with my past (and perhaps future?) collaborator and fellow Berkeley grad Nick Proudfoot, about math and just about everything else. He has some pretty interesting ideas about extending our previous work on hypertoric varieties, though a lot of technical hurdles need to be overcome.

There also seemed to be a thick general atmosphere of job gossip, which, while interesting, was not really what I wanted to be thinking about 2 weeks after getting my Ph.D. It must be the time of year, (and the fact that Nick just went through a job search. For the curious, he’ll be going to the University of Oregon).

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