Things That Deserve (but won’t get) Longer Blog Postings
Here’s a selection of news that deserves longer blog postings that, for one reason or another, I’m unable or unwilling to provide…
This year’s Abel Prize goes to John Milnor. With an excellent blog posting about this from Fields Medalist Tim Gowers, why should I try and compete?
I’ve been waiting for the US budget situation to clarify before writing about its implications for physics and math research, but it looks like that isn’t going to happen anytime soon. The US Congress is now engaged in a bizarre and irresponsible exercise of trying to run the country by each week fighting over not next year’s budget, not next quarter’s, not next month’s, but next week’s. At the moment there’s a budget for the next week and a half, but no one seems to know what will happen after this. The president has issued a proposed FY2012 budget, but there’s no reason to believe it will have anything to do with whatever the reality of funding later this year turns out to be. Trying to make plans and run a large laboratory like Fermilab under these conditions must be a nightmare. Last week there was a HEPAP meeting in Washington, with presentations that explain the current situation. A good excuse for not writing more about the future implications of federal funding decisions is that no one is actually making such decisions.
Last week Langlands supposedly gave a talk at the IAS, On Functoriality; on the Correspondence; and on Their Relation, Part I (I’m not sure if or when there will be a Part II). I wasn’t able to attend, but perhaps video will someday be available. Langlands provides a link to a document of “work in progress” entitled Functoriality and Reciprocity. In it, he gives his reflections on the current state of attempts to precisely formulate and understand the conjectures generally referred to as “Langlands functoriality” and the “Langlands Correspondence” (or “Langlands reciprocity”). These conjectures come in versions for algebraic number fields, function fields, and so-called “geometric Langlands” over the complex numbers, in each case in local and global versions.
Much of the document consists of Langland’s description of his struggle to understand some issues in the geometric Langlands story, including the work of Witten and collaborators relating this to 4 and 6d quantum field theories. Another topic is that of the Abelian theory, and attempts to understand it locally. A very good reason to not write more about this is that I don’t understand it very well, although, paradoxically, I find Langlands writing about what confuses him rather easier to follow than when he writes about what he has completely understood. Another good reason is that I’m busily learning more about some of this, and maybe someday I’ll be less confused and able to write something more sensible here.
Also from the IAS, there’s video of a talk by Arkani-Hamed to the mathematicians available here, about work on scattering amplitudes. I’m curious to know what they made of it.
Also on the Langlands front, again in a category of things I don’t understand well enough to write more about, see this new Seminaire Bourbaki report on the Fundamental Lemma from Thomas Hales.
Update: There’s a Newsday story about Milnor here, unfortunately only the first bit is free. He explains what he is going to do with the million bucks: buy more leg-room on airplane flights (he’s 6’3″).