Dustin Clausen is giving a course at the IHES starting today on “Weil Anima” (or maybe “Weil-Moore Anima”. They’ve already put up video of the talk here (also available on Youtube). For an earlier talk by Clausen on this material from last year, see “Refining Weil groups” at the Manin memorial conference.
I just watched the IHES Clausen talk, which was a mind-blowing experience, highly recommended if you’ve been following this subject in recent years. Unfortunately I can’t do any sort of justice here to the sweep of fascinating new ideas about math at its deepest level that the talk covers, mainly because of lack of competence, but also because of lack of time.
Trying to find time to think about the talk clarified for me the current state of my intellectual life. Thinking about the larger world (or even the local world outside my office window…) has become thoroughly depressing. I really should stop following the news in any form to preserve my mental health. This argues for concentrating on thinking about the problems in math, physics and their overlap that I’d most like to understand better.
As far as deep ideas about physics goes, paying attention to what’s been going on in the subject long ago became depressing. The situation in mathematics is completely different, with Scholze, Clausen and many others making dramatic progress towards unearthing a wonderful world of new structure at the deepest level in mathematics. A big problem is that this is intellectually extremely challenging material to follow, and I don’t right now have the necessary time. Besides the Clausen talks, this month there’s a program in Marseilles on Langlands-related stuff, with videos starting to appear that would doubtless be helpful if I had the time to watch them.
I’m trying to get the details of a new way of thinking about Wick rotation written down, and to make progress on that is a full-time effort. It’s rewarding in its own way, as I’m learning new things, but it’s extremely slow, spending most of the time stuck on trying to understand things like where signs come from. Learning beautiful new ideas that someone much more industrious spent years slogging through trying to get straight is a lot more appealing.
Finally, as a long-term goal, there’s the tantalizing fact that the twistor line plays a central role in the new ideas Clausen is talking about, and at the same time it plays a central role (as a point of space-time) in what I’ve been trying to do. That deep ideas about physics and about mathematics are closely linked is something I firmly believe, so I don’t think these two very different contexts for the twistor line have nothing to do with each other. I’d love to be thinking more about this, but need to stop blogging and get back to getting the Wick rotation paper finished…
