This is a picture of Alexander Grothendieck, taken near the end of his life:
You shall not pass!
I took this picture of a page in a book that was just lying around in Oberwolfach a couple of weeks ago (I think the book was published by the Fields Institute). Unfortunately, I failed to note down an exact attribution -- if anyone knows the name of this book/the photographer, please let me know.
EDIT: Commenter DH writes that the source of this photo is Masters of Abstraction, by photographer Peter Badge.
This is a continuation of a previous post. Recall that we wanted to prove the following claim:
Claim. Let \(\rho\) be a representation of \(SL_4\) such that no irreducible subrepresentation of \(\rho\) descends to \(SL_4/\mu_2\). Then if \(\rho\) is self-dual, we have that $$8\mid\dim \rho.$$
Read MoreStill at UGA -- I just saw a great talk by Jason van Zelm (a student of Nicola Pagani who apparently does not have a webpage), constructing non-tautological cycles on \(\overline{\mathscr{M}_g}\) for \(g\geq 12\)...
Read MoreI'm at UGA for the week, in between SWAG and TAAAG. Today Danny Krashen gave a great talk on this paper of Auel, First, and Williams. The paper is one of the latest in a long tradition of papers which construct counterexamples by making a topological computation and then approximating the relevant topological spaces by algebraic varieties. (To my knowledge, this technique began with Totaro, but it has been exploited to great effect by Antieau, Williams, and most recently, fellow Ravi student Arnav Tripathy.) ...
Read MoreLet \(n\) be a large positive integer. Recently I've been looking for a family of curves \(f_n: \mathscr{C}_n\to \mathbb{P}^1\) with the following properties:
I'm currently at SWAG, the awesomely named Summer Workshop in Algebraic Geometry at Georgia.
Jonathan Wise gave a really amazing talk today about logarithmic geometry, which got me very excited about the possibility of using log geometry to compute various structures on fundamental groups of degenerating curves (e.g. Hodge structures, Galois actions, etc). It was also by far the best introduction to the subject I've seen. Yu-jong Tzeng gave a nice introduction to algebraic cobordism, and sketched a proof of Goettsche's formula for the Euler characteristic of the Hilbert scheme of points of a surface, which was quite elegant. Renzo Cavalieri gave a beautiful overview of Pixton's work on the double ramification cycle(s); I'm really interested in understanding where the products over graphs in Pixton's formulas "come from" geometrically, but so far I've been unable to figure out a rigorous statement. Finally, Dmitry Zakharov spoke about his recent work with Clader, Janda, and Zvonkine on applying Pixton's work to prove various classical tautological relations. Overall a really great conference so far.
Here's a question Dmitry asked at dinner, which I think is pretty interesting. Given that we expect the motion of the 10+ objects in the solar system to be chaotic, can we explain the fact that it has been relatively stable over the past 4 or so billion years? How long can we expect this stability to continue. Dimitry reassures me that numerical evidence indicates we have at least a few million years, but I think the Bayesian argument that we have at least a billion is kind of weak. I'd be very interested to hear an argument from physical (rather than probabilistic) principles analyzing the long-term stability of the solar system.
I'm thinking of starting a blog. Let's see how this goes.