En Passant III

Question: When you are sick in bed, can you do any mathematics? I just spent the past few weeks with a sinus infection and was completely unable to do anything productive, that is, apart from writing an NSF grant (which I guess was somewhat productive). Oh, and I did watch the entire series of “the thick of it” and a bunch of QI episodes.

Some further notes on my trip to Europe. I met some people for the first time. Kathrin Bringmann was very nice; we chatted a little about the possibility of a representation theoretic theory of mock automorphic forms. Harald Helfgott talked about his recent work (nicely described here), but also made constant references during lunch to the consumption of human flesh (perhaps the two are related). He also bested me in a game of chess (my excuse is that there was an implicit agreement to to play as fast as possible, but after a blunder gave him a winning position, he grounded it out like a man who knows he’s a few log factors ahead).

Samir Sisek gave a talk about his nice paper with with Freitas on Fermat over some totally real fields, in which they prove (for example) that there are no solutions for large enough primes \(p\) over all real quadratic fields \(\mathbf{Q}(\sqrt{d})\) with \(d\) squarefree and \(3 \mod 8\). I had actually given the problem of proving Fermat for infinitely many real quadratic fields to one of my students a few weeks ago, so this was good timing, I guess.

Bilu, Parent, and Rebolledo gave a great sequence of talks on there work. This was always a paper that I thought I should read at some point, but now I don’t have to. Excellent!

The work of Roberts and Venkatesh is fun, I may blog about that when Roberts gives a talk at Northwestern in a few months time.

Don Zagier has a function which he cannot define, and I have a function which I cannot compute. We conjecture that they are the same. Don also gave me the following puzzle, which I pass on to you:

Show this bold Prussian that brings slaughter, slaughter brings rout!