Fortnightly links (170)

This installment is so late that calling it monthly links wouldn't even salvage it... I've been writing papers instead of blogposts recently, so stay tuned for some updates on that front.

• Asher Auel, Avinash Kulkarni, Jack Petok, Jonah Weinbaum: A census of cubic fourfolds over $\mathbb{F}_2$ does something really cool. Back in 1914 Dickson classified (by hand) all smooth cubic surfaces over $\mathbb{F}_2$. There are 36 smooth cubic surfaces over $\mathbb{F}_2$. Using automated methods, the classification of cubic 3-folds and cubic 4-folds over $\mathbb{F}_2$ is now also established. There are 1 069 562 smooth cubic 4-folds! And it is possible to do point and line counts, and all kinds of investigations. A few weeks ago Jack also explained to me what is going to appear in the work-in-progress [3], and I'm sure that will also be featured in the fortnightly links in due time.

• Terence Tao: Embracing change and resetting expectations is an essay on the role that AI might play in research mathematics soon. Highly recommended read!

  Maybe I can ask AI to write the fortnightly links for me soon? The benefit would be that they are on time, but all the fun would be lost, so rather not really!

• List of Erdős problems is a nice interactive website dedicated to all the problems (or at least, many) that have been phrased by Erdős, listing what is (not) known about them.

• Anton Fonarev: Derived category of moduli of parabolic bundles on $\mathbb{P}^1$ advertises a conjecture on the derived category of the moduli space of parabolic bundles on $\mathbb{P}^1$, expanding on some discussion Anton and I had a few years ago. I have some joint work-in-progress coming out, hopefully by the end of the summer, generalising this conjecture (and the BGMN conjecture, or Tevelev theorem), and I'm excited tell you all soon!

• Alexander Kuznetsov, Evgeny Shinder: Derived categories of Fano threefolds and degenerations is a really cool preprint that explains how to fix one of the first conjectures in the theory of derived categories of Fano 3-folds, explaining a relationship between Fano 3-folds of index 1 and 2 (in the Picard rank 1 case). The introduction (and the rest) of the paper is a highly recommended read, if you care about derived categories of Fano 3-folds.