Recent progress around Cohen-Lenstra heuristics (notes from a Bourbaki talk)

These are the notes from the recent Bourbaki seminar I gave about just some of the remarkable work people have done around the Cohen-Lenstra conjectures in the past few years. I have to submit the final version of this by the end of the month, so any comments on these notes are very welcome! Here’s the abstract: “In 1983, Henri Cohen and Hendrik Lenstra proposed a conjecture about the distribution of the N-torsion of the class group of a random quadratic field, supported by what was at the time a large amount of computational evidence. The Cohen-Lenstra heuristics, which are still almost entirely unproven, have become one of the central foundational problems in arithmetic statistics. Recent years have seen a rapidly accelerated pace of development in Cohen-Lenstra problems. I will give a tour of these developments, including the work of Wood and her collaborators developing a fully fleshed out roster of generalized Cohen-Lenstra conjectures, with support from topology; Smith’s…