Jordan Ellenberg --- Recent Progress around Cohen–Lenstra Heuristics

samedi 28 mars 2026, 14:30 → 15:30 Europe/Paris

Amphithéâtre Charles Hermite (IHP - Bâtiment Borel)

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 theorems proving the Cohen--Lenstra conjectures for the 2-primary part of the class group, as part of more general theorems about Selmer groups in quadratic twists, leading to a resolution of the minimalist conjecture for elliptic curves; and recent work by Koymans and Pagano in the $2$-primary case, expanding on Smith's work and proving Stevenhagen's conjecture on the negative Pell equation.