Matroids and the Integral Hodge Conjecture for Abelian Varieties - Philip Engel

Workshop on Recent Developments in Hodge Theory and O-minimality 2:30pm|Simonyi Hall 101 Topic: Matroids and the Integral Hodge Conjecture for Abelian Varieties Speaker: Philip Engel Affiliation: University of Illinois Date: March 09, 2026 We will discuss a proof that the integral Hodge conjecture is false for a very general abelian variety of dimension ≥ 4. Associated to any regular matroid is a degeneration of principally polarized abelian varieties. We introduce a new combinatorial invariant of regular matroids, which obstructs the algebraicity of the minimal curve class, on the very general fiber of the associated degeneration. In concert with a result of Voisin, one deduces (via the intermediate Jacobian) the stable irrationality of a very general cubic threefold. This is joint work with Olivier de Gaay Fortman and Stefan Schreieder.