Uploaded March 2026 | Updated September 2026, 3 weeks ago
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.
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.
