Topic: Hodge theory

Philip Engel explains a counterexample to the integral Hodge conjecture for very general abelian varieties of dimension at least four. Degenerations of principally polarized abelian varieties are associated with regular matroids, and a new matroid invariant obstructs algebraicity of the minimal curve class on a very general fiber. Combining this obstruction with a theorem of Voisin and the intermediate Jacobian gives stable irrationality of a very general cubic threefold. The work is joint with Olivier de Gaay Fortman and Stefan Schreieder.

Gregorio Baldi surveys recent results on how the Hodge locus is distributed in mixed variations of Hodge structures, including the pure setting. The presentation also examines concrete applications of these results to moduli spaces.