Philip Engel is currently an assistant professor at UIC. Before that, he was a Bonn Junior Fellow at the University of Bonn for one year, an assistant professor at University of Georgia, and a postdoc at Harvard. He loves talking about math and meeting new people. His research is in algebraic geometry and Hodge theory, especially moduli and degenerations of Calabi-Yau varieties. He is also fascinated by tilings and have thought a bit about Hurwitz theory.

Abstract: Associated to any regular matroid of rank on elements, one can associate a multivariable semistable degeneration of principally polarized abelian -folds over a -dimensional base. I will discuss joint work with de Gaay Fortman and Schreieder, proving that a combinatorial invariant of the matroid obstructs the algebraicity of the minimal curve class, on the very general fiber of the associated degeneration. Corollaries include the failure of the integral Hodge conjecture for abelian varieties of dimension and the stable irrationality of very general cubic threefolds.