Abstract: I will explain a surprising connection between non-tautological classes on the moduli space of abelian varieties and tautological relations on the moduli space of curves. The story begins with joint work with Larson and Schmitt on the Gorenstein problem for compact type moduli and joint work with Oprea and Pandharipande on the product loci on moduli spaces of abelian varieties. I will also discuss recent progress by Iribar López toward extending the story to Noether-Lefschetz loci on the moduli space of abelian varieties.