Aitor Iribar Lopez: Modularity on Ag through Mathai-Quillen forms

Abstract: In joint work in progress with Greer and Garcia, we prove that the loci of abelian varieties that contain an elliptic curve can be arranged into a modular form, with values in the cohomology of Ag. The proof uses a concrete description of the Kudla-Millson form using Mathai-Quillen forms.

In the talk I will explain briefly what the Mathai-Quillen formalism is, which can be of independent interest to algebraic geometers, how we use it for the proof, and future directions