Joint PU/IAS Number Theory

In this talk, I will present recent work on the intersection theory of modular correspondences. Specifically, we study the intersection numbers of modular correspondences of square-free level, focusing both on the nonsingular intersections and the "singular" intersections in the special case of level 1. We provide explicit formulas for these intersection numbers and show how they are related to the derivatives of a certain Eisenstein series. This talk is based on joint works with Qiao He and Ryan Chen.