Moments of Families of Elliptic Curves

Moments of Families of Elliptic Curves

Explore new developments in higher moment sums of 1-parametric families of elliptic curves in this 50-minute lecture from the Hausdorff Center for Mathematics. Delve into connections between these sums, modular forms, and algebraic curves. Examine a result on the second moment of cubic curves, revealing its link to intermediate Jacobians in threefolds. Investigate proofs of modularity for certain rigid Calabi-Yau threefolds, utilizing higher moments, universal families of elliptic curves, and Deligne's results, while bypassing the conventional Faltings-Serre method approach.