Ben Breen – Clemson University

Abstract: Recent advances in explicit methods for Hilbert modular forms (HMFs) have allowed researchers to quickly access the Fourier coefficients of a basis for the C-vector space of HMF’s with a given level and weight. Our collaboration is working on computing the structure of graded rings of Hilbert modular forms. Applications include accessing Fourier coefficients of Hilbert modular forms in high weight and explicit parameterizations of abelian varieties with real multiplication and torsion structure.