Exploring modular forms and the cohomology of local systems on moduli spaces by counting points

Abstract

This is a report on a joint project in experimental mathematics with Jonas Bergström and Carel Faber where we obtain information about modular forms by counting curves over finite fields.

27 pages; expanded version of a talk at the Mittag-Leffler Institute

References in corpus (3)

• Sur la cohomologie des systèmes locaux sur les espaces des modules des courbes de genre 2 et des surfaces abéliennes
• Generators for modules of vector-valued Picard modular forms
• Eisenstein congruences for split reductive groups