Gerard van der Geer: Modular Forms for Genus Two and Three

Modular forms play a central and important role in modern mathematics. The best-known modular forms are elliptic modular forms; a natural generalization are vector-valued Siegel modular forms of genus g. For genus 2 and 3 these modular forms are intimately connected with the moduli of curves of genus 2 and 3. We give an explicit way to describe such vector-valued modular forms for genus 2 and 3. This is based on joint work with Fabien Clery and Carel Faber.