Modular Forms, Moduli and Invariant Theory

Abstract

Siegel modular forms generalize the usual elliptic modular forms and show up in many parts of mathematics: algebraic geometry, number theory and even in mathematical physics. But they are difficult to construct. We show that invariant theory enables us to efficiently construct all (vector valued) Siegel modular forms of degree two and three from from certain basic modular forms provided by the geometry of curves.

This is joint work with Fabien Cléry, Carel Faber and Alexis Kouvidakis.

About the speaker

Gerard van der Geer is professor emeritus at the University of Amsterdam. He works in algebraic geometry and arithmetic geometry with emphasis on moduli spaces and modular forms. He worked on Hilbert modular surfaces,curves over finite fields, cycle classes on moduli of abelian varieties and on modular forms. He got a honorary doctorate of the University of Stockholm.