What are Jacobi forms and what are they good for?

Abstract

The theory of Jacobi forms was created in 80's of the last century by Eichler and Zagier.This theory turned out to have many useful applications ranging from combinatorics overphysics and algebraic geometry to number theory. It complements the classical theory ofelliptic modular forms. In this talk we try to explain the notion of Jacobi forms and itsmain applications in number theory and arithmetic geometry. In the second part of thetalk we indicate recent affords to extend the classical theory to a theory of Jacobi formsover number fields.