Title: Constructing modular forms as Sudoku for number theorists

Abstract: We describe a very personal view on usual elliptic modular forms. We shall describe modular forms in terms of graphs and in a way which can even be understood by non-mathematicians. We promise that after the talk everybody can compute quickly modular forms by hand. 

For the experts: The machinery working behind our talk is, of course, Eichler-Shimura cohomology and Manin symbols. But none of this will show up in the talk (except for one or two slides of background illumination for the ambitious).

Title: Theta Blocks

Abstract: As it turned out a while ago there is an easy, yet extremely

powerful construction of Jacobi forms, which has also consequences for the

theory of elliptic modular forms. Despite its simpleness this construction is

related to various interesting problems concerning trigonometric polynomi-

als, the arithmetic theory of lattices and the theory of Kac-Moody algebras.

We shall report about this construction, the mentioned connections to other

theories and recent results. Many of these results would not have been dis-

covered without a lot of preceding computational experimentation. We shall

also try to report about this aspect. The talk is partly based on joint work

with Valery Gritsenko and Don Zagier.