Title: Transverse Geometry and Modular Forms

Abstract: I shall illustrate the interplay between the transverse geometry of
foliations and modular forms. In one direction, the analogue of the
Godbillon-Vey cocycle becomes a rational cocycle on SL(2,Q), of arithmetic
significance. In the opposite direction, the Rankin-Cohen brackets, promoted
to brackets on modular Hecke algebras, give rise to a family of `quantum'
deformations of the Hopf algebra that encodes the transverse symmetry
of codimension 1 foliations. This is joint work with A. Connes.