Perfect forms and the cohomology of modular groups.

Abstract :  Perfect forms are those positive definite real
quadratic forms which are uniquely determined (up to scalar
multiplication) by their minima on integral vectors.
We shall dicuss how to use their classification in order
to compute the cohomology of the groups $SL_N(\bf Z)$,
for $N$ at most seven. This is joint work with P.Elbaz-Vincent
and H.Gangl.