The first topic of this talk will be the description of the Schwartz space
of a Nash manifold. (A generalization of the usual Schwartz space over R to
semi-algebraic manifolds as described in the paper by Aizenbud and
Gurevitch.) After some elementary examples, we will show how to use this concept,
together with some homological algebra, to compute the space of invariant trilinear
forms on induced representations of PGL(2,R). Time permitting, we
will discuss how to extend these ideas to other real rank 1 groups.

This is joint work with Birgit Speh.