Interpolating sequences for Complete Nevanlinna Pick spaces

In this talk we will discuss some problems about interpolation in Hilbert spaces of analytic functions and their multiplier algebras. In particular we give a positive answer to a question raised by J. E. McCarthy and J. Agler about strong separation and simply interpolating sequences in reproducing kernel Hilbert spaces with the complete Nevanlinna Pick property. Furthermore, we use a result of A. F. Beardon from Fuchsian groups to show that, in the same class of spaces, there exist sequences with infinite associated measure which are simply interpolating.