Why doing analysis on trees, besides the intrinsic interest? We show as application the characterization of the Carleson measures (or "trace measures") for the Dirichlet space. The seminar requires virtually no prerequisite on holomorphic functions.

We discuss interpolating sequences for RKHS, with special emphasis on the Dirichlet space. The general plan is to cover in a few hours: - interpolation in RKHS in general; - the case of RKHS with the complete Nevanlinna-Pick property; - the Dirichlet space; -the problem of "onto interpolation" on the Dirichlet space; - the weighted Dirichlet spaces (with the construction of Peter Jones). It would be nice to finish with the recent result of Alexandru Aleman, Michael Hartz, John E. McCarthy, Stefan Richter (https://arxiv.org/abs/1701.04885) characterizing the interpolating sequences for the spaces having the complete Nevanlinna-Pick property and their multiplier spaces (volounteers are welcome!).