abstract: In these talks I will present some recent results, obtained with A. Della Vedova, on the Futaki invariants for complete intersections Fano manifolds. In particular I will explain how to construct destibilizing test configurations with smooth central fibers and discuss how this phenomen can be general. I will also present some recent results with G. La Nave on the stability of the Kahler Ricci flow, in particular showing that if a test configuration has a central fiber with mild singuilarities and K-Eisntein metric, then the Ricci flow on the degenerating manifold converges up to diffeomorphisms to this metric.