A note on Berezin-Toeplitz quantization of the Laplace operator

Given a Hodge manifold, it is introduced a self-adjoint operator on the space of endomorphisms of the global holomorphic sections of the polarization line bundle. Such operator is shown to approximate the Laplace operator on functions when composed with Berezin-Toeplitz quantization map and its adjoint up to an error which tends to zero when taking higher powers of the polarization line bundle

Singularities and K-semistability

In this paper we extend the notion of Futaki invariant to big and nef classes in such a way that it defines a continuous function on the \K\ cone up to the boundary. We apply this concept to prove that reduced normal crossing singularities are sufficient to check $K$-semistability. A similar improvement on Donaldson's lower bound for Calabi energy is given.Comment: Major revision of previous upload. 18 page

On the K-stability of complete intersections in polarized manifolds

We consider the problem of existence of constant scalar curvature Kaehler metrics on complete intersections of sections of vector bundles. In particular we give general formulas relating the Futaki invariant of such a manifold to the weight of sections defining it and to the Futaki invariant of the ambient manifold. As applications we give a new Mukai-Umemura-Tian like example of Fano 5-fold admitting no Kaehler-Einstein metric and a strong evidence of K-stability of complete intersections on Grassmannians.Comment: 19 page

Clinical Psychology of Aging: the Italian Manifesto

In the context of Italian aging population, clinical psychology can play a crucial role in enabling older adults to cope with the multiple challenges associated with the aging process and disease-related issues. This manifesto was  written by the 'Clinical Psychology of Aging' working group, which is part of the Italian Association of Psychology (AIP) consisting of academic experts in this field  who collaborated to elaborate the contents highlighting the most relevant dimensions of the clinical psychology of aging. Specifically, the aging process was addressed from multiple points of view (i.e., theoretical perspectives, multidimensional assessment, interventions), and the role of the clinical psychologists in the National Health System along with training issues were discussed in the attempt to specify  the unique contribution  of the clinical psychology in aging