__Summary__

The aim of this project is to investigate open issues in Probability and Mathematical Statistics, as motivated by Cosmological and Astrophysical applications. In particular, the following main fields are covered:

- Random Fields on the Sphere: Isotropy, Gaussianity, Spectral Representations;
- Statistical Analysis of Spherical Data;
- Wavelets, Nonparametric Estimation, Image Reconstruction;
- Geometric Methods, Excursion Probabilities, Multiple Testing;
- Applications to Astrophysical Data Analysis: CMB, Cosmic Rays, Gravitational Lensing.