PASCAL · Probabilistic And Statistical methods for Cosmological AppLications

This is an interdisciplinary project at the interface between Mathematical Statistics, Probability and Cosmological Applications. The principal focus is on the harmonic analysis for isotropic, mean square continuous spherical random fields, with a view to applications to Cosmic Microwave Background radiation data analysis. We will focus in particular on the following issues:1) the characterizations of isotropy in harmonic space, the analysis of higher order polyspectra and their applications to non-Gaussianity analysis;2) the constructions of spherical needlets/wavelets and their stochastic properties;3) the analysis of random sections of spin fiber bundles on the sphere, as motivated by the analysis of CMB polarization and weak gravitational lensing4) adaptive density estimation for directional data, as motivated by Cosmic Rays data analysis.