Annuncio Seminari congiunti ASI - Dipartimento Matematica Tor Vergata
9 Gennaio 2020
Aula Dal Passo, Edificio Sogene

Ore 14: Gianluca Polenta, ASI Space Science Data Centre

Title: Cosmology through CMB maps

Abstract: The Cosmic Microwave Background is a fundamental source of
information for cosmology. In the standard inflationary scenario, the
CMB can be described to first order as a Gaussian random field on the
sphere, and as such cosmological information is encoded in the two-point
correlation function or in the angular power spectrum. To derive these
quantities as well as the likelihood function needed to estimate the
cosmological parameters, a number of estimators have been developed
following different trade-off between optimality, unbiasedness, and
computational resources, also depending on the characteristics of the
dataset to be analysed. In this talk I will review the different classes
of estimators used in the CMB data analysis, focusing in particular to
the solutions adopted for the ESA Planck satellite, which produced CMB
full sky maps of unprecedented quality. Finally, I will briefly discuss
how CMB non-Gaussianity, isotropy, and those anomalies found in the
analysis of Planck data can be used to further test the inflationary
paradigm.

Ore 15: Domenico Marinucci, Department of Mathematics, University of
Rome Tor Vergata

Title: Critical Points, Multiple Testing and Point Source Detection for
Cosmological Data

Abstract: In this talk, we shall review some mathematical issues arising
in the analysis of Cosmic Microwave Background (CMB) radiation data;
many of these issues can be related to the investigation of functionals
of independent interest in random geometry. We will first review some
results on harmonic analysis for spherical random fields, on the
construction of spherical wavelets and on their stochastic properties;
we will then show how to compute the asymptotic distribution of critical
points for Fourier/wavelet components of random fields, and we will
establish some ergodicity results, in the high-frequency limit. We will
then investigate how to exploit these results to implement multiple
testing procedures for detection of point sources (Galaxies) in CMB
Data; the resulting tests will be shown to exhibit a number of
optimality properties. Applications to CMB data from the Planck
collaboration will also be briefly illustrated.