Statistics and Stochastic Seminar: Geometry and topology of spin random fields

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Event: PVSeminar #57
Speaker: Domenico Marinucci (L’Università degli Studi di Roma Tor Vergata, The Italian Republic)
Title: Geometry and topology of spin random fields
Dates: Thursday 23 May / 16:00 AEST
Location: Darwin Convention Centre, 10 Stokes Hill Rd, Darwin, NT
Zoom link: https://unimelb.zoom.us/j/85717338005?pwd=ZzZLMmVCRjA5OU1ycS9iWWFPb1ptZz09
Password: 122074 (just in case)

Abstract: The investigation of the geometric properties of the excursion sets for isotropic random fields has been the object of a considerable amount of research over the last decade. In this talk, we discuss how to generalize some of these results to the case of random fields which are not scalar valued, but they are rather random sections of a non-trivial fiber bundle: these are the so-called spin (spherical) random fields, which play a key role in Cosmology, especially in connection with the analysis of Cosmic Microwave Background (CMB) polarization. In particular, we discuss how to characterize their expected geometry and topology: i.e., we investigate the asymptotic behaviour, under scaling assumptions, of general classes of functionals of (properly defined) excursion sets, including Lipschitz–Killing Curvatures and Betti Numbers.

Based on joint works with Antonio Lerario, Maurizia Rossi and Michele Stecconi.

A PDF file with the talk slides might become available for downloading from our seminar’s Webpage at https://probvic.wordpress.com/pvseminar/ prior to the talk (the above Zoom link has already been posted there).