Dear all, It is our pleasure to invite you all to the Padova Seminars in Probability and Finance on May, 17th at 14:30, at the department of Mathematics in Padova for the seminar by: Domenico Marinucci (University of Rome "Tor Vergata") Title: Geometry and Topology of Spin Random Fields Date: May 17, 2024, at 14:30, 2AB45 Abstract: Spin random fields are very important in many physical applications; they can be viewed as random sections of the s-th complex tensor power of the tangent bundle of the 2-sphere. In this talk, we discuss how to characterize their expected geometry and topology. In particular, we investigate the asymptotic behaviour, under scaling assumptions, of general classes of geometric and topological functionals for (properly defined) excursion sets; we cover both the cases of fixed and diverging spin parameters s. In the special case of monochromatic fields (i.e., spin random eigenfunctions), we show how their asymptotic behaviour is non-universal; we can obtain complex versions of Berry's random waves and of Bargmann-Fock's model as subcases of a new general class, depending on the rate of divergence of the spin parameter. We shall also discuss how these random fields can be reparametrised into complex-valued random functions on the group of rotations SO(3), and we discuss the expected values of the same geometric functionals in this new framework. Based on joint works with Javier Carròn Duque, Antonio Lerario, Maurizia Rossi and Michele Stecconi. Best wishes, Alberto and Alekos