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Speaker: Maurizia Rossi (Università Milano Bicocca)

Date and time:  Friday, NOVEMBER 25 at 15.30 
Place: room 2AB40 at the Department of Mathematics, University of Padova Zoom link: https://unipd.zoom.us/j/83301000752 (meeting ID: 833 0100 0752)
available also on the webpage  https://www.math.unipd.it/~bianchi/seminari/

Abstract: In this talk we investigate the geometry of random spherical harmonics
(Gaussian Laplace eigenfunctions on the round sphere). In particular we study the distribution,
for large eigenvalues, of Lipschitz-Killing Curvatures (LKCs) of their excursion sets at any threshold.
The main result we discuss is an asymptotic equivalence, in mean-square, between these functionals
and the L2-norm of the random eigenfunction times a suitable map of the threshold (that vanishes at zero).
 This formula allows one to determine limiting distribution, correlation phenomena and moderate deviations
for these LKCs, and generalizes - in the case of random spherical harmonics - those obtained by Adler and Taylor
 for their expected value. If time permits, we digress slightly to investigate the local geometry of spin spherical 

random fields, that is, random sections of the spin line bundles of the sphere.
This talk is mainly based on a number of joint works on random spherical harmonics with V. Cammarota, D. Marinucci
and I. Wigman + a recent work on spin random fields written jointly with A. Lerario, D. Marinucci and M. Stecconi.