Dear Colleagues,

We would like to invite you to the following seminar that will take place on November 25 at 15.30. The seminar will be held in person and online via the Zoom platform.

The organizers, Alessandra Bianchi, Giorgia Callegaro, Marco Formentin _____________________________________________________

*Speaker*: Maurizia Rossi (Università Milano Bicocca)

*Title*: Gaussian Kinematic Formulas for Random Spherical Harmonics

*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.