Dear Colleagues, we would like to invite you to the following seminar by Anna Paola Todino (Università Milano Bicocca) to be held this Wednesday (April 27th) at Dipartimento di Matematica in Pisa and online via Google Meets.

After the seminar, in the same location (on site and online), Francesca Pistolato (future PhD student at Université du Luxembourg) will give a short talk, details below.

The organizers, A. Agazzi and F. Grotto

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Location: Sala Seminari, Dipartimento di Matematica, Pisa Google Meet Link: https://meet.google.com/gji-phwo-vbg

Time: April 27th, 2022, 14:00-15:00 CET Speaker: Anna Paola Todino (UniMiB) Title: Alternative forms of random spherical harmonics Abstract: In the last decade, lot of efforts have been devoted to the analysis of the high-frequency behaviour of geometric functionals (Lipschitz-Killing Curvatures) for the excursion sets of random eigenfunctions on the unit sphere (spherical harmonics). The asymptotic behavior of their expected values and variances have been investigated and quantitative central limit theorems have been established in the high energy limits. In order to generalize these results, a local study was also introduced by considering subdomains of the sphere. This topic is linked to Berry's conjecture on planar random waves and finds its motivation in cosmological applications. Another interesting issue concerns the Gaussianity hypothesis of the random field. In this direction we introduce a model of Poisson random waves on the 2-dimensional sphere and we study Quantitative Central Limit Theorems when both the rate of the Poisson process and the energy (i.e. frequency) of the waves (eigenfunctions) diverge to infinity. We consider finite-dimensional distributions, harmonic coefficients and convergence in law in functional spaces, and we investigate carefully the interplay between the rates of divergence of eigenvalues and Poisson governing measures.

Time: April 27th, 2022, 15:00-15:30 CET Speaker: Francesca Pistolato Title: A Small-Scale Reduction Principle for the Nodal Length of Monochromatic Random Waves Abstract: We prove an asymptotic mean square equivalence between the nodal length of monochromatic random waves and their sample trispectrum in the small-scale regime. We make use of coupling techniques for non-stationary Gaussian fields, and the so-called Small-Scale Central Limit Theorem for the nodal length, both proved by Dierickx, Nourdin, Peccati, Rossi in 2020. Consequently, we deduce the conjectured equivalence from the analogous one for Berry's random wave model, proved by Vidotto in 2020.