Thursday 20 October, from 12.00 to 13.00, room 207 viale Romania 32 00197 Rome Speaker: Domenico Marinucci (Università degli Studi di Roma Tor Vergata) Title: The geometry of random eigenfunctions Abstract: The characterization of the geometric properties for the excursion sets of random fields on generic manifolds is a classical topic of probability theory; it has been very much revived recently by the discovery of the Gaussian Kinematic Formula by Adler and Taylor (2007). This formula provides a fully explicit characterization of the expected value for so-called Minkowski functionals of excursion sets under very broad circumstances. In this talk, we review some very recent results pointing at a generalization of this formula to the variance of Minkowski functionals and to a corresponding Central Limit Theorem, in the case of random eigenfunctions. The talk is based on a recent paper with Valentina Cammarota; if time permits, we will also discuss some related results involving also Giovanni Peccati, Maurizia Rossi and Igor Wigman. ******************************************************* Marco Scarsini Dipartimento di Economia e Finanza LUISS Viale Romania 32 00197 Roma, ITALY URL: http://docenti.luiss.it/scarsini/