Nell'ambito dei Tè di Matematica, per celebrare il pensionamento di Elisabetta Scoppola, mercoledì *29 ottobre* alle *ore 16:00*, Fabio Martinelli terrà un seminario dal titolo *"An Introduction to the Mathematical Theory of Anderson Localization"*. Abstract: In 1958, the physicist P. W. Anderson published the paper "Absence of Diffusion in Certain Random Lattices," which contributed to winning him the Nobel Prize in 1977 for the discovery of the phenomenon now known as "Anderson localization." In the simplest case, Anderson localization states that a Schroedinger operator with a random potential on, e.g., a d-dimensional lattice has a pure-point spectrum with exponentially localized eigenstates if the randomness of the potential is sufficiently strong. In his Nobel lecture Anderson said "...*Localization was a different matter: very few believed it at the time, and even fewer saw its importance; among those who failed to fully understand it at first was certainly its author. It has yet to receive adequate mathematical treatment, and one has to resort to the indignity of numerical simulations to settle even the simplest questions about it." *Proving Anderson localization was one of the great problems in mathematical physics in the early 1980s, and E. Scoppola greatly contributed to its solution in the hard case d > 1. On the occasion of her retirement, I will provide a brief overview of the Anderson model and eigenfunction localization, as well as some of the more recent developments. If time allows, I will also try to describe how the basic multiscale analysis underlying the proof of Anderson localization can be applied to other, quite different, contexts. Il seminario si svolgerà in presenza presso il Dipartimento di Matematica e Fisica dell'Università di Roma Tre, Lungotevere Dante 476, *aula M1*.