Martedì 20 giugno 2023 alle ore 14:00, Aula 211 Dipartimento di Matematica e Fisica di Roma Tre, Largo San Leonardo Murialdo,1- 00146 Roma. Speaker: Giorgio Cipolloni (Princeton Center for Theoretical Science) Title: Quantum Unique Ergodicity and its fluctuations for Wigner matrices. Abstract: We prove that the eigenvectors of Wigner matrices satisfy the Eigenstate Thermalization Hypothesis (ETH), which is a strong form of Quantum Unique Ergodicity (QUE) with optimal speed of convergence. Then, using this a priori bound as an input, we analyze the Stochastic Eigenstate Equation (SEE) and prove a Wigner matrix analog of the Berry random wave conjecture.