Professor Liverani has held visiting positions in many Universities among which: Fields Institute (Toronto, Canada), Ecole Normale Superiore (Paris, France), Universiteʼ de Paris Dauphine (Paris, France), CIRM (Marseille, France), Pen State University (Pennsylvania, USA), Universiteʼ di Paris XIII (Paris, France), University of Maryland (Maryland, USA), CNRS (France), Universiteʼ de Paris 7 (Paris, France), IHES (Paris, France), Courant Institute (New York, USA).
He has published almost 70 articles on international Physics and Mathematical journals in the areas of Dynamical Systems, Analysis, Probability, Quantum Mechanics and Non-Equilibrium Statistical Mechanics.
He is the recipient of several Grants including the prestigious ERC Advanced Grant from the European Research Council.
He is currently the Co-editor in Chief of Nonlinearity and he is editor of Communication In Mathematical Physics and of the Bollettino della Unione Matematica Italiana. Also he is part of several editorial board of international journals: Ergodic Theory and Dynamical Systems, Journal of Dynamical Systems and Control Systems and Journal of Statistical Physics. For long time he has been part of the editorial board of Discrete and Continuous Dynamical Systems and Mathematical Physics Electronic Journal.
The rigorous study of hyperbolic billiards was started by Sinai in 1970 and since then it has grown in many directions due to the importance of this seemingly simple model for many branches of mathematics and physics. Today it is still a very active field of research. In fact, in the last years several new results have been obtained and new applications have been proposed. I will present an idiosyncratic selection of results and open problems concerning hyperbolic billiards.