Postal Address: Dipartimento di Matematica, Largo Bruno Pontecorvo 5, 56127 Pisa, Italia Email: francesco.grotto at unipi.it DISAMBIGUATION: a friend and former colleague of mine has the same name as me, Francesco Grotto; even if we both have been students of Scuola Normale Superiore, he is a scholar in classical studies. Scientific Interests My research activity mostly focuses on applications of Probability Theory and Stochastic Analysis to 2D Fluid Dynamics: I have been working in particular on invariant measures of fluid dynamical (S)PDEs, interacting particle systems (point vortex models) and their scaling limits.More recently, I have become interested on limit theorems for Gaussian random fields and their application to Random Wave models. All my publications are available on arXiv, below a list with links to the published versions: Stationary Solutions of Damped Stochastic 2-dimensional Euler's Equation Electronic Journal of Probability (2020), doi:10.1214/20-EJP474 A Central Limit Theorem for Gibbsian Invariant Measures of 2D Euler Equations Joint work with Marco Romito, Communications in Mathematical Physics (2020), doi:10.1007/s00220-020-03724-1 Fokker-Planck equation for dissipative 2D Euler equations with cylindrical noise Joint work with Franco Flandoli and Dejun Luo Theory of Probability and Mathematical Statistics (2020), doi:10.1090/tpms/1130 Essential Self-Adjointness of Liouville Operator for 2D Euler Point Vortices Journal of Functional Analysis (2020), doi:10.1016/j.jfa.2020.108635 Decay of Correlation Rate in the Mean Field Limit of Point Vortices Ensembles Joint work with Marco Romito, Stochastics and Dynamics (2020), doi:10.1142/S0219493720400092 Equilibrium Statistical Mechanics of Barotropic Quasi-Geostrophic Equations Joint work with Umberto Pappalettera, Infinite Dimensional Analysis, Quantum Probability and Related Topics (2021), doi:10.1142/S0219025721500077 Gaussian invariant measures and stationary solutions of 2D Primitive Equations Joint work with Umberto Pappalettera, Discrete and Continuous Dynamical Systems - B (2021), doi:10.3934/dcdsb.2021154 Infinitesimal Invariance of Completely Random Measures for 2D Euler Equations Joint work with Giovanni Peccati, Theory of Probability and Mathematical Statistics (2021), doi:10.1090/tpms/1178 Burst of Point Vortices and Non-Uniqueness of 2D Euler Equations Joint work with Umberto Pappalettera, Archive for Rational Mechanics and Analysis (2022): 89-125, doi:10.1007/s00205-022-01784-2 An Example of Intrinsic Randomness in Deterministic PDEs Joint work with Franco Flandoli and Benjamin Gess, Stochastics and Dynamics (2022): 89-125, doi:10.1142/S0219493722400238 Uniform Approximation of 2D Navier-Stokes Equations with Vorticity Creation by Stochastic Interacting Particle Systems Joint work with Mario Maurelli and Eliseo Luongo, Nonlinearity (2023), doi:10.1088/1361-6544/ad0aab Zero-noise dynamics after collapse for three point vortices Joint work with Marco Romito and Milo Viviani, Physica D: Nonlinear Phenomena 457 (2024), doi:10.1016/j.physd.2023.133947 Among my recent preprints: Nonlinear Functionals of Hyperbolic Random Waves with Giovanni Peccati, Fluctuations of Polyspectra in Spherical and Euclidean Random Wave Models with Leonardo Maini and Anna Paola Todino, Gibbs Equilibrium Fluctuations of Point Vortex Dynamics with Eliseo Luongo and Marco Romito, Random Splitting of Point Vortex Flows with Andrea Agazzi and Jonathan Mattingly. Organization of Events I am an organizer of the Seminars on Probability, Statistics and Stochastic Analysis of University of Pisa, Scuola Normale Superiore, University of Firenze and University of Siena.Together with Anna Paola Todino I will be organizing the INdAM workshop Analysis and Geometry of Random Fields, to be held in Rome on 4-6th September 2024. Teaching (Italian) Informazioni e materiale didattico sono disponibili sui canali Teams dei relativi corsi. Le dispense dello scorso anno per il corso di Statistica (CdL Informatica) sono disponibili a questo link.Per programmi ed orari delle lezioni si rimanda alla pagina unimap. |
