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, asterisks (*) mark a selection: 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 Fluctuations of Polyspectra in Spherical and Euclidean Random Wave Models Joint work with Leonardo Maini and Anna Paola Todino, Electronic Communications in Probability 29 (2024), doi:10.1214/24-ECP578 Decay of time correlations in point vortex systems Joint work with Silvia Morlacchi, Physica D: Nonlinear Phenomena 463 (2024), doi:10.1016/j.physd.2024.134169 (*)Random Splitting of Point Vortex Flows Joint work with Andrea Agazzi and Jonathan Mattingly, Electronic Communications in Probability 29 (2024), doi:10.1214/24-ECP594 (*)Gibbs Equilibrium Fluctuations of Point Vortex Dynamics Joint work with Eliseo Luongo and Marco Romito, Annals of Applied Probability (in press), arxiv preprint Among my recent preprints: Nonlinear Functionals of Hyperbolic Random Waves with Giovanni Peccati, Anomalous Regularization in Kraichnan's Passive Scalar Model with Lucio Galeati and Mario Maurelli, Anomalous Regularization in Kazantsev-Kraichnan Model with Marco Bagnara and Mario Maurelli. 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 have organized the INdAM workshop Analysis and Geometry of Random Fields, 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. |
