Academic Biography - Mathematics and Dynamical Systems Academic Biography Mathematician Specialized in Dynamical Systems Introduction I am a mathematician specialized in Dynamical Systems. My research focuses on the following areas: Stability and instability of nearly-integrable Hamiltonian systems, encompassing Nekhoroshev theory, KAM theory, and Arnold diffusion. I have also explored some connections of this field with real-algebraic geometry. Discrete dynamics in low dimension, in particular the study of invariant curves and chaotic phenomena in twist maps of the annulus (e.g., billiards). Research Interests Hamiltonian Dynamics Arnold diffusion KAM Theory Nekhoroshev Theory Billiards Twist Maps Semi-Algebraic Geometry Career & Appointments 2025–Present Assistant Professor University of Girona 2024–2025 Juan de la Cierva Postdoctoral Researcher Polytechnic University of Catalonia 2023–2024 Part-time Lecturer Polytechnic University of Catalonia 2023–2024 Postdoctoral Researcher University of Barcelona 2022–2023 Attaché Temporaire d'Enseignement et de Recherche (Lecturer) Université Paris Dauphine Education 2019-2023 PhD in Pure Mathematics Université Paris-Saclay & Università degli studi Roma Tre Thesis: Stability in Hamiltonian Systems: steepness and regularity in Nekhoroshev Theory 2016-2017 Master 2 in Analysis and Probability Université Paris Dauphine 2015-2016 Master 2 in Dynamics of Gravitational Systems Sorbonne Université 2014-2015 Master 1 of Physics Sorbonne Université 2010-2014 Bachelor of Physics Alma Mater Studiorum Università di Bologna Publications Articles Barbieri, S., Niederman, L. (2020). Sharp Nekhoroshev estimates for the three-body problem around periodic orbits. Journal of Differential Equations, 268, 3749-3780. Barbieri, S. (2022). On the algebraic properties of exponentially stable integrable Hamiltonian systems. Annales de la Faculté des Sciences de Toulouse, 31(5), 1365-1390. Barbieri, S., Marco, J.-P., & Massetti, J. E. (2022). Analytic smoothing and Nekhoroshev estimates for Hölder steep Hamiltonians. Communications in Mathematical Physics, 396(1), 349-381. Barbieri, S., Niederman, L. (2023). Bernstein-Remez inequality for algebraic functions: a complex analytic approach. Nonlinear Analysis, 237, 113371. Barbieri, S., Farré, G. (2024). Nearly-optimal effective stability estimates around Diophantine tori of Hölder Hamiltonians. Journal of Dynamics and Differential Equations. https://doi.org/10.1007/s10884-024-10397-0 Barbieri, S., Biasco, L., Chierchia, L., & Zaccaria, D. (2025). Singular KAM Theory for Convex Hamiltonian Systems. Regular and Chaotic Dynamics, 30(4), 538-549. Barbieri, S. (2025). Semi-algebraic geometry and generic Hamiltonian stability. Advances in Mathematics, 482(C), 110643.Barbieri, S., Clarke, A. (2025) Existence and Nonexistence of Invariant Curves of Coin Mappings. Nonlinearity, Volume 38, Number 12, 125015. Preprints Works in Preparation Barbieri, S., Biasco, L. Singular KAM Theory and quantitative Morse-Sard Theory Barbieri, S., Langella, B. Nekhoroshev estimates for Diophantine-Steep Hamiltonians Barbieri, S., Fontich, E., Guàrdia, M. On diffusion in steep non-convex systems Collaborators L. Niederman (Université Paris Saclay and Observatoire de Paris) L. Biasco (Università degli Studi Roma Tre) L. Chierchia (Università degli Studi Roma Tre) B. Langella (Scuola Italiana di Studi Superiori Avanzati, Trieste) J.-P. Marco (Sorbonne Université) J. Massetti (Università di Roma Tor Vergata) M. Guàrdia (Universitat de Barcelona) E. Fontich (Universitat de Barcelona) A. Clarke (Universitat Politècnica de Catalunya)