[1] Alfonso Sorrentino.
On the total disconnectedness of the quotient Aubry set.
Ergodic Theory Dynam. Systems 28 (1): 267 - 290, 2008.
[2] Alfonso Sorrentino.
On the structure of action-minimizing sets for Lagrangian systems.
Ph.D. thesis, Princeton University, 157 pp. ISBN: 978-0549-52575-2, ProQuest LLC, 2008.
[3] Albert Fathi, Alessandro Giuliani and Alfonso Sorrentino.
Uniqueness of invariant Lagrangian graphs in a homology or a cohomology class.
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Vol. VIII (4): 659 - 680, 2009.
[4] Alfonso Sorrentino and Claude Viterbo.
Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms.
Geom. & Topol. 14 (4): 2383 - 2403, 2010.
[5] Alfonso Sorrentino.
On the integrability of Tonelli Hamiltonians.
Trans. Amer. Math. Soc. 363 (10): 5071 - 5089, 2011.
[6] Daniel Massart and Alfonso Sorrentino.
Differentiability of Mather’s average action and integrability on closed surfaces.
Nonlinearity 24 (6): 1777 - 1793, 2011.
[7] Leo T. Butler and Alfonso Sorrentino.
Weak Liouville-Arnol’d theorems and their implications.
Comm. Math. Phys. 315 (1): 109 - 133, 2012.
[8] Alfonso Sorrentino.
A variational approach to the study of the existence of invariant Lagrangian graphs.
Boll. Unione Mat. Italiana Serie IX, Vol VI (2): 405 - 440, 2013.
[9] Gabriel P. Paternain and Alfonso Sorrentino.
Symplectic and contact properties Mañé's critical value on the universal cover.
Nonlinear Differential Equations Appl. (NoDEA) 21(5): 679 - 708, 2014.
[10] Alfonso Sorrentino.
Computing Mather’s β-function for Birkhoff billiards.
Discrete and Contin. Dyn. Syst.- A, 35 (10): 5055 - 5082, 2015.
[11] Alfonso Sorrentino.
Action-minimizing methods in Hamiltonian dynamics: an introduction to Aubry- Mather theory.
Monograph in the Series: Mathematical Lecture Notes Vol. 50, Princeton University Press, 2015.
[12] Alfonso Sorrentino.
Lecture notes on Mather’s theory for Lagrangian systems.
Publicationes Matemática del Uruguay,16: 169-192, 2016.
[13] Marco Mazzuccheli and Alfonso Sorrentino.
Remarks on the symplectic invariance of Aubry-Mather sets.
C. R. Acad. Sci. Paris, Ser. I 354: 419-423, 2016.
[14] Stefano Marò and Alfonso Sorrentino.
Aubry-Mather theory for conformally symplectic systems.
Comm. Math. Phys., 354 (2): 775-808, 2017.
[15] Antonio Siconolfi and Alfonso Sorrentino.
Global results for Eikonal Hamilton-Jacobi equations on networks.
Analysis & PDE, 11 (1): 171-211, 2018.
[16] Guan Huang, Vadim Kaloshin and Alfonso Sorrentino.
On Marked Length Spetrum of Generic Strictly Convex Billiard Tables.
Duke Math. Journal, 167 (1): 175 - 209, 2018.
[17] Guan Huang, Vadim Kaloshin and Alfonso Sorrentino.
Nearly circular domains which are integrable close to the boundary are ellipses.
Geom. and Funct. Analysis (GAFA), 28 (2): 334-392, 2018.
[18] Vadim Kaloshin and Alfonso Sorrentino.
On the local Birkhoff conjecture for convex billiards.
Annals of Mathematics, 188 (1): 315-380, 2018.
[19] Vadim Kaloshin and Alfonso Sorrentino.
On the integrability of Birkhoff billiards.
Philosophical Transactions of the Royal Society A, Volume 376, Issue 2131, 2018.
[20] Alfonso Sorrentino.
I matematici giocano... a biliardo (In Italian)
Matematica, Cultura e Società, Rivista dell’Unione Matematica Italiana, Serie I, vol. 4, N.2, 2019.
[21] Alfonso Sorrentino and Alexander P. Veselov.
Markov numbers, Mather’s beta function and stable norm.
Nonlinearity, 32 (6): 2147 - 2156, 2019.
[22] Alfonso Sorrentino.
On John Mather’s seminal contributions in Hamiltonian dynamics.
Methods and Applications of Analysis (Issue in memory of John N. Mather), 26 (1): 37-64, 2019.
[23] Alfonso Sorrentino.
On the integrability of Birkhoff billiards.
Oberwolfach report, European Mathematical Society Publishing, 16 (3): 1861-1863, 2019.
[24] Vadim Kaloshin and Alfonso Sorrentino.
Inverse problems and rigidity questions in billiard dynamics.
Ergodic theory and Dynamical Systems (Issue in memory of A. Katok), 42 (03): 1023-1056, 2022
[25] Carlo Carminati, Stefano Marmi, David Sauzin and Alfonso Sorrentino.
On the regularity of Mather's β-function for standard-like twist maps.
Advances in Mathematics, 377: 107460,2021.
[26] Stefano Galatolo and Alfonso Sorrentino.
Quantitative statistical stability and linear response for irrational rotations and diffeomorphisms
of the circle
Discrete and Continuous Dynamical Systems, Series A, 42 (2): 815-839, 2022.
[27] Marie-Claude Arnaud, Jessica Massetti and Alfonso Sorrentino.
On the fragility of periodic tori for families of symplectic twist maps.
Advances in Mathematics, 429: 109175, 2023.
[28] Antonio Siconolfi and Alfonso Sorrentino.
Aubry-Mather theory on graphs.
Nonlinearity 36 (11): 5819, 2023.
[29] Alfonso Sorrentino.
On the fragility of periodic tori for families of symplectic twist maps.
Oberwolfach report, European Mathematical Society Publishing, 20 (3), 2023.
[30] Corentin Fierobe, Vadim Kaloshin, Alfonso Sorrentino.
Lecture notes on Birkhoff billiards: dynamics, integrability and spectral rigidity.
Modern aspects of dynamical systems (Cetraro, Italy, 2021).
Lecture notes in Mathematics Vol. 2347, Springer, pp. 1-58, 2024 (Editors: Claudio Bonanno, Alfonso Sorrentino, Corinna Ulcigrai).
Preprints
• Alfonso Sorrentino.
Homogenization of the Hamilton-Jacobi equation.
ArXiv: 1904.01359, 2015 (revised 2019).
• Corentin Fierobe, Alfonso Sorrentino.
On the existence of periodic invariant curves for analytic families of twist maps and billiards.
ArXiv: 2407.1790, 2024.
• Rafael Ruggiero, Alfonso Sorrentino.
On the set of asymptotic homologies of orbits on invariant Lagrangian graphs.
ArXiv: 2409.16010, 2024.
• Corentin Fierobe, Alfonso Sorrentino, Amir Vig.
Deformational Spectral rigidity of axially-symmetric symplectic billiards.
ArXiv: 2410.13777, 2024.
• Marco Pozza, Antonio Siconolfi, Alfonso Sorrentino.
Homogenization of Hamilton-Jacobi equations on networks.
ArXiv: 2411.03803, 2024.
Research
Publications
(see also ArXiv)
Publications
Preprints
Seminars
(Some) Slide-presentations:
• Proprietà simplettiche e variazionali di sistemi Hamiltoniani convessi (pdf)
Plenary talk session "Nonlinear Analysis and Dynamical Systems"
XIX Congresso UMI (Italian Mathematical Union), Bologna, September 2011.
• Poincaré ed Arnol’d: dalla meccanica classica alla geometria simplettica (pdf)
Tè di Matematica (Divulgative talk for students), Roma Tre University, January 2014.
• The principle of least action in geometry and dynamics (pdf)
University of Rome Tor Vergata, September 2014.
• Biliardi Matematici (pdf)
Divulgative talk for students at Maths Olympiad, Roma Tre University, March 2015.
• On the homogenization of the Hamilton-Jacobi equation (pdf)
Analysis Seminar, University of Rome “La Sapienza”, May 2016.
• Hamilton-Jacobi equation on networks (pdf)
SIAM meeting on Control and its applications, Pittsburgh, July 2017.
• On the Birkhoff Conjecture for Convex Billiards (pdf)
Workshop "An Analysist, a geometer and a probabilist walk into a bar"
Cardiff University, June 2018.
• Mathematicians play... billiards (pdf)
Award of the Guido Fubini prize for mathematics, Accad. delle scienze di Torino, October 2018.
• Dynamical and Spectral Properties of Mathematical Billiards (pdf)
Department Colloquium, Université Nice Sophia Antipolis, February 2019.
• Inverse problems and rigidity questions in billiard dynamics (pdf)
Nonlinear meeting - Milan 2020, Politecnico di Milano, January 2020.
• Action-minimizing methods in Hamiltonian dynamics and invariant Lagrangian graphs (pdf)
On-line seminar "Geometry, Topology and their applications", Novosibirsk, May 2020.
• The Hamilton-Jacobi equation on networks: from weak KAM and Aubry-Mather theories to Homogenization (pdf)
On-line seminar "One world PDE seminar", October 2020.
• "E π si muove:" una storia di urti, pi greco e biliardi matematici (pdf) (In Italian)
On-line seminar, Salone dello studente del lazio, November 2020.
• On the persistence of periodic Lagrangian tori for symplectic twist maps (pdf)
Conference "GLADS22" (in honour of Tere Seara's 60 birthday), July 2022.
• The Hamilton-Jacobi equation on networks: from Aubry-Mather theory to Homogenization. (pdf)
Highlights in nonlinear analysis (in honour of S. Terracini's 60th birthday), June 2023.
Videos of some lectures and seminars:
• Symplectic and variational methods for the study of invariant Lagrangian graphs (video)
Workshop: New perspectives on the N-boy problem
Banff International Research Station, January 2013.
• Dynamical and Spectral properties of mathematical billiards (video)
MSRI Program: Hamiltonian systems, from topology to applications, through Analysis
Introductory Workshop, Berkeley, August 2018.
• The Hamilton-Jacobi equation on networks: from weak KAM and Aubry-Mather theories to
Homogenization (video)
On-line seminar "One world PDE seminar", October 2020.
• Inverse problems and rigidity questions in billiard dynamics (video)
Geometry, Dynamics and Mechanics Seminar
University of Padua (Italy), January 2021.
• Inverse problems and rigidity questions in billiard dynamics (video)
Analysis Seminar
University of Western Australia at Perth (Australia), May 2021.
• The Hamilton-Jacobi equation on networks: weak KAM and Aubry-Mather theories (video)
The University of Sydney (Australia), September 2021.
• On the persistence of periodic Lagrangian tori for symplectic twist maps (video)
Conference: Differential geometry, billiards and geometric optics
CIRM-Luminy, France, October 2021.
• On the persistence of periodic Lagrangian tori for symplectic twist maps (video)
Symplectic geometry seminar, IAS Princeton, November 2023.
Seminars: slides and video