Research

Publications

(see also ArXiv)

Publications

Preprints

Seminars

Seminars: slides and video

(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.



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)

          Dynamical Systems Seminar

          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.





          

[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.     



     Preprints


     Alfonso Sorrentino.

          Homogenization of the Hamilton-Jacobi equation, preprint 2015 (revised version 2018).

          ArXiv: 1904.01359


     Marie-Claude Arnaud, Jessica Massetti and Alfonso Sorrentino.

          On the persistence of periodic tori for symplectic twist maps and rigidity of integrable twist maps, preprint 2022.

               ArXiv: 2202.00313


     Antonio Siconolfi and Alfonso Sorrentino.

          Aubry-Mather theory on graphs. Preprint 2021.

               ArXiv:   2102.1106