Prof Alfonso Sorrentino

Associate Professor in  Mathematical Analysis (MAT/05)

Dipartimento di Matematica

Università degli Studi di Roma “Tor Vergata”

Office: 1205

Tel.: (+39) 06 72594663

Fax: (+39) 06 72594699

email: sorrentino(at)

Mailing Address:

Dipartimento di Matematica

Università degli Studi di Roma “Tor Vergata”

Via della Ricerca Scientifica 1

00133 Rome, Italy

Research Interests: Hamiltonian and Lagrangian systems, symplectic geometry.

Curriculum vitae et studiorum:  pdf

Publications and Preprints: (see also Arxiv)

[1“On the total disconnectedness of the quotient Aubry set”.

        Ergodic Theory Dynam. Systems 28 (01): 267-290, 2008.

[2“On structure of action-minimizing sets for Lagrangian systems”.

        Ph.D. Thesis Princeton University, 2008. Publ. on. ProQuest: AAT 3305777, ISBN: 9780549525752.

[3“Uniqueness of invariant Lagrangian graphs in a homology or cohomology class”, with A. Fathi and A. Giuliani.

        Ann. Sc. Norm. Super. Pisa Cl. Sci., Vol VIII (4): 659-680, 2009.

[4] “Action minimizing properties and distances on the group of Hamiltonian diffeomorphisms”, with C.Viterbo. Preprint 2010: ArXiv: 1002.3915v1    mp_arc: 10-39.

        Geometry & Topology 14 (4): 2383 - 2403, 2010.

[5“Differentiability of Mather’s average action and integrability on closed surfaces”, with D. Massart.

        Nonlinearity, 24: 1777-1793, 2011.

[6]  “On the integrability of Tonelli Hamiltonians”.

        Trans. Amer. Math. Soc. 363 (10): 5071–5089, 2011.  ArXiv: 0903.4300; mp_arc: 09-55..

[7“Weak Liouville-Arnol’d Theorems and their Implications”, with Leo Butler.

        Comm. Math. Phys. 315 (1): 109–133, 2012. ArXiv: 1011.0172 mp_arc: 10-179

[8] “A variational approach to the study of the existence of invariant Lagrangian graphs”.

         Boll. Unione Mat. Ital. Serie IX, Vol. VI  (2): 405 - 440, 2013. ArXiv: 1309.1019

[9] “Symplectic and contact properties of the Mañé critical value of the universal cover”, with Gabriel Paternain.

         NoDEA: Nonlinear Differential Equations Appl., 21: 679- 708, 2014. ArXiv: 1309.1001

[10] “Computing Mather’s beta-function for Birkhoff billiards”.

         Discrete and Continuous Dyn. Systems Series A, 35 (10): 5055- 5082, 2015. ArXiv: 1309.1008

[11Action-Minimizing Methods in Hamiltonian Dynamics. An Introduction to Aubry-Mather Theory”.

        Mathematical Notes Series Vol. 50 (Princeton University Press), 2015. (A previous version on ArXiv: 1011.0590 )

[12] “Remarks on the symplectic invariance of Aubry-Mather sets”, with Marco Mazzucchelli,

          C. R. Acad. Sci. Paris, Ser. I 354: 419-423, 2016.

[13] “Lecture notes on Mather’s theory for Lagrangian systems”,

         Publicationes Matemática del Uruguay, 16: 169-192, 2016.

[14] “Homogenization of the Hamilton-Jacobi equation”, preprint 2015.

[15“On the Marked Length Spetrum of Generic Strictly Convex Billiard Tables”, with Guan Huang and Vadim Kaloshin,

          Duke Math. Journal, 167 (1): 175 - 209, 2018.  ArXiv: 1603.08838

[16] “Aubry-Mather theory for conformally symplectic systems”, with Stefano Marò,

          Comm. Math. Phys., 354 (2): 775-808, 2017.  ArXiv: 1607.02943

[17] “Global results for Eikonal Hamilton-Jacobi equations on networks”, with Antonio Siconolfi,
Analysis & PDE, 11 (1): 171-211, 2018. ArXiv: 1612.01152

[18“On local Birkhoff conjecture for convex billiards”, with Vadim Kaloshin, Preprint 2016. ArXiv: 1612.09194

[19] “Nearly circular domains which are integrable close to the boundary are ellipses”, with Guan Huang  and Vadim Kaloshin.

         To appear on Geometric and Functional Analysis (GAFA), 2018. ArXiv: 1705.10601

[20] “Markov numbers, Mather’s beta function and stable norm”, with Alexander P. Veselov, Preprint 2017. ArXiv: 1707.03901


                                Teaching Material 

Upcoming conferences, schools and meetings:

  1. -Analysis and Dynamics, Congress in honour of Luigi Chierchia’s 60th Birthday, Marina di San Gregorio (Patù, Lecce, Italy): 12-15 October 2017.

  2. -Conference on Hamiltonian Systems (a tribute to the memory of John N. Mather), Monte Verità Conference Center, Ascona (Switzerland), 29 Oct. - 03 Nov 2017.

  3. -International Conference on Singularity Theory & Dynamical Systems (in memory of John N. Mather), Yau Mathematical Sciences Center (Sanya, China), 11-15 Dec 2017

  4. -Winter School on Hamiltonian Dynamics and Symplectic geometry, Padova, 12-17 February 2018.

  5. -Weak KAM Rio 2018, ICM Satellite Conference, Rio de Janeiro 23-27 July 2018.

Other Material:

[aSlides of a talk given at XIX Congresso UMI (Italian Mathematical Union), September 2011 [in italian]

[b“Sulle soluzioni quasi-periodiche di sistemi Hamiltoniani differenziabili”, Laurea Thesis Università degli Studi “Roma Tre”, 2003.

[cSlides of a divulgative talk “Poincaré ed Arnol’d: dalla meccanica classica alla geometria simplettica”, January 2014 [in italian]

[dSlides of a divulgative talk “Biliardi Matematici”, March 2015 [in italian]

[eSlides of a talk “On the homogenization of the Hamilton-Jacobi equation”, May 2016 (Analysis Seminar, University of Rome “La Sapienza”).

[fSlides of a talk “Hamilton-Jacobi equation on networks”, July 2017 (SIAM meeting at Pittsburgh).