Prof. Alfonso Sorrentino

Associate Professor in  Mathematical Analysis (MAT/05)

Dipartimento di Matematica

Università degli Studi di Roma “Tor Vergata”

Via della ricerca scientifica 1, 00133 Rome (Italy)

Office: 1205

Tel.: (+39) 06 72594663

Fax: (+39) 06 72594699

email: sorrentino(at)

Research Interests: Hamiltonian and Lagrangian systems, dynamical 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.

        Geometry & Topology 14 (4): 2383 - 2403, 2010. ArXiv: 1002.3915v1    mp_arc: 10-39.

[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 (revised version 2018).

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

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

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

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

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

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

         Geometric and Functional Analysis (GAFA), 28 (2): 334-392, 2018. ArXiv: 1705.10601

[19“On the local Birkhoff conjecture for convex billiards”, with Vadim Kaloshin.

          Annals of Mathematics, 188 (1): 315-380, 2018. ArXiv: 1612.09194

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

        Nonlinearity, 32 (6): 2147-2156, 2019. ArXiv: 1707.03901

[21] “On the integrability of Birkhoff Billiards”, with Vadim Kaloshin, Preprint 2018.

         Philosophical Transactions of the Royal Society A, Volume 376, Issue 2131(Finite dimensional integrable systems: new trends and methods), 2018.

[22] “On John Mather’s contributions in Hamiltonian Dynamics”, Preprint 2018.

         To appear on Methods and Applications of Analysis (Special Issue in memory of John N. Mather).

Upcoming conferences, schools and meetings:

  1. -Conference: C^0 aspects of symplectic geometry and Hamiltonian dynamics, Haifa (Israel), 12-16 May 2019. Invited Speaker

  2. -INdAM Meeting: Interactions of Symplectic topology and dynamics, Cortona (Italy), 16-22 Giugno 2019. Organizer.

  3. -Conference: New Trends in Hamilton-Jacobi: PDE, Control, Dynamical Systems and Geometry, Fudan University, Shaghai (China), 1-5 July 2019. Invited Speaker.

  4. -Oberwolfach Workshop “Dynamische Systeme”, Oberwolfach (Germany), 7-13 July 2019. Invited participant.

  5. -XXI Congresso UMI, Pavia (Italy), 2-7 September 2019. Organizer of the Session S03: “Dynamical systems and differential equations”.

  6. -Conference: Dynamics, Equations and Applications (DEA), Krakov (Poland), 16-20 September 2019. Invited Speaker.

  7. -V Escola Brazileira de Sistemas Dinamicos, Belo Horizonte (Brazil), 7-11 October 2019. Invited Lecturer.

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).

[gSlides of a talk “On the Birkhoff Conjecture for Convex Billiards”, June 2018 (Workshop at Cardiff University).

[iSlides of a talk “Mathematicians play... billiards”, October 2018 (in occasion of the award of the Guido Fubini prize 2018).

[lSlides of the Department Colloquium at Université Nice Sophia Antipolis, “Dynamical and Spectral Properties of Mathematical Billiards”, February 2019.