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

[11] “Action-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] “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.

To appear on Nonlinearity, Preprint 2017. 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).