Publications

Below you can find a list of published and unpublished material. You may also want to check MathSciNet or the ArXiv for my publications.

Lecture Notes

• Lectures on Integrability of Lie Brackets - together with Marius Crainic. Geometry & Topology Monographs 17 (2011) 1-107. Lecture notes for the 2005 Summer School in Poisson Geometry held at ICTP-Trieste.
• Lições de Geometria Diferencial (in Portuguese) - Lecture notes for the course in differential geometry that I tought to the students in the Undergraduate Program in Mathematics at IST. Available in the Portuguese arXive.
• Notas de Cálculo Diferencal e Integral (in Portuguese) - together with M. Abreu and M. Ricou. Lecture notes for the first course in Calculus at IST that I tought to engineering students.
• Introdução ao Integral de Lebesgue (in Portuguese) - These are lecture notes for a Honors Course in Advanced Calculus for undergraduate science and engineering students at IST. Available in the Portuguese arXive.
• Uma breve excusão à Rua das Matemáticas (in Portuguese) - These are lecture notes for a Summer Course for talented high school students, that participated in Programa Diagonal (year 2005).

Research Papers

Note: If you would like to have information about papers in preparation please .

• Integration of Coupling Dirac Structures, together with Olivier Brahic, (in preparation).
• The Classifying Lie Algebroid of a Geometric Structure I: Classes of Coframes, together with Ivan Struchiner. To appear in Transactions of the AMS. Preprint arXiv:1103.5850.
• Modular classes of Poisson maps, together with Raquel Caseiro. To appear in Annales de l'Institut Fourier. Preprint arXiv:1103.4305.
• A h-principle for symplectic foliations, together with Pedro Frejlich. International Mathematics Research Notices 2012, no. 7, (2012), 1505-1518.
• A geometric approach to Conn's linearization theorem, together with Marius Crainic. Annals of Math 173 (2011), 1119-1137.
• Stability of symplectic leaves, together with Marius Crainic. Inventiones Mathematicae 180, no. 3, (2010), 481-533.
• Integrability of Poisson-Lie group actions, together with David Iglesias Ponte. Lett. Math. Phys. 90, (2009) 137-159.
• The momentum map in Poisson geometry, together with Juan Pablo Ortega and Tudor Ratiu. Amer. J. of Math. 131, no. 5, (2009) 1261-1310.
• Lie Algebroids and Classification Problems in Geometry, together with Ivan Struchiner. São Paulo J. of Math. Sci. 2 no. 2, (2008) 263-284.
• Poisson fibrations and fibered symplectic groupoids together with Olivier Brahic, in Poisson Geometry in Mathematics and Physics, 41--60, Contemporary Mathematics, 450, American Mathematical Society, Providence, RI; 2008.
• The symplectization functor, in Proceedings of XV International Workshop on Geometry and Physics (Puerto de la Cruz, Tenerife, 2006) Publ. R. Soc. Mat. Esp. 11, (2008) 67-82.
• Integrable hierarchies and the modular class, together with Pantelis Damianou, Annales de l'Institut Fourier, 58 no. 1, (2008) 107-137.
• A note on proper Poisson actions Proceedings of the 10th International Conference in Modern Group Ananlysis, Oct. 2004, Eds. N.H.Ibragimov, C.Sophocleous, P.A.Damianou, Larnaca, Cyprus, (2005) 77-84.
• Rigidity and flexibility in Poisson geometry, together with Marius Crainic Trav. Math., 16 (2005), 53-68.
• Exotic Characteristic Classes of Lie Algebroids, together with Marius Crainic. In Quantum Field Theory and Noncommutative Geometry, Lecture Notes in Physics, Vol. 662. Eds. Carow-Watamura, Ursula; Maeda, Yoshiaki; Watamura, Satoshi, Springer-Verlag, Berlin, 2005.
• Linearization of Poisson brackets, together with Philippe Monnier Lett. Math. Phys. 69, (2004) 89-114.
• Integrability of Poisson brackets, together with Marius Crainic, J. of Differential Geometry 66, (2004) 71-137.
• Integrability of Lie brackets, together with Marius Crainic. Annals of Mathematics 157, (2003) 575-620.
• Invariants of Lie algebroids, Differential Geometry and its Applications 19, (2003) 223-243.
• From the Toda lattice to the Volterra lattice and back, together with Pantelis Damianou, Reports on Math. Phys. 50, (2002) 361-378.
• Lie Algebroids, Holonomy and Characteristic Classes, Advances in Mathematics 170, (2002) 119-179. Odd enough, this one had some impact!
• Hyperelliptic Prym Varieties and Integrable Systems, together with Pol Vanhaecke, Commun. Math. Phys. 221, (2001) 169-196.
• Connections in Poisson Geometry I: Holonomy and Invariants, J. of Differential Geometry 54, (2000) 303-366.
• Deformation Quantization and Poisson Geometry, Resenhas IME-USP 4, (2000) 327-361.
• Contravariant Connections on Poisson Manifolds, in Proceedings of the Summer School on Differential Geometry, Eds. A. M. Breda, F. Carvalho, J. Costa, B. Wegner, Univ. Coimbra, 1999.
• Dynamics on the Attractor of the Lotka-Volterra Equation, together with Pedro Duarte and Waldyr Oliva, J. Diff. Equations 149, (1998) 143-189.
• Hamiltonian Dynamics of the Lotka-Volterra Equations - together with Waldyr Oliva, Proceedings of the Equadiff 95 Conference, Lisbon, Eds. L. T. Magalhães, C. Rocha, L. Sanchez, World Scientific, Singapure, (1998).
• Integrability of the Periodic KM System - together with João P. Santos, Reports on Math. Phys. 40, (1997) 475-484.
• Completely Integrable bi-Hamiltonian Systems, J. Dynam. Diff. Eq. 6, (1994) 53-69.
• A Note on Poisson Symmetric Spaces, in Proceedings of the Cornelius Lanczos International Centenary Conference. Eds. J. Davis Brown, Moody T. Chu, Donald C. Ellison, Robert J. Plemmons, SIAM Philadelphia, USA (1994) 638-642.
• On the master symmetries and bi-Hamiltonian structure of the Toda lattice, J. Phys. A: Math. Gen. 26, (1993) 3797-3803.

Books (Author)

• Introdução à Álgebra (2.5 Mb)- together with M. Ricou (in Portuguese). This is a textbook in Algebra, written for the students in the Undergraduate Program in Mathematics at IST. It has been published by IST Press. (Note: the electronic version differs somewhat from the published version; in the latter several typos and mistakes have been corrected).

Books (Editor)

• Geometry and Physics: XVI International Fall Workshop, R.L. Fernandes and R. Picken (eds.), AIP Conference Proceedings Volume 1023, 228 p., 2008.

PhD Thesis

• Completely Integrable Bi-Hamiltonian Systems, Ph.D. Thesis, University of Minnesota, 1994. Supervised by Peter J. Olver.

Lectures on line

• Stability of symplectic leaves - Lecture delivered at Coloque Paulette Libermann at IHP (December 2009).
• Lie's Third Theorem - Lecture delivered at Universidad Autónoma de Barcelona (April 2008).
• Reduction and Integrability - Lecture delivered at ESI (August 2007).
• Symmetry beyond groups - Introductory lecture about groupoids delivered at the Mathematics, Systems and Robotics Seminar, the joint ISR-CAMGSD seminar (May 2004).
• Invariants of Lie algebroids - Lecture delivered for my Habilitation ("Agregação") in Mathematics (June 2002).