Research - 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Below you can find a list of published and unpublished material.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.
Research Papers
Note: If you would like to have information about papers in preparation please contact me at ruiloja (at) illinois.edu.
- The Global Solutions to a Cartan's Realization Problem, together with Ivan Struchiner. Preprint arXiv:1907.13614.
- On deformations of compact foliations, together with Matias del Hoyo. Proceedings of the AMS 147, no. 10, (2019), pp 4555–4561.
- Genus Integration, Abelianization and Extended Monodromy, together with Ivan Contreras. International Mathematics Research Notices 2019, no 7.
- Associativity and Integrability, together with Daan Michiels. Transactions of the AMS 373 (2020), no 7, pp 5057-5110.
- Regular Poisson Manifolds of Compact Types (PMCT 2), together with Marius Crainic and David Martinez Torres. Accepted for publication in Astérisque. Preprint arXiv:1603.00064.
- Riemannian metrics on differentiable stacks, together with Matias del Hoyo. Mathematische Zeitschrift 292 (2019), Issue 1–2, pp 103–132.
- Poisson Manifolds of Compact Types (PMCT 1), together with Marius Crainic and David Martinez Torres. Accepted for publication in Journal für die reine und angewandte Mathematik (Crelle). Preprint arXiv:1510.07108.
- Global Action-Angle Variables for Non-Commutative Integrable Systems, together with Camille Laurent-Gengoux and Pol Vanhaecke. Journal of Symplectic Geometry 16 no. 3 (2018), 645-699.
- Picard groups of Poisson manifolds, together with Henrique Bursztyn. Journal of Differential Geometry 109 (2018), 1-38.
- Riemannian Metrics on Lie Groupoids, together with Matias del Hoyo. Journal für die reine und angewandte Mathematik (Crelle) 735 (2018), 143–173. .
- Integration of Coupling Dirac Structures, together with Olivier Brahic. Pacific Journal of Mathematics. 278 no. 2 (2015), 325-367.
- Integrability and Reduction of Hamiltonian Actions on Dirac Manifolds, together with Olivier Brahic, Indagationes Mathematicae 25 no. 5 (2014), 901–925.
- The Classifying Lie Algebroid of a Geometric Structure I: Classes of Coframes, together with Ivan Struchiner. Transactions of the AMS 366 no 5 (2014), 2419–2462.
- Modular classes of Poisson maps, together with Raquel Caseiro. Annales de l'Institut Fourier, 63 no. 4 (2013), 1285-1329.
- 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.
Lecture Notes
- Normal Forms and Lie Groupoid Theory. In Geometric Methods in Physics. XXXIII Workshop, Białowieża, Poland, June 29 – July 5, 2014 Eds. P. Kielanowski et al. Trends in Mathematics. Birkhäuser Basel 2015.
- 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.
- Lectures on Differential Geometry Lecture notes for courses in differential geometry that I tought at UIUC and at IST. Available also in Portuguese at 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 excursão 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).
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).