Page for Alejandro Cabrera

Professor Adjunto - Departamento de Matematica Aplicada (Math)


Rio de Janeiro, Brasil


Office: C - 125A

Phone/fax: (+55 21 ) 2562-7508 (ramal 216)

Email address: acabrera (em) labma (pt) ufrj (pt) br


Teaching/Aulas: Geometria não Euclidiana 2017-2: Notas


Research: My research focuses on areas lying in the intersection between differential geometry and mathematical physics.

My topics of research include (super) symplectic and Poisson geometry, Lie algebroids and Lie groupoids, as well as their many applications to (quantum) field theories, integrable systems and geometrical mechanics.


Links: an article about applying some formulas I derived in gymnastics: (el pais)



  1. A construction of local Lie groupoids using Lie algebroid sprays, with I. Marcut and M. A. Salazar, submitted. (arxiv)


  1. Minimal time splines on the sphere, with P. Balseiro, J. Koiller and T. Stuchi, accepted in Sao Paulo Math J.

  2. Lie theory of vector bundles, Poisson geometry and double structures, with H. Bursztyn and M. del Hoyo, accepted to proceedings of ICMP-2015. (arxiv)

  3. Obstructions to the integrability of VB-algebroids, with O. Brahic and C. Ortiz, accepted Journal of Symplectic Geometry. (arxiv)


  4. Dirac Geometry of the Holonomy Fibration, with M. Gualtieri and E. Meinrenken, Communications in Mathematical Physics (2017), 355(3), 865-904. (arxiv)

  1. About simple variational splines from the Hamiltonian viewpoint, with P. Balseiro, J. Koiller and T. Stuchi, Journal of Geometric Mechanics, Volume 9, Number 3, September 2017, pp. 257–290. doi:10.3934/jgm.2017011.

  2. van Est isomorphism for homogeneous cochains, with T. Drummond, Pacific Journal of Mathematics 287-2 (2017), 297–336. DOI 10.2140/pjm.2017.287.297. (arxiv)

  3. Vector bundles over Lie groupoids and algebroids, with H. Bursztyn and M. del Hoyo, Advances in Mathematics, Volume 290 (2016), Pages 163-207. (arxiv)

  4. Differentiability of correlations in relativistic quantum mechanics, with E. de Faria, E. Pujals and C. Tresser, J. Math. Phys. 56, 092104 (2015); DOI 10.1063/1.4931176. (arxiv)

  5. Formal symplectic realizations, with B. Dherin, Int Math Res Notices (2016) 2016 (7): 1925-1950. doi:10.1093/imrn/rnv187. (arxiv)

  6. Multisymplectic geometry and Lie groupoids, with H. Bursztyn and D. Iglesias, D.E. Chang et al. (eds.), Geometry, Mechanics, and Dynamics, Fields Institute Communications Volume 73, 2015, pp 57--73 ; Springer New York. (arxiv)

  7. AKSZ construction from reduction data, with F. Bonechi and M. Zabzine, JHEP Volume 2012, Number 7 (2012), 68. (arxiv)

  8. Symmetries and reduction of multiplicative 2-forms, with H. Bursztyn, Journal of Geometric Mechanics, Volume 4, Issue 2, June 2012, Pages: 111 - 127. (arxiv)

  9. Multiplicative forms at the infinitesimal level, with H. Bursztyn, Mathematische Annalen Volume 353, Number 3 (2012), 663-705. (arxiv)

  10. Linear and multiplicative 2-Forms, with H. Bursztyn and C. Ortiz, L. Lett. Math. Phys. 90, (dec 2009) 59-83 (arxiv)

  11. Poisson-Lie T-Duality and non trivial monodromies, with H. Montani, M. Zuccalli, J. Geom. Phys. 59 (2009) 576-599(arxiv).

  12. Base-controlled mechanical systems and geometric phases, J. Geom.Phys. 58 (2008) 334-367 (arxiv).

  13. A Generalized Montgomery Phase Formula for Rotating Self Deforming Bodies, J.Geom.Phys. 57 (2007), 1405-1420 (arxiv).

  14. Hamiltonian Loop group actions and T-duality for group manifolds, with H. Montani J. Geom. Phys. 56 (2006), 1116-1143 (arxiv).

    ------------ (preprints:)

  1. Some geometric features of Berry’s phase, preprint (arxiv - 2007).