Page for Alejandro Cabrera

Professor Associado

Departamento de Matematica Aplicada (Math) – UFRJ

Rio de Janeiro, Brasil

Sala: C – 125A, Tel: (+55 21) 2562-7036,

Email:

Teaching/Aulas:
Métodos em Teoria de Campos Quântica (ago-nov 2020)

Research: My research focuses on developments of differential geometry, both theoretical and with applications, in particular, to mathematical physics. My topics of research include (super) symplectic and Poisson geometry, Lie theory of algebroids and groupoids, as well as their many applications to quantization, (quantum) field theories and geometric mechanics.

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

Papers:

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

  1. Quotients of multiplicative forms and Poisson reduction, with C. Ortiz, (arxiv)

----------------(accepted:)

  1. Discrete dynamics and differentiable stacks, with M. del Hoyo and E. Pujals, accepted in Revista Matematica Iberoamericana. (arxiv)

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

------------------(published:)

  1. Local formulas for multiplicative forms, with I. Marcut and M. A. Salazar, Transformation Groups https://doi.org/10.1007/s00031-020-09607-y, (arxiv)

  2. On local integration of Lie brackets, with I. Marcut and M. A. Salazar, J. Reine Angew. Math. (Crelle’s journal), Volume 2020, Issue 760, Pages 267–293. (arxiv)

  3. Obstructions to the integrability of VB-algebroids, with O. Brahic and C. Ortiz, Journal of Symplectic Geometry. Vol. 16, No. 2 (2018), pp. 439-483. (arxiv)

  4. Minimal time splines on the sphere, with P. Balseiro, J. Koiller and T. Stuchi, São Paulo J. Math. Sci. (2017). https://doi.org/10.1007/s40863-017-0078-4

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

  6. 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. (arxiv)

  7. 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)

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

  9. 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)

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

  11. 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)

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

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

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

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

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

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

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

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

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

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