Alejandro Cabrera
Professor Associado
Departamento de Matematica Aplicada (Math) – IM – UFRJ
Rio de Janeiro, Brasil
Sala:
C – 125A,
Tel:
(+55
21) 2562-7036,
Email:
Aulas:
–
Geometria
Não Euclidiana (nocturno)
(2020-2,
mar’21-jun’21)
Pesquisa/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 in gymnastics some
geometric formulas
I derived: (el
pais)
Papers:
----------------(preprints:)
Generating functions for local symplectic groupoids and non-perturbative semiclassical quantization, (arxiv)
Quotients of multiplicative forms and Poisson reduction, with C. Ortiz, (arxiv)
----------------(accepted:)
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:)
Discrete dynamics and differentiable stacks, with M. del Hoyo and E. Pujals, Revista Matematica Iberoamericana Volume 36, Issue 7, 2020, pp. 2121-2146. (arxiv)
Local formulas for multiplicative forms, with I. Marcut and M. A. Salazar, Transformation Groups (2020), https://doi.org/10.1007/s00031-020-09607-y, (arxiv)
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)
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)
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
Dirac Geometry of the Holonomy Fibration, with M. Gualtieri and E. Meinrenken, Communications in Mathematical Physics (2017), 355(3), 865-904. (arxiv)
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)
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)
Vector bundles over Lie groupoids and algebroids, with H. Bursztyn and M. del Hoyo, Advances in Mathematics, Volume 290 (2016), Pages 163-207. (arxiv)
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)
Formal symplectic realizations, with B. Dherin, Int Math Res Notices (2016) 2016 (7): 1925-1950. doi:10.1093/imrn/rnv187. (arxiv)
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)
AKSZ construction from reduction data, with F. Bonechi and M. Zabzine, JHEP Volume 2012, Number 7 (2012), 68. (arxiv)
Symmetries and reduction of multiplicative 2-forms, with H. Bursztyn, Journal of Geometric Mechanics, Volume 4, Issue 2, June 2012, Pages: 111 - 127. (arxiv)
Multiplicative forms at the infinitesimal level, with H. Bursztyn, Mathematische Annalen Volume 353, Number 3 (2012), 663-705. (arxiv)
Linear and multiplicative 2-Forms, with H. Bursztyn and C. Ortiz, L. Lett. Math. Phys. 90, (dec 2009) 59-83 (arxiv)
Poisson-Lie T-Duality and non trivial monodromies, with H. Montani, M. Zuccalli, J. Geom. Phys. 59 (2009) 576-599(arxiv).
Base-controlled mechanical systems and geometric phases, J. Geom.Phys. 58 (2008) 334-367 (arxiv).
A Generalized Montgomery Phase Formula for Rotating Self Deforming Bodies, J.Geom.Phys. 57 (2007), 1405-1420 (arxiv).
Hamiltonian Loop group actions and T-duality for group manifolds, with H. Montani J. Geom. Phys. 56 (2006), 1116-1143 (arxiv).
------------ (other preprints:)
Some geometric features of Berry’s phase, preprint (arxiv - 2007).