Page
for **Alejandro
Cabrera**

Professor - Departamento de Matematica Aplicada (Math)

UFRJ

Rio de Janeiro, Brasil

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

**Teaching/Aulas:**

– CVGA(IF)**–
**Métodos
em Teoria de Campos Quântica

**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 quantization, (quantum) field theories and geometric
mechanics.**Link:
**an
article about applying some formulas I derived in gymnastics: __(el
pais)__

**Papers:**

Local formulas for multiplicative forms, with I. Marcut and M. A. Salazar, accepted in

**Transformation Groups**, (arxiv)Discrete dynamics and differentiable stacks, with M. del Hoyo and E. Pujals, accepted in

**Revista Matematica Iberoamericana**. (arxiv)Lie theory of vector bundles, Poisson geometry and double structures, with H. Bursztyn and M. del Hoyo, accepted in

**proceedings of ICMP-2015**. (arxiv)

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

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/s40863-017-0078-4Dirac Geometry of the Holonomy Fibration, with M. Gualtieri and E. Meinrenken,

**Communications in****Mathematical****Physics**(2017), 355(3), 865-904. (arxiv)

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

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

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