Page
for **Alejandro
Cabrera**

Professor Adjunto - Departamento de Matematica Aplicada (Math)

UFRJ

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: **Fundamentos
de Geometria 2017-1:
**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)__

**Papers:**

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

__(arxiv)__

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

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

About simple variational splines from the Hamiltonian viewpoint, with P. Balseiro, J. Koiller and T. Stuchi, accepted in Journal of Geometric Mechanics.

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

__(arxiv)__Dirac Geometry of the Holonomy Fibration, with M. Gualtieri and E. Meinrenken, accepted Communications in Mathematical Physics

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

__(arxiv)__

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

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, International Mathematics Research Notices 2015; 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, Math.Ann. 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).