Research interests: Poisson, Dirac, and Jacobi Geometry, its symmetries and reductions. Lie groupoids and its intereaction with mathematical physics
Reduction of cosymplectic groupoids (Acepted in Letters in Mathematical Physics, D. Lopez)
A survey on information geometry: statistical manifolds and statistical models (Acepted in ACCEFYN Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales, O Garatejo)
On the geometry of compatible Poisson and Riemannian structures (Journal of Geometry and Physics, A. Vargas)
Existence and uniqueness of radial solutions of semi-linear equations on manifolds (Journal of Mathematical Analysis and Applications, O. Riaño)
A new canonical affine BRACKET formulation of Hamiltonian Classical Field theories of first order (RACSAM, J.C Marrero, Francois Gay-Balmaz)
Poly-symplectic geometry and the AKSZ Formalism (Reviews in Mathematical Physics, I.Contreras)
On polar actions invariant solutions of semi-linear equations on manifolds. Journal of Mathematical Analysis and Applications, (Journal of Mathematical Analysis and Applications, E. Becerra, J.C. Galvis)
Poly-Poisson sigma models and their relational poly-symplectic groupoids. Journal of Mathematical Physics, (Journal of Mathematical Physics, I. Contreras)
On Higher Dirac Structures, International Mathematics Research Notices (IMNR International Mathematics Research Notices , H. Bursztyn, R. Rubio)
Poly-symplectic Groupoids and Poly-Poisson Structures, (Letters in Mathematical Physics)
Preprints
Some talks:
Workshop: symmetries in geometry and physics, Peru 2025
First workshop in PDE: Theory and Applications, Puerto Rico 2025
Gone Fishing 2025, Washington University at St Louis, March 2025
Workshop on Poisson geometry, USP Sao Paulo BR, October 2023
ONEW on higher Dirac structures, online 2021
Colima workshop on geometry, Colima MX, October 2018
Gone fishing, Notre Dame USA, June 2017
Congreso Latinoamericano de Matemáticas, Barranquilla Col July 2016
9th International young research workshop on geometry and mechanics, Zaragoza SP, 2015
Olga Garatejo, Estructuras duales en modelos estadisticos y productos warped
Diego Rodriguez, Hamiltonian systems for Vlasov-Maxwell system and symmetries in dimension 3 (Tesis meritoria)
Beyond Research courses: Computational methods of mechanical systems 2021, Symplectic integrators 2025
Interacciones de Geometría Diferencial y Física Matemática
(Interactions between differential geometry and mathematical physics)joint with prof. Carolina Neira (Dept. Mathematics), prof. Leonardo Castañeda (OAN), prof. Juan Pablo Beltran (Dept. Physics) at Universidad Nacional de Colombia, Bogotá and Ivan Contreras (Amherts College MA)
On Higher Poisson and Higher Dirac Structures, at IMPA under supervision of H. Bursztyn