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Dirac constraints in field theory and exterior differential systems
(American Institute of Mathematical Sciences, 2010-03)
The usual treatment of a (first order) classical field theory such as electromagnetism has a little drawback: It has a primary constraint submanifold that arise from the fact that the dynamics is governed by the ...
Isomonodromic deformations through differential Galois theory
(Medellín - Ciencias - Doctorado en Ciencias - MatemáticasEscuela de matemáticasUniversidad Nacional de Colombia - Sede Medellín, 2019-10-13)
The text begins with a brief description of differential Galois theory from a geometrical perspective. Then, parameterized Galois theory is developed by means of prolongation of partial connections to the jet bundles. The ...
On moment maps and Jacobi manifolds
(Universidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasDepartamento de MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá, 2021)
The main goal of this work is to introduce the idea of a Hamiltonian action in the context of Jacobi structures on line bundles.
This work aims to make these construction without relying on the "Poissonization trick". ...
Non-commutative differential calculus of some algebras of polynomial type having PBW bases
(Bogotá - Ciencias - Maestría en Ciencias - MatemáticasDepartamento de MatemáticasUniversidad Nacional de Colombia - Sede Bogotá, 2020-06-12)
In this work, we study the notion of differential calculus associated to an associative algebra, from its origin in manifolds geometry, to some generalizations in non commutative differential geometry. In particular, we ...
Methodological approaches to support process improvement in emergency departments: a systematic review
(International Journal of Environmental Research and Public Health, 2020)