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Extension of polynomials and John's theorem for symmetric tensor products.
(American Mathematical Society, 2007-12)
We show that for every infinite-dimensional normed space E and every k ≥ 3 there are extendible k-homogeneous polynomials which are not integral. As a consequence, we prove a symmetric version of a result of John.
On the section conjecture in anabelian geometry
(Universidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasDepartamento de MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá, 2020-11)
In this work, we study and present in detail some ground ideas of anabelian geometry, from its origin in number field and arithmetic results to the statements proposed by Grothendieck, studying theory of fundamental groups ...
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 ...
Zariski cancellation problem for skew PBW extensions
(Bogotá - Ciencias - Doctorado en Ciencias - MatemáticasDepartamento de MatemáticasUniversidad Nacional de Colombia - Sede Bogotá, 2020-06-19)
A special question for noncommutative algebras is Zariski cancellation problem. In this thesis we establish cancellation for some special classes of algebras such as skew PBW extensions, some Artin--Schelter regular algebras ...
Algebraic properties of weak quantum symmetries
(Universidad Nacional de ColombiaBogotá - Ciencias - Doctorado en Ciencias - MatemáticasFacultad de CienciasBogotá,ColombiaUniversidad Nacional de Colombia - Sede Bogotá, 2023-07-24)
This thesis investigates the properties of weak bialgebras and weak Hopf algebras, their (co)representations, and applications in groupoids, path algebras, and Lie algebroids. The research employs algebraic and categorical ...