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Traces in symmetric monoidal categories
(Medellín - Ciencias - Maestría en Ciencias - MatemáticasEscuela de matemáticasUniversidad Nacional de Colombia - Sede Medellín, 2019-09-13)
The objective of this work is to generalize basic ideas from linear algebra and topology, such as traces and fixed points, into a categorical context. Each of those generalizations has important objects and ideas behind, ...
Dynamical algebra of quasi-exactly-solvable potentials
(American Physical Soc, 2014)
Estrutura algébrica de hierarquias integráveis e problemas de valor de contorno
(Universidade Estadual Paulista (UNESP), 2014)
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 ...
Maximality of noncommutative rings over orders
(Departamento de MatemáticasUniversidad Nacional de Colombia - Sede Bogotá, 2019-07-31)
La teoría de órdenes ha sido ampliamente estudiada desde la última parte del siglo XX. En el contexto no conmutativo, la maximalidad de órdenes ha sido revisada para objetos clásicos de tipo polinomial como las extensiones ...
Normal Forms for Polynomial Differential Systems in R-3 Having an Invariant Quadric and a Darboux Invariant
(World Scientific Publ Co Pte Ltd, 2015)
The Auslander-Reiten Quiver of Equipped Posets of Finite Growth Representation Type, some Functorial Descriptions and Its Applications
(Bogotá - Ciencias - Doctorado en Ciencias - MatemáticasDepartamento de MatemáticasUniversidad Nacional de Colombia - Sede Bogotá, 2020-05-18)
The theory of representation of partially ordered sets or posets was introduced in the early 1970's as an effort to give an answer to the second Brauer-Thrall conjecture. Recall that one of the main goals of this theory ...