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Representación integral de soluciones de problemas no locales
(Universidad Nacional de Colombia, 2022-09)
En este trabajo estudiamos un problema semilineal que involucra un operador de tipo no local a través de la transformada de Fourier. Investigamos existencia y unicidad local de soluciones vía el principio de Duhamel y las ...
Geometric, dynamical, and topological considerations of horseshoe-type functions
(Universidad Nacional de Colombia, 2023)
In this thesis we will address the study of a version of the Smale’s horseshoe function and the baker’s function, along with their dynamical properties, from a topological perspective. To this end, fundamental notions ...
Schottky Problem
(Universidad Nacional de Colombia, 2023-08)
An accessible introduction to the Schottky problem is given, with explicit computations included. The Schottky problem asks what abelian varieties are jacobian varieties, where a jacobian variety is a certain complex torus ...