Differential algebra study differential equations from an algebraic point of view, it was introduced by Joseph Ritt saying that a differential algebraic structure(ring, field, algebra) is the structure joint of a finitely ...

Se estudia a fondo la construcción de las descomposiciones de Heegaard, haciendo énfasis en el por qué es una herramienta central en el estudio de las 3-variedades. Para esto, analizamos las 3-variedades desde las categorías ...

En el presente trabajo estudiamos el Principio de Concentración-Compacidad, desarrollado por el matemático francés Pierre-Louis Lions, y realizamos algunas aplicaciones en las áreas de las Ecuaciones Diferenciales Parciales ...

En este trabajo, nos centramos en estudiar la conjetura de Artin sobre raíces primitivas, hablamos sobre los argumentos heurísticos de Artin para plantear su idea, y estudiamos los teoremas más importantes referente a la ...

The notion of a Whitney dual for a graded partially ordered set (poset) $P$ with a minimum element $\hat{0}$ has been introduced recently by Gonz\'alez D'Le\'on and Hallam with some interesting connections to other areas ...

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, ...

In this thesis we study the heat equation on graphs from the perspective of information theory. To this end, we introduce the discrete heat equation using the probabilistic approach of random walks on graphs. Then we present ...

The aim of this work is to study some aspects of the obstacle problem: existence and uniqueness of a solution using variational inequalities; regularity of the solution using the penalization method; a regularity result ...

The method of finitely additive measures along finite support iterations was introduced by Saharon Shelah in 2000 (see [She00]) to show that, consistently, cov(N ) may have countable cofinality. In 2019, Jakob Kellner, ...

This dissertation is about Atiyah-Segal's theorem of completion. The first part studies the basic concepts of vector bundles and representation theory. Then we study K-theory and equivariant K-theory. Lastly, we construct ...