I am a fierce advocate of the promotion, accessibility, popularization and desacralization of mathematics. As a researcher, I am interested in applications of model theory (a branch of mathematical logic) to algebra and geometry. Specifically, my work has been focused on developing extensions of classic differential Galois theory to more general algebraic contexts. In addition, I have spent time studying the connections and interactions between mathematics and narrative arts and, more recently, I have got interested in the use of mathematical tools to extract information from large collections of documents in applications to social sciences.

Teaching mathematics is my passion. I believe education is the most effective way of contributing to the construction of a more egalitarian and open society. This document (written during Fall 2011) collects some of my current guiding principles when it comes to think about mathematics and education.

**Iterative differential Galois theory: a model theoretic approach**(pdf)J. Symbolic Logic, Volume 76, Issue 1 (2011), 125-142This paper offers a generalization of the classic differential Galois theory to positive characteristic iterative differential fields (also known as Hasse fields). It is proven, using model theoretic techniques) that there is a well behaved theory of non-lineal differential Galois extensions associated to logarithmic iterative differential equations on algebraic groups over the constants.

**Hechos y palabras: la realidad colombiana vista a través de la prensa escrita**(link)

(Words and facts: an analysis of Colombian reality through the written news media)Documentos CEDE, Volume 46, Universidad de los Andes (2011)In collaboration with Juan Manuel Caicedo (CMU) and Alejandro Gaviria (U. de los Andes), this paper introduces a database of twenty years of Colombian news articles. It is shown how the basic analysis of n-grams can provide insight and perspective on the socio-political and economical reality of the country. It suggests that this kind of analysis could be used to provide approximate measurements of unquantifiable (or only partially quantifiable) phenomena (e.g., corruption, violence, political struggle).

**Auge, muerte e inesperada resurrección de una teoría matemática de la narrativa**(pdf)

(Rise, death and unexpected resurrection of a mathematical theory of narrative)To be published in*Mathematics and Contemporary Culture*, ed. Fernando Zalamea, Universidad Nacional de Colombia (2011)This short essay (English translation on the works) revolves around the notion of structure in narrative. It uses this notion to suggest similarities between the construction of stories and the practice of mathematics. It argues that the development of narrative structure is a kind of mathematical problem in disguise and therefore its solutions have (yet to be discovered and formalized) mathematical value.

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- Uses of internality: An updated description of my research, making emphasis on the equational approach to differential Galois theory (Model Theory Seminar, McMaster University, March 2011.)
- A few things logic can say about differential equations: A presentation of my research for a broad audience of mathematicians (Pure Math Colloquium, University of Waterloo, March 2011.)
- Some applications of model theory to differential Galois theory: Slides for an introductory talk on the subject for model theory students (Model Theory at Kirishima, Japan, March 2010.)
- Model theory and differential Galois theory, an introduction: Rough notes for a (quite elementary) talk at the Logic Seminar (University of Waterloo, January 13th, 2010.)
- Iterative differential equations and Galois groups: Slides for my job talk (Université Lyon 1, May 6th, 2008.)
- Strongly normal extensions of iterative differential fields: Slides for a short talk I gave at the
*Atelier MODNET de Théorie des modèles des corps*(Luminy, France, November 15th, 2007.)

Blog: http://finiterank.com/notas

Twitter: @bluelephant

bluelephant@gmail.com

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**Nadie sabe quién es quién**El Espectador, 2010Columna sobre la actitud pasiva ante la violencia cotidiana en Colombia.

**Esa señorita texana**El Malpensante, 2008Un artículo sobre la muerte de Farrah Fawcett.

**La tetralogía del monstruo**Pie de Página, 2008Un comentario sobre la serie de libros de Enki Bilal.

**Roberto Bolaño: a naïve introduction to the geometry of his fictions**Quarterly Conversation, 2007A playful article about the interconnections between the different novels of Roberto Bolaño.

**Sudoka**HermanoCerdo, 2011Un relato sobre contar y ceder. Incluído en

*Inframundo*.*Basada en hechos reales*Ochoymedio.info, 2009Un comentario sobre la película de

*Alvin y las ardillas*.

Me gusta contar historias y jugar con textos. He publicado dos libros de relatos.

También he escrito artículos sobre literatura, cine, cultura, política, ciencia, tecnología y farándula para El Espectador, Ochoymedio.info, Revista Matera, Mapache, Pie de Página, El Malpensante, The Quarterly Conversation y Arcadia.

Por otro lado, soy coeditor y diseñador de HermanoCerdo, una revista digital sobre literatura y artes marciales en español.

En verano de 2011 terminé *Para poder llegar*, una novela corta de ciencia ficción sobrenatural para niños que trata sobre viajes al espacio, super-poderes, ausencias y el miedo a la pérdida y la muerte. Espero encontrar durante los próximos meses un editor que la trate con el cariño que se merece.

En Rango Finito publico notas personales con regularidad.