Publications

Below is a list of my publications and preprints.

Research articles

Tropical ideals do not realise all Bergman fans (arXiv)
(with Jan Draisma

Chern-Schwartz-MacPherson cycles of matroids (arXiv)

Tropical ideals (journal(arXiv)
Compositio Mathematica, Vol. 154 (3), 2018.

Compressed sensing of data with a known distribution (journal) (arXiv)
Applied and Computational Harmonic Analysis, Vol. 45 (3), 2018.

Tropical schemes, tropical cycles, and valuated matroids (arXiv
(with Diane Maclagan)
Journal of the European Mathematical Society, to appear.

Positively oriented matroids are realizable (journal) (arXiv)
(with Federico Ardila and Lauren Williams)
Journal of the European Mathematical Society, Vol. 19 (3), 2017.

Positroids and non-crossing partitions (journal) (arXiv)
(with Federico Ardila and Lauren Williams)
Transactions of the American Mathematical Society, Vol. 368 (1), 2016.

Stiefel tropical linear spaces (journal) (arXiv)
(with Alex Fink)
Journal of Combinatorial Theory, Series A, Vol. 135, 2015.

Local tropical linear spaces (journal) (arXiv)
Discrete & Computational Geometry, Vol. 50 (3), 2013.

Computing tropical linear spaces (journal) (arXiv)
Journal of Symbolic Computation, Vol. 51, 2013.
- Make sure to check TropLi: a software tool for computing tropical linear spaces.

Isotropical linear spaces and valuated Delta-matroids (journal) (arXiv)
Journal of Combinatorial Theory, Series A, Vol. 119 (1), 2012.
- Some nice computations I did for this paper.

Valuations for matroid polytope subdivisions (journal) (arXiv)
(with Federico Ardila and Alex Fink)
Canadian Journal of Mathematics, Vol. 62 (6), 2010.

Aspectos combinatorios de las subdivisiones matroidales (pdf)
Master's thesis, July 2007.

A labelling of the faces in the Shi arrangement (journal)
Rose-Hulman Undergraduate Mathematics Journal, Vol. 8 (1), 2007.

Aspectos combinatorios del arreglo de Shi (pdf)
Undergraduate thesis, January 2006.

Expository articles

Introducción a la teoría de politopos (pdf)
(with Simón Soto
- Basado en el minicurso del evento Días de Combinatoria 2017.