Publications

Below you can find links to my research and expository articles.

Research articles

Chern classes of tropical manifolds (arXiv)
(with Lucía López de Medrano and Kris Shaw)

Moments, sums of squares, and tropicalization (arXiv)
(with Grigoriy Blekherman, Rainer Sinn, Cynthia Vinzant, and Josephine Yu) 

Paving tropical ideals (journal) (arXiv)
(with Nicholas Anderson)
Journal of Algebraic Combinatorics, Vol. 56, 2022.

Varieties of tropical ideals are balanced (journal) (arXiv)
(with Diane Maclagan)
Advances in Mathematics, Vol. 410, Part A, 2022.

Moduli spaces of codimension-one subspaces in a linear variety and their tropicalization (journal) (arXiv)
(with Philipp Jell, Hannah Markwig, and Benjamin Schröter)
Electronic Journal of Combinatorics, Vol. 29 (2), 2022.

Positively hyperbolic varieties, tropicalization, and positroids (journal) (arXiv)
(with Cynthia Vinzant and Josephine Yu)
Advances in Mathematics, Vol. 383, 2021.

Tropical ideals do not realise all Bergman fans (journal) (arXiv)
(with Jan Draisma)
Research in the Mathematical Sciences, Vol. 8, Art. 44, 2021.

Chern-Schwartz-MacPherson cycles of matroids (journal) (arXiv)
(with Lucía López de Medrano and Kris Shaw)
Proceedings of the London Mathematical Society, Vol. 120 (1), 2020.

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

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

Tropical schemes, tropical cycles, and valuated matroids (journal) (arXiv)
(with Diane Maclagan)
Journal of the European Mathematical Society, Vol. 22 (3), 2020.

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

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

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

Tropical combinatorics (journal)
(with Ngoc Tran and Josephine Yu)
Notices of the American Mathematical Society, Vol. 70 (1), January 2023.

Introducción a la teoría de politopos (journal) (pdf)
(with Simón Soto)
- Basado en el minicurso del evento Días de Combinatoria 2017.
Lecturas Matemáticas, Vol. 40 (2), 2019.