Research

• My research evolves around combinatorial objects, algebraic structures on them and their interaction with representation theory and geometry. More specifically matroids, polytopes, Ehrhart theory, (quasi)symmetric functions, Hopf algebras, are usually the kind of objects showing up in my research.

Papers

You can check them in my Google Scholar site or in arxiv

• Quotients of uniform positroids (with A. Chavez, D. Tamayo). Electronic J. Comb. 29-1 (2022).

• Generalized lattice point visibility in $\mathbb{N}^k$ (with P. Harris, S. Estupiñan). Involve. 14-1 (2921).

• Kostant's partition function and multiplex juggling sequences (with C. Hanusa, P. Harris, A. Morales, A. Simpson). Annals of Comb. 24 2020

• A combinatorial model for computing volumes of flow polytopes (with R. Gonzalez, C. Hanusa, P. Harris, A. Khare, A. Morales, M. Yip). Trans. Amer. Math. Soc. 372 (2019).

• Hypergraphic polytopes: combinatorial properties and antipodes (with N. Bergeron, J. Machacek) J. of Combinatorics. 10-3 (2019).

• The antipode of linearized Hopf monoids (with N. Bergeron). Algebraic Combinatorics. 2-5 (2019).

• Antipodes and involutions (with Bruce Sagan). J. of Comb. Theory Series A 148 (2017).

• Combinatorial Hopf algebras of simplicial complexes (with J. Hallam, J. Machacek). SIAM J. of Discrete Math. 30-3 (2016).

• Fomin-Greene monoids and Pieri operations (with N. Bergeron) Fields Institute Comm. 71 (2014).

• Schubert polynomials and k-Schur functions (with N. Bergeron) Electronic J. of Comb. 21-4 (2014).

• Combinatorial Hopf algebra of superclass functions of type D J. of Alg. Comb. 38-4 (2013).

• Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras (joint with 27+ authors) Adv. in Math. 229 (2012).

• Matroid polytopes and their volumes (with Federico Ardila and Jeffrey Doker) Discrete and Com. Geom. 43-4 (2010).

Preprints

• Lattice path matroids and quotients (with K. Knauer). 2022.

• Stable set polytopes and theri 1-skeleta (with F. Alinieifard, N. Bergeron, S. Li, F. Saliola). 2019

In preparation

• A quantum MN rule for the cohomology of the flag variety (with N. Bergeron, L. Colmenarejo, F. Saliola, F. Sottile).

• Ehrhart theory of lattice path matroids (with K. Knauer, J. Valencia)

• Shellability of flags of positroids. (with A. Dochtermann, Y. Li, K. Knauer)

Students:

Maestría:

• Luis Calderón. En desarrollo.

• Jerónimo Valencia. Thesis: Teoría de Ehrhart y caminos reticulares. (Noviembre 2021)

• Santiago Estupiñan. Thesis: Permutahedra and power-sum symmetric functions (March 2021)

• Jonathan Niño (codirected w Mauricio Velasco). Thesis: Calculation of invariant rings under the action of finite groups. (May 2019)

• Daniel Tamayo. Thesis: Combinatorics of quotients of positroids. (May 2019)

Pregrado:

• Mariana Ramirez. En progreso.

• Tomás Bermudez (codirected w Dave Karpuk). Thesis: Subspace packing in grassmannian space. (2020)

• Felipe Rueda. Thesis: Polinomios de Tutte y Schur positividad. (2019)

• Jerónimo Valencia. Thesis: Cocientes de matroides, antípodas y f-vectores. (2019)

• Carlos Sánchez. Thesis: Volúmenes de politopos de flujo de subgrafos caracol. (2019)

• Santiago Estupiñan. Thesis: Problemas de visibilidad en N^n. (2018).

• Eliana Tolosa (2018-I UN). Thesis: Grupo de caracteres de un álgebra de Hopf de matroides.

• Julian Pulido (2017-II UN). Thesis: Politopos Unipotentes.