Research

• My research evolves around combinatorial objects, algebraic structures on them and their interaction with representation theory and geometry. More specifically (quasi)symmetric functions, Hopf algebras and discrete objects involved in these worlds are at the center of my interests.

Papers:

Here is my cv and here are my papers -some in preparation-.

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

• 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

• Kostant's partition function and multiplex juggling sequences (with C. Hanusa, P. Harris, A. Morales, A. Simpson). 2020
• Quotients of uniform positroids (with A. Chavez, D. Tamayo). 2019
• 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).
• Generalized lattice point visibility in $\mathbb{N}^k$ (with P. Harris, S. Estupiñan).

Current and past seminars:

Los Andes y otras:

Semestral : Seminario Sabanero de Combinatoria

2017-II : Polinomios de Schubert

York University:

Applied Algebra Seminar

Algebraic Combinatorics Seminar at Fields

Students:

Maestría:

• Jerónimo Valencia (current)
• Santiago Estupiñan (current).
• 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:

• Felipe Rueda. Thesis: Polinomios de Tutte y Schur positividad. (Diciembre 2019)
• Jerónimo Valencia. Thesis: Cocientes de matroides, antípodas y f-vectores.
• Tomás Bermudez (codirected w Dave Karpuk). Thesis: Subspace packing in grassmannian space.
• Carlos Sánchez. Thesis: Volúmenes de politopos de flujo de subgrafos caracol.
• Santiago Estupiñan. Thesis: Problemas de visibilidad en N^n. (Diciembre 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.