# 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

• Hypergraphic polytopes: combinatorial properties and antipodes (with N. Bergeron, J. Machacek) To appear in Journal of Combinatorics.
• A combinatorial model for computing volumes of flow polytopes (with R. Gonzalez, C. Hanusa, P. Harris, A. Khare, A. Morales, M. Yip). To appear in Transactions of the AMS.
• Cancelation free formula for the antipode of linearized Hopf monoids (with N. Bergeron). To appear in Algebraic Combinatorics.
• 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``
• Generalized lattice point visibility in \$\mathbb{N}^k\$ (with P. Harris, S. Estupiñan) Submitted.
• Polytopes of independent sets of relations (with F. Alinieifard, N. Bergeron, S. Li, F. Saliola). arxiv:1804.00360.

In preparation

• A quantum MN rule for the cohomology of the flag variety (with N. Bergeron, L. Colmenarejo, F. Saliola, F. Sottile). In preparation.
• Concordance of positroids (with A. Chavez, D. Tamayo). In preparation.

Current and past seminars:

Los Andes:

2017-II : Polinomios de Schubert

York University:

Applied Algebra Seminar

Algebraic Combinatorics Seminar at Fields

Students:

Maestría:

Jonathan Niño (codirección con Mauricio Velasco)

Santiago Estupiñan (actualmente)

Daniel Tamayo (actualmente)