**Algebra and Combinatorics:** In algebra, I am mostly interested in the study of the phenomenon of non-uniqueness of factorizations into irreducibles in integral domains and atomic monoids using techniques of number theory, combinatorics, and convex geometry. My research in combinatorics focuses on posets and matroids. I am also interested in polytopes, cluster algebras, finite groups, and graphs.

*On the system of sets of lengths and the elasticity of submonoids of a finite-rank free commutative monoid*

Journal of Algebra and Its Applications (to appear)

Available on Arxiv: https://arxiv.org/pdf/1806.11273.pdf*The elasticity of Puiseux monoids*

(with C. O'Neill)

Journal of Commutative Algebra (to appear)

DOI: https://projecteuclid.org/euclid.jca/1523433696*How do elements really factor in Z[sqrt(-5)]?*

(with S. Chapman and M. Gotti),

In: Advances in Commutative Algebra, Springer Trends in Mathematics

(Eds. A. Badawi and J. Coykendall)*Systems of sets of lengths of Puiseux monoids*

Journal of Pure and Applied Algebra, Vol. 223 (2019) 1856-1868.*Increasing positive monoids of ordered fields are FF-monoids*

Journal of Algebra, Vol. 518 (2019) 40-56.*Puiseux monoids and transfer homomorphisms*

Journal of Algebra, Vol. 516 (2018) 95-114.*Minimal presentations of shifted numerical semigroups*

(with R. Conaway, J. Horton, C. O'Neill, R. Pelayo, M. Williams, and B. Wissman)

International Journal of Algebra and Computations, Vol. 28 (2018) 53-68.*Atomicity and boundedness of monotone Puiseux monoids*

(with M. Gotti)

Semigroup Forum, Vol. 96 (2018) 536-552.*Dyck paths and positroids from unit interval orders*

(with A. Chavez)

Journal of Combinatorial Theory Series A, Vol. 154 (2018) 507-532.*On the atomic structure of Puiseux monoids*

Journal of Algebra and its Applications, Vol. 16 (2017) 1750126.*On delta sets and their realizable subsets in Krull monoids with cyclic class groups*

(with S. Chapman and R. Pelayo)

Colloquium Mathematicum, Vol. 137 (2014), 137-146.*On positroids induced by rational Dyck paths*

SÃ©minaire Lotharingien de Combinatoire, Vol. 80B (2018) 12pp.*Dyck paths and positroids from unit interval orders*

(with A. Chavez)

SÃ©minaire Lotharingien de Combinatoire, Vol. 78B (2017) 12pp.*Atomic and antimatter semigroup algebras with rational exponents**Tilings and matroids on the lattice points of a regular simplex*

(with H. Polo)*Positroids induced by rational Dyck paths**On the molecules of numerical semigroups, Puiseux monoids, and Puiseux algebras*

(with M. Gotti)