## Research Interest:

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

## Scientific Publications:

*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 Proc. in Mathematics (to appear)

(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.
## Published Extended Abstracts:

*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.
## Manuscripts Submitted to Peer-Reviewed Journals:

*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 system of sets of lengths and the elasticity of submonoids of N^d*
*On the molecules of Puiseux monoids*

(with M. Gotti)