My research focuses on topics in geometric group theory and combinatorics, particularly those topics where geometry, topology, algebra, and combinatorics interact. More specifically, I study Artin groups, Coxeter groups, parking functions and their generalizations.

Research Statement

Publications

Under Review

7. Enumerating k-Naples Parking Functions with Catalan Objects

with Pamela E. Harris, João Pedro Carvalho, Gordon Rojas Kirby, Nico Tripeny, Andrés Vindas Meléndez

6. On (t,r) broadcast domination of certain grid graphs

with Natasha Crepeau, Pamela E. Harris, Sean Hays, Marissa Loving, Joseph Rennie, and Alexandro Vasquez.

5. Visualizing the support of Kostant's weight multiplicity formula for the rank two Lie algebras

with Pamela E. Harris, Marissa Loving, Juan Ramirez, Joseph Rennie, Eduardo Torres Davila, and Fabrice O. Ulysse.

Published

4. On Kostant's weight q-multiplicity formula for sl_4(C)

with Rebecca E. Garcia, Pamela E. Harris, Marissa Loving, Lucy Martinez, David Melendez, Joseph Rennie, and Daniel Tinoco. Applicable Algebra in Engineering, Communication and Computing (2020). ​

with Jerrell Cockerham, Melissa Gutierrez Gonzalez, Pamela E. Harris, Marissa Loving, Amaury V. Minino, Joseph Rennie, Gordon Rojas Kirby, Bulletin of the Belgian Mathematical Society, Simon Stevin 27(5), 641-662.

2. A generalization of parking functions with backward movement

with Alex Christensen, Pamela E. Harris, Zakiya Jones, Marissa Loving, Andres Ramos Rodriguez, Joseph Rennie. The Electronic Journal of Combinatorics 27(1) (2020), #P1.33.

1. Nowhere-zero k-flows on graphs

with Matthias Beck, Alyssa Cuyjet, Molly Stubblefield, and Michael Young. Annals of Combinatorics 18 (2014), 579-583.

Ph.D. Dissertation

Pure Salvetti complexes and Euclidean Artin groups

University of California, Santa Barbara, 2020 (advisor: Jon McCammond)