In June of 2022, I completed a master's thesis with advisors Federico Ardila and Mariel Supina at San Francisco State University.

My thesis explores the Hopf monoid structure of generalized permutahedra, in particular we looked at a Hopf monoid morphism called the Brion map. The Brion morphism maps a generalized permutahedron to a collection of posets associated to its vertices. We compute this map explicitly for the Hopf monoids of permutahedra, associahedra, and orbit polytopes, and we explore the dual Brion map of the primitive Lie monoids associated to these three Hopf monoids.

In 2019, I participated in the Pomona Research in Mathematics Experience (PRiME) REU and was advised by Alex Barrios and Edray Goins. 

• Algebra and Combinatorics of the Brion Map on Generalized Permutahedra (with Mariel Supina)
  (In preparation)

• Master's Thesis Poster, Presented at the Latinx in Mathematical Sciences Conference 2022 and at the Western Algebraic Geometry Symposium 2023

• Undergraduate Directed Reading Program Poster, 2019 at UC Santa Barbara