I am a first year graduate student at the University of Washington in Seattle. My research interests are in algebraic geometry and combinatorics.
I completed my undergraduate degree at Amherst College, where I conducted an honors thesis under the guidance of Ivan Contreras and Alejandro Morales, proving that the Laplacian of a triangulation of an orientable manifold keeps track of the number of simplicialy homotopy equivalent complexes. I transferred to Amherst from Bristol Community College in Spring 2018.
I firmly believe in Fredrico Ardila's axioms:
Axiom 1: Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
Axiom 2: Everyone can have joyful, meaningful, and empowering mathematical experiences.
Axiom 3: Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
Axiom 4: Every student deserves to be treated with dignity and respect.
Research
Papers
On discrete gradient vector fields and Laplacians of simplicial complexes, with I. Contreras, submitted. Preprint available at arXiv:2105.05388.
Quantum Jacobi forms and sums of tails identities, with A. Folsom, E. Pratt, N. Solomon, submitted.
Expository Articles
An introduction to geodesics: the shortest distance between two points. Preprint available at arXiv:2007.02864.
Past Projects
Honors Thesis: Enumeration of Discrete Gradient Vector Fields on Simplicial Complexes (document, talk)
Advisors: Ivan Contreras (Amherst College), Alejandro Morales (UMass Amherst)
Summer 2020: Quantum Jacobi Forms and Sums of Tails Identities (talk, poster)
Advisor: Amanda Folsom (Amherst College)
Summer 2019: Graph Quantum Mechanics and Discrete Morse Theory (poster)
Advisor: Ivan Contreras (Amherst College)
Summer 2018: Normality of Toric Rings and Rees Algebras of Pinched Strongly Stable Ideals (poster)
Advisor: Gabriel Sosa (Colgate College)
You can find a repository of some basic code I've written on my GitHub.