I am a third-year mathematics PhD student at the University of Washington.
I am Coptic Egyptian and use they/them pronouns.
My research interests are primarily in geometry, topology, and combinatorics, as well as applications of these areas to neuroscience, physics, and chemistry.
I'm currently working on projects relating to Brill-Noether theory, tropical geometry, and discrete Morse theory.
Papers and preprints:
A tropical framework for using Porteous' formula, in progress.
On discrete gradient vector fields and Laplacians of simplicial complexes, joint with Ivan Contreras. Published in Annals of Combinatorics. 2022. (journal)
Quantum Jacobi forms and sums of tails identities, joint with Amanda Folsom, Lizzie Pratt, and Noah Solomon. Published in Research in Number Theory. 2021. (journal)
Graduate Seminars:
I am in charge of organizing the following weekly seminars.
Ongoing seminars:
Combinatorial Algebraic Geometry Seminar (co-organized with Cameron Wright)
Past seminars:
Algebraic Geometry Reading Seminar (co-organized with Alex Wang)
Knot Number Theory Reading Seminar (co-organized with Alex Galarraga)
Teaching:
I am the instructor for MATH 441: Topology.
Previously, I have been the teaching assistant for the following courses:
ART 255/MATH 180: Making Meaning: Art and Mathematics as Embodied Practices
MATH 125: Calculus with Analytic Geometry II
I also really like combining art and mathematics! Here I am sculpting a Clebsch surface.
I firmly believe in Federico 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.