Nadir Hajouji

Projects

Visualizing Elliptic Curves

We created a new way of visualizing elliptic curves over finite fields, that replaces the classical ambient space with a complex analytic elliptic curve. Our illustration method requires finding lifts of Frobenius of the curve we want to visualize, so to make them, we had to come up with an algorithm that can compute these lifts for any elliptic curve. The algorithm will be explained in an upcoming paper in collaboration with Steve Trettel, but we have a lot to share on this project already:

  • The interactive app — A user interface that makes it easy to access the data used to obtain our pictures, and learn about the tools we used. There is a mini “crash course” that gives a brief summary of the math, with examples and interactive applets throughout.

  • The art gallery — rendered artwork from an ongoing collaboration with Steve Trettel.

  • github.com/nhajouji/ecfplat A repository that contains the code used to do some the algebraic computations required to make our illustrations.

Recognition & press

  • Bridges 2025 — peer-reviewed paper on the mathematics and art (PDF linked from the gallery).
  • ICM 2026 — artwork from the project will be exhibited at the International Congress of Mathematicians.
  • In preparation — a technical paper, and an article for The Mathematical Intelligencer.
Launch the interactive app → Visit the art gallery → View the code →

Artwork © Nadir Hajouji & Steve Trettel.

Data Science & Machine Learning

Through The Erdős Institute I completed intensive bootcamps in data science and deep learning, each capped by a team project — both finished in the top five of their cohort.

  • Wonderpus Octopus (2024) — neural networks modeling chlorophyll against biogeochemical features. Erdős Deep Learning Bootcamp. Certificate & code
  • Recipe recommender (2024) — a sentence-transformer plus matrix-factorization recommendation engine. Erdős Data Science Bootcamp. Certificate & code