Nadir Hajouji

Research & Writing

My research is in algebraic geometry and number theory — elliptic curves, modular curves, and their arithmetic — with a side interest in cryptography.

Papers

  • Elliptic Curves and the Hopf Fibration (2025)
  • Supersingular Isogeny Graphs from Algebraic Modular Curves (2023)
  • Modular Curves and Mordell–Weil Torsion in F-theory (2019) — with P. K. Oehlmann. arXiv:1910.04095

Thesis

  • Trace Zero Points on Elliptic Fibrations — PhD thesis, UC Santa Barbara, 2020. PDF

Expository writing

Notes written to explain ideas I find beautiful, in the same make-it-visible spirit as my teaching.

  • Moduli Space of (Real) Elliptic Curves — PDF
  • Moduli Space of (Real) Genus One Curves — PDF
  • The Prime Number Theorem for Arithmetic Progressions — PDF
  • The Gamma Function — PDF
  • Siegel Modular Forms — undergraduate thesis, Reed College. PDF