Nathaniel Hurst

Nathaniel Hurst

Undergraduate, Department of Mathematics — UC Santa Barbara

About

I am an undergraduate mathematics major at UC Santa Barbara (expected graduation 2027, GPA 3.96/4.0). My interests lie in and mathematical cryptography and numerical analysis.

Projects & Research

Möbius strip
2025 · Directed Reading Program
The Quillen-Suslin Theorem

Studied the Quillen-Suslin theorem under faculty mentorship through UCSB's Directed Reading Program, focusing on the relationship between algebraic vector bundles over affine space and finitely generated projective modules.

3-isogeny volcano graph
2025 · Preliminary Arizona Winter School (PAWS)
Introduction to Mathematical Cryptography

Completed a nine-week virtual program organized alongside the Arizona Winter School, covering classical and modern cryptographic methods. Topics progressed from Diffie–Hellman key exchange and the discrete logarithm problem through elliptic curve cryptography and quantum-resistant approaches, with problem sets using SageMath to analyze the underlying number-theoretic hardness assumptions.

Community notes annotation
2024–25 · Undergraduate Research (Economics)
Misinformation and Community Notes

Researched interactions between misinformation and correction protocols, including Twitter Community Notes. Managed databases with data from over 1M tweets and developed data visualizations for research presentations.

Tools & Visualisers

Bézier curve
2026 · Personal Project
Bézier & Spline ExplorerAI

An interactive browser-based tool for drawing and exploring Bézier Curves and Cubic Splines. Supports free-draw and math/animation modes, 3D projection, undo/redo, a custom font designer, and animated examples. Built using Claude Code.

Contact