Partially Ordered

Hello, I’m Joseph.

I’m a fourth-year math PhD candidate at the University of Utah. I like algebraic geometry and derived categories. When not doing math, you can catch me on a trail run, baking breads and sweet treats, or playing music poorly.

Partially Ordered is my math blog and programming portfolio.

Featured posts

April 2026

Brauer Group

An introduction to Brauer groups, first for a field (i.e., Spec k for a geometer) and then for a scheme.

AlgebraAlgebraic Geometry

June 2025

Representation Theory

Basics on the representation of complex semisimple Lie algebras, with some examples worked out.

Algebra

April 2025

Beilinson's Resolution of the Diagonal

An explanation of Beilinson's famous 'Problems in Linear Algebra', in particular showing how his paper gives a full strong exceptional collection and a derived equivalence to quiver representations.

Algebraic GeometryCategory Theory

Featured projects

Marching Cubes preview

Marching Cubes

Marching Cubes Algorithm, implemented in JavaScript with WebGL.

View project →GitHub

Particles preview

Particles

Physically simulated particles, rendered with WebGL.

View project →GitHub

Random Geometry

A Jupyter notebook about sampling random planar trees, building up to random maps.