Hello, I'm Joseph.

I'm a first-year Math PhD student at the University of Utah. I like algebraic geometry and topology or anything nearby. When not doing math, you can catch me running, climbing, or playing guitar.

Partially Ordered is my math blog and programming portfolio.

Featured Posts

De Rham's Theorem

December 2023

De Rham's theorem provides an important connection between topology and smooth manifolds---that for manifolds, the de Rham cohomology is exactly the (real) singular cohomology, and the isomorphism is given by integration. Read more

Covering Spaces

August 2022

Covering spaces are a cool thing in topology. Finding covering spaces is like unwrapping a topological space. There are intimate connections between the fundamental group and covering spaces. Read more


October 2021

The FTFGMPID is one heck of an over powered theorem. It pretty quickly gives you the classification of finitely generated abelian groups, the Jordan normal form, etc. Read more

Featured Projects

Marching Cubes

Marching Cubes Algorithm, Implemented in Javascript with WebGL


Physically Simulated Particles, Rendered with WebGL


A Real Time Strategy Game, made with Python, Flask, Javascript, and Socket.io.