December 2023
De Rham’s Theorem
De Rham’s theorem provides an important connection between topology and smooth manifolds: de Rham cohomology is real singular cohomology, with the isomorphism given by integration.
Topology
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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
August 2022
Covering Spaces
Covering spaces are a cool thing in topology. Finding covering spaces is like unwrapping a topological space, with intimate connections to the fundamental group.
Topology
Read more →July 2022
Nullstellensatz
Hilbert’s Nullstellensatz bridges algebra and geometry. This article develops commutative algebra before arriving at a proof.
Algebra
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