
Hodge theory and persistent homology
Connections between two sorts of approximate topology through the singular value decomposition.

Flowcoloring duality
A discussion of an interesting interplay between algebraic topology and the combinatorics of graphs.

UMAP
My attempt to understand a new algorithm for lowdimensional visualization of point cloud data.

A topologist's proof of the matrixtree theorem

Spectral Sheaves
A summary of my thesis proposal.

Mapper and cosheaves
Some notes on a couple of papers fleshing out the connections between Mapper, Reeb graphs, and cosheaves.

Some lessthanintuitive examples with cellular sheaves
A few weird things I discovered while building intuition for cellular sheaves.