# intermittently posted mathematical thoughts

### Sheaves and Probability, Part 3

A topological perspective on message passing.

### Sheaves and Probability, Part 2

A first try at using sheaves to solve marginalization problems in graphical models.

### Sheaves and Probability, Part 1

How to represent some structures from statistics and probability using cellular sheaves and cosheaves.

### Hybrid Systems and Homotopy Theory

Doing topology and engineering at the same time can be tricky.

### Homology via Matrix Reduction 2: The Long Exact Sequence of a Pair

Algebraic topology is really just matrix algorithms.

### Homology via Matrix Reduction

Algebraic topology is just matrix algorithms.

### Buridan's Principle

Making decisions is actually impossible.

### Hodge theory and persistent homology

Connections between two sorts of approximate topology through the singular value decomposition.

### Flow-coloring duality

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

### UMAP

My attempt to understand a new algorithm for low-dimensional visualization of point cloud data.

### A topologist's proof of the matrix-tree 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 less-than-intuitive examples with cellular sheaves

A few weird things I discovered while building intuition for cellular sheaves.

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