Aven Bross

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Very ample divisors on curves, 11 Dec 2018

All of the sources that I have found characterizing very ample divisors reference Hartshorne or otherwise use, in my opinion, “non-elementary” arguments. Here are some “elementary” proofs that I worked out with some fellow grad students.

Belyi's Theorem, 02 Dec 2018

Belyi’s Theorem is an arithmetic-geometric result that has the unusual quality of being both fairly recent and provable with only the material from a first course in classical algebraic geometry.

Applying to grad school, 23 Jun 2018

I have spent a lot of time applying to grad schools, here are some useful things that I found during my search.

Path 3-coloring plane graphs, 15 Jun 2018

A path coloring of a graph partitions its vertex set into color classes such that each class induces a disjoint union of paths. In my computer science masters project I implemented several algorithms to compute path colorings of graphs embedded in the plane.

The permutationlock domain, 10 Jun 2018

The domain name “permutation lock” is something that I came up with back in high school when I learned that the locking mechanism on a “combination lock” does not fit with the combinatorial notion of a combination.