## Two lemmas on Matlis Duality

A short note on Matlis duality that I made mostly for my own reference. I'm definitely not the first person to prove these results, but I'm not sure where else to find them explicitly stated and proven.

## Subadditivity formulas for test ideals

These are slides from a preliminary report I gave at the special session on commutative algebra at the AMS Western Sectional. The conference took place at Pullman, WA on April 22-23, 2017.

## Birational classification (for a non-mathematical audience)

I spoke at the Leonardo museum in March, 2017 as part of their Math Medley event. The purpose of this 15-minute talk was to help introduce a non-mathematical audience to pure math research by discussing one of the big open problems in algebraic geometry. In particular, I tried to convey that lots of math research is going on to this day. I also tried to demonstrate that, though it may look complicated and esoteric, modern math research is still trying to answer some basic and very natural questions.

## Singularities in characteristic p

This was a talk given at the student algebraic geometry seminar in 2016. In these notes, I briefly define the log canonical threshold, and then describe an analogue in characterstic p, the F-pure threshold. Then I mention other ways to measure singularities in positive characteristic and their relationships with the characteristic-0 picture, both known and conjectured. I based this talk on several surveys in the literature.

## A history of commutative algebra

I gave a talk on the history of commutative algebra, tracing it back to the study of diophantine equations and Fermat's last theorem. Along the way, we talk about Kummer's theory of ideal numbers. This talk was aimed at a general audience of graduate students (in pure and applied math) at Utah's GSAC colloquium.

## Marden's Theorem

I gave a talk on Marden's theorem in January 2014. The following are presentation slides and a python script for drawing triangles and their steiner inellipses using the proof of the theorem.