Research

Here I have descriptions of my research projects and at the bottom I have a list of my publications. I see that many students postdocs and professors have research tabs on their website that are very out of date. Since many people struggle to keep a page like this manually updated, the list of publications at the bottom is updated by querying dblp. Hopefully this means it will never be out of date!

Active Projects

Metrinome

Metrinome is a code analysis tool that formalizes the complexity of a method as the number of paths through an abstraction of that method as a function of depth. If these paths increased exponentially that would be considered more complex than if they increased quadratically. Metrinome is a tool that can compute the asymptotic behavior of this path explosion for code written in many different languages.

Search Synthesis via Hylomorphism

The goal of this project is to formalize an existing search synthesis algorithm in terms of anamorphism and catamorphism. The algorithm builds a decision tree based on information gain after training on a dataset, which can be formalized as an anamorphism. Then for a particular element the algorithm takes the decision tree and collapses it down into a prediction, which can be formalized as a catamorphism.

Completed Projects

Computational Representation Theory

We designed algorithms for the computation of subranking and subset summary statistics in a way that maximized sharing of intermediary values and minimized the number of addition operations. We then formalized those algorithms in the language of group frames.

Trace Ideals overn Numerical Semigroup Rings

The goal of this project is to categorize the structure of trace ideals over numerical semigroup rings. Trace ideals are powerful algebraic tools that can be used to classify rings and modules. Numerical semigroups rings are a pervasive type of ring that pop up in many areas of mathematics like algebraic geometry and number theory and they have a number of properties that make them a convenient object for study with trace ideals.