 |
Research
As a graduate student my advisor was Ravi Vakil, and my project was to extend some results of Mináč and Swallow concerning the module structure of certain Galois cohomology groups. I also considered extensions of these problems to Étale cohomology groups, a project I'm still investigating.
I had the privilege to work with John Swallow while I was an undergrad at Davidson college, and through John I was introduced to Ján Mináč and their Galois module work. Since then I have worked on several projects which aim to extend their initial results concerning pth power classes of field extensions of degree p to more general settings.
Papers and Preprints
Below is a list of the papers I have worked on. Clicking on the ± will show you a short description of the contents of the paper; clicking on it again will remove the description. You can download a PDF version of each paper by clicking on the paper title.
Work with Undergraduates
I've had the benefit of working with many excellent undergraduate students. Below is a list of research projects I have pursued with some of the most enthusiastic of these students.
In the fall of 2009, Jen Berg and I started a project in which we explore generalization to Artin-Schreier theory of some Galois modules (and their implications) related to Kummer theory.
- In the fall of 2008, Greg Hurst came to me interested in studying recursive algorithms for computing Bell numbers. His initial idea turned into the collaborative paper "An elementary (number theory) proof of Touchard's congruence" which was recently submitted for publication. (For more information, consult the above section)