I like working on problems arising from the interaction between algebraic number theory, Galois theory and group theory. Much of my work centers on questions about the structure of the Galois groups associated to certain field extensions with restricted ramification. What kinds of groups can arise? Can they be classified in some way? Given a particular group, can one say anything about how frequently this group should occur in certain natural families of extensions?
I also like thinking about computational problems in symbolic algebra, both theoretically and in terms of getting practical answers to questions that arise in my other work. I often make use of computational algebra systems like Magma, GAP and PARI/GP.
Research with Undergraduates
I enjoy supervising undergraduate research projects and honors theses. Recent research projects have focused on investigating the periodicity of sequences defined by recurrences over various finite algebraic structures. Honors theses can develop out of a research project or be purely expository.
If you are a W&L student and are potentially interested in working on a project or thesis with me, then please stop by my office some time. Be aware that most of my current research projects require some background in abstract algebra (Math 321/392), although I’m also open to student suggestions. Most projects take place over the summer. Funding is available through the Summer Research Scholars program.
For some general information about theses, see this page: Honors Thesis.
Publications and Preprints
* indicates co-author was an undergraduate when work was completed.
15. On certain quotients of p-class tower groups of quadratic fields, (arXiv)
8. Different Partners, Different Places: Mathematics applied to the construction of four-couple folk dances, (pdf)
with G. M. Roodman,
Journal of Mathematics and the Arts, 7 (2013), 17–28.
6. An irreducibility lemma, (pdf)
with F. Hajir,
J. Ramanujan Math. Soc., 23, No. 1 (2008), 1–9.
2. Computing left Kan extensions,
with M. Leeming, R. F. C. Walters,
J. Symbolic Comput. 35 (2003), 107–126.
1. Integral equation approximation for inhomogeneous fluids: functional optimization,
with M. Booth, A. D. J. Haymet and A. G. Schlijper,
Molecular Physics, Vol. 95, No. 3 (1998), 601–619.
Other Notes and Materials
- MathSciNet reviews that I’ve written for various papers.