My specialty is algebraic number theory. I study unit and ideal class groups of
number fields, the Galois theory of extensions with restricted ramification, the
arithmetic of elliptic curves, and special values of L-functions. My past PhD students
are Mairead Greene (Rockhurst University) and Laura Hall-Seelig ( Merrimack College).
I'm currently working on a monograph on asymptotically good families of curves,
codes, number fields, and graphs.

Articles

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Algebraic Properties of a Family of Generalized Laguerre Polynomials, Canadian Journal of Mathematics (2009)

We study the algebraic properties of Generalized Laguerre Polynomials for negative integral values of the...

 

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Specializations of one-parameter families of polynomials (with S Wong), Annales De L Institut Fourier (2006)

Let K be a number field, and suppose λ(x,t)∈K[x,t] is irreducible over K(t). Using algebraic...

 

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Finitely ramified iterated extensions (with W Aitken and C Maire), International Mathematic Research Notices (2005)

Let K be a number field, t a parameter, F = K(t), and φ(x)∈ K...

 

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On the Galois Group of generalized Laguerre polynomials, Journal de théorie des nombres de Bordeaux (2005)

Using the theory of Newton Polygons, we formulate a simple criterion for the Galois group...

 

Other

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Modular forms and elliptic curves over the field of fifth roots of unity (with PE Gunnells and Dan Yasaki), Mathematics and Statistics Department Faculty Publication Series (2010)

Let F be the cyclotomic field of fifth roots of unity. We computationally investigate modularity...