Number theorists are like lotus-eaters -- having tasted this food they can never give it up.
-Leopold Kronecker
My research roughly breaks down into three categories. Click on the category below to read more about that particular topic.
- Arithmetic Geometry: Jacobian Varieties
- Analytic Number Theory: Parity of powers modulo p
- Postdoctoral Projects: Mathematics Education Research
Publication List
Publications
- Decimations of l-sequences and permutations of even residues mod p. (with J. Bourgain, T. Cochrane, and C. Pinner). SIAM Journal on Discrete Mathematics 23 (2009), no. 2, 842-857. [pdf]
- Decomposing Jacobians of curves with extra automorphisms. Acta Arith. 132 (2008), no. 3, 231-244. [pdf]
- PhD Thesis: Elliptic factors in Jacobians of low genus curves. University of Illinois at Urbana-Champaign, (2007). [pdf]
- Cwatset Isomorphism and Its Consequences. (with C. Girod, M. Lepinski, and J. Mileti). Rose-Hulman Mathematical Sciences Technical Report Series, vol 1 (2000).
Submitted Papers and Preprints
- The l-rank structure of a global function field. (with L. Berger, J.-L. Hoelscher, Y. Lee, and R. Scheidler). Submitted. [pdf]
- Studio College Algebra at Kansas State University. (with A. Bennett, R. Manspeaker, and R. Natarajan). Submitted.
- On the parity of k-th powers mod p: A generalization of a problem of Lehmer. (with J. Bourgain, T. Cochrane, and C. Pinner). In Preparation.
- Elliptic factors in Jacobians of hyperelliptic curves with certain automorphism groups. Preprint. [pdf]
Jacobian Varieties
Analytic Number Theory
Postdoctoral Project: Education Research
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