My main research interests involve arithmetic geometry, which is roughly the crossroads of algebraic geometry and number theory. I am also interested in various problems in cryptography.

Summary of

- "Klein Four Actions on Sets and Graphs" - American Mathematical Monthly, 124(6):543–547, 2017. PDF
- "Critical Groups of Graphs with Dihedral Actions II" - European Journal of Combinatorics Volume 61, March 2017, Pages 25–46 Journal PDF
- "Cyclic Critical Groups of Graphs" - joint with Ryan Becker, Australasian Journal of Combinatorics Vol. 64 (2016) 366-375 Journal PDF
- "Optimal Strategy for Defending A Chain in Risk" - joint with Todd Neller, Mathematics Magazine, 88(3):217-230, 2015 Journal PDF
- "Sandpiles, Spanning Trees, and Plane Duality" - joint with M. Chan, M. Macauley, D. Perkinson, C. Werner, and Q. Yang. SIAM J. Discrete Math, 29(1):461-471, 2015 Cupola Journal PDF
- "Chutes and Ladders with Large Spinners" - joint with Darcie Connors, College Mathematics Journal, 45(4):289-295, 2014 Cupola Journal
- "Critical Groups of Graphs with a Dihedral Action" - joint with Criel Merino, European Journal of Combinatorics, Volume 39, July 2014, Pages 95-112 Journal PDF
- "Compositions of Integers with Bounded Parts" - INTEGERS Vol. 14 (2014) A6, Journal Cupola PDF
- "A Frobenius Problem Related to Actions On Curves in Characteristic p" -Glasgow Journal of Mathematics, Volume 56 (2014), pp.143-148 PDF Journal
- "A First Year Seminar on Cryptography" - Cryptologia Vol. 37 (2013), no. 4, 305-310 Journal
- "The Secretary Problem From The Applicants Point of View".
*Martin Gardner In The Twenty-First Century*Edited by Michael Henle and Brian Hopkins. Mathematical Association of America Press, 2013. pp. 243-248 - "Eisenhart and Coble: Two Prominent Gettysburg Alumni in Mathematics" - Notices of the American Mathematical Society Volume 60 (2013) No. 5, pp. 558-566 Journal Cupola
- "Pointless Hyperelliptic Curves" - joint with Ryan Becker, Finite Fields and Their Applications, Vol. 21 (2013), pp. 50-57 Journal PDF Cupola
- "Non-genera of curves with automorphisms in characteristic p", in
*Computational Algebraic and Analytic Geometry*, Contemporary Mathematics, vol. 572, Amer. Math. Soc., Providence, RI, 2012, pp. 89-95. - "Solving The Debt Crisis on Graphs" - MAA Focus Vol. 32 (2012), no. 4
- "The Secretary Problem From The Applicants Point of View" - College Mathematics Journal, Volume 43, Number 1, January 2012 , pp. 76-81. Cupola
- "Communal Partitions of Integers" - INTEGERS, Vol. 11 (2011) A70 Cupola Journal
- "Curve Interpolation and Coding Theory" - Journal of Undergraduate Mathematics and its Application, Vol. 31 (2010), no. 3, 189-196
- "Addendum to 'Hyperelliptic curves with prescribed p-torsion'" - joint with Rachel Pries,Manuscripta Mathematica, Vol. 133(2010), 545-546.
- "Basis for Riemann-Roch G-Modules for y
^{2}= x^{p}-x over GF(p)" - joint with David Joyner & Amy Ksir, International Journal of Information and Coding Theory, Vol. 1, No. 3 (2010) pp. 298 - 312 PDF - "The 2-ranks of Hyperelliptic Curves With Extra Automorphisms" - International Journal of Number Theory, Volume 5 (2009), no. 5, 1-14 PDF Journal
- "Galois structure and De Rham invariants of Elliptic Curves" - joint with Sonin Kwon, Journal of Number Theory Volume 129 (2009), no. 1, 1-14 PDF
- "The automorphism group of a generic curve with given p-rank" - joint with Jeff Achter & Rachel Pries, Michigan Mathematical Journal, Volume 56 (2008), no. 3, 583-592 PDF
- "Klein-four covers of the projective line in characteristic two", Albanian Journal of Mathematics. Vol. 1 (2007), 3--11 . Journal PDF
- "On The Moduli Space Of Klein Four Covers Of The Projective Line" with Rachel Pries,
in
*Computational Aspects of Algebraic Curves*, ed. T. Shaska, Lecture Notes Series in Computing, WorldScientific, Volume 13, (2005) - "Hyperelliptic Curves with Prescribed p-torsion" with Rachel Pries, Manuscripta Math. Vol. 117 (2005), no. 3, 299--317. Journal PDF
- "Questions on p-torsion of Hyperelliptic Curves" with Rachel Pries, Rendiconti del Seminario Matematico della Universita di Padova. Volume 113 (2005) Journal PDF
- "Brauer Group Invariants Associated to Orthogonal Epsilon Constants", Bulletin of the London Mathematical Society, Volume 37 (2005), no. 2, 172-178. Journal PDF
- "Epsilon Constants and Orthogonal Representations", Compositio Mathematica Volume 140, No 5 September 2004 Journal PDF
- "If I Never Get Back: Marathon Games" - joint with Phil Lowry, Baseball Research Journal, 2004
- "Fair-Weather Fans: The Correlation Between Attendance and Winning Percentage" - Baseball Research Journal, 2003 Cupola
- "Embedding Problems and Finite Quotients" with Ted Chinburg, Pacific Journal of Mathematics Volume 205, No. 1 July, 2002 pdf ps
- "Orthogonal Epsilon Constants For Tame Actions of Finite Groups on Surfaces", doctoral dissertation, May 2002 pdf

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