Darren's Research Page
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.
Papers
What follows is a list of mathematical things I have written that someone has found worthy of publication. Where possible, I have tried to give links to read the papers. This list is almost certainly out of date, so you might try looking me up at arXiv, Mathscinet, or The Cupola.
- "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 y2 = xp-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
I also like to review books. Some of my favorite reviews can be found here.
Math Links
Number Theory
Web
Mathscinet
Math ArXiv
Cryptography Archive
Crypto ePrints
Mathematical Association of America
American Mathematical Society
Math
Journals