2012 Research Experiences for Undergraduates
Computational Algebraic Geometry, Combinatorics and Number Theory
Research Projects

Please note that some of these works are still in progress!

Graph NIM

The undergraduate participants in this group were Allison Nelson, Sydney Ryan and Chao Xu. They were mentored by recent Clemson PhD graduate Janine Janoski They studied the game of graphical NIM and determined families of graphs which are first or second palyer wins.

REU Write up

Extensions of Function Fields

The undergraduate participants in this group were Alfeen Hasmani, Lindsey Hiltner, Angela Kraft and Daniel Scofield. They were mentored by Clemson graduate student Kirsti Wash. They studied the finite extensions of the field of formal Laurent series over F_p.

REU Write up
Preprint published in the Rocky Mountain Journal of Mathematics

Aliquot Cycles over Number Fields

The undergraduate participants in this group were David Heras and Andrew Qian. They were mentored by Clemson graduate student Rodney Keaton. They studied Aliquot sequences of prime ideals in number fields for elliptic curves. This work generalizes work of Silverman and Stange who first posed the generalization of aliquot cycles to elliptic curves.

Preprint submitted for publication

Frobenius distributions of elliptic curves

The undergraduate participants in this group were Brandon Tran, Minh-Tam Trinh and Phil Wertheimer. They were mentored by Clemson graduate student Dania Zantout. They studied questions related to the distribution of primes relative to certain properties of elliptic curves. More precisely, they studied the distribution of the traces a_E(p) of the Frobenius morphism of elliptic curves E. The addressed the question of how often the trace obtains an extremal value and the question of how often the trace is itself a prime.