2002 Research Experiences for Undergraduates
Computational Number Theory and Combinatorics
Research Projects

Elliptic Curves Group

This group consisted of Jonathan Battista, Johnathan Bayles and Dmitriy Ivanov. They investigated the Lang-Trotter conjecture and worked towards proving that the conjecture is true on average for elliptic curves with various rational torsion subgroups.

Elliptic Curves Report

Partition Function Group

This group consisted of Jimena Davis, Elizabeth Perez and Chip Swannack. They developed fast algorithms for computing the coefficients of the partition function and generated extensive data for this function. They used this data to study various conjectures related to the arithmetic of the partition function.

Partition Function Report

Kings Problem Group

This group consisted of Anatoliy Kats, Micah Leamer and Chip Swannack. They investigated methods for improving known bounds for the Kings Problem. The group formulated a recurrence using tensor products of matrices and examined the properties of recurrences of this type. A generating function was found for the Segre characteristic of Jk tensor n (where Jk is a Jordan Block of size k).

Kings Problem Report