Professional Information

Resume

If you have any questions about specific details or would like references, please e-mail me.

Publications

Includes information about published papers as well as notes, supporting Maple code for various papers, and selected sets of slides from talks.

Research Statement, Fall 2005

This research statement details possible further work in areas where I have done research in the past.

Projects

Good abc Triples Database, Spring 2006

Update: May 2006

The database now contains all good abc triples c value is less than or equal to 10⁸. Also there is a new python/SAGE script that is running faster for ranges of c values greater than 10⁷.

This spring a colloquium talk given by H. W. Lenstra described the idea of compiling a list (for which a database is a very convenient storage device) of all good abc triples whose c value is less than 10¹⁸. In the talk a good abc triple is defined to be a set of 3 positive integers a, b, c such that

1. a + b = c
2. gcd(a,b,c) = 1
3. c > rad(abc)

where rad(n) is the product of all primes dividing n for n a positive integer.

The good abc triples database access page currently contains all good abc triples whose c value is less than or equal to 5 x 10⁷. The data currently in the database was generated using python script files run in the computer algebra system SAGE. Generating this data with the current python file takes about a week on an Opteron PC with 8G of memory running SAGE on Linux.

Research Notes

Fibonacci Triangles URAP of Spring 2005.

Update: June 2006

This draft includes the work done with David Kettlestrings and proof of the nonexistence of Fibonacci triangles (F_n-k, F_n, F_n) for 5 < k < 10.

During the spring semester of 2005 David Kettlestrings worked with me in the Undergraduate Research Apprenticeship Program on a Fibonacci triangles project. A Fibonacci triangle is a triangle whose area is an integer and whose sidelengths are Fibonacci numbers. An example of a Fibonacci triangle is the triangle whose sidelengths are (5, 5, 8) and it is easy to see that any possible Fibonacci triangle must be isosceles. Harborth, Kemnitz, and Neville have shown any other Fibonacci triangle must be of the type (F_n-k, F_n, F_n) for k> 5 and conjectured that (5, 5, 8) is the only Fibonacci triangle. During the semester David and I have shown that no Fibonacci triangles exist for k=7, 8, 9, 10 as well.