Research

I am an assistant professor at the Cal Poly, San Luis Obispo mathematics department. I study number theory and the theory of partitions. A partition of a positive integer n is any sequence of non-decreasing non-negative integers that sum to n.

For example, the 7 partitions of 5 are (5), (4,1), (3,2), (3,1,1), (2,2,1), (2,1,1,1), and (1,1,1,1,1).

A famous identity in the theory of partitions is Euler's generating function

where p(n) denotes the number of partitions of the integer n.

Papers

1. 4-core partitions and class numbers, (Coauthor: Ken Ono), Acta Arithmetica, 65, 1997, pages 249-272.
2. Rook Theory and t-cores, (Coauthors: Jim Haglund and Ken Ono), Journal of Combinatorial Theory, Series A, 84 1998, no. 1, 9--37.
3. Calculating p(n) modulo small primes using quadratic forms. Journal of Number Theory, 70, 1998, no. 2, 121--126.
4. The number of edges on generalizations of Paley graphs, International Journal of Mathematics and Mathematical Sciences, 27, 2001, no. 2.
5. Generalized Vandermonde Identities, coauthored with Don Rawlings, submitted to Mathematics Magazine.
6. Moment Generating Functions for Adjacency Statistics, coauthored with Don Rawlings, Rudy Angeles, and Mark Tiefenbruck, submitted to the Journal of Statistical Planning and Inference.
7. The existence of (e,r)-core partitions, in preparation.
8. The existence of self-conjugate t-core partitions, in preparation to be coauthored with John Baldwin and Abe Kunin.
9. On Simultaneous s-cores and t-cores, Dave Aukerman and Ben Kane, (advised by Lawrence Sze) in preparation.

Note: Papers 3, 6, 7 and 8 are .tex files that require the Scientific WorkPlace Viewer, a free download, in order to view.

Upcoming Conferences

1. Additive Number Theory, Nov. 17-20, 2004
2. West Coast Number Theory Conference, Dec. 16-20, 2004

Experimental

• Using Macromedia Flash to teach Newtonian Physics
• Random