Teaching:

For the spring semester of 2009, I am teaching the following course:

1. Math/PPE 180 - Analytical Methods in Economics, Law and Medicine (link to Blackboard)

Research:

My research is in the field of Algebraic Combinatorics. In particular, I have spent a lot of time trying to understand the combinatorics of Macdonald polynomials. I recently completed a post-doc at the University of California-Davis working with Anne Schilling on a focused research group studying affine Schubert calculus.

Some Papers/Preprints:

1. On the uniqueness of promotion operators on tensor products of type A crystals (with Anne Schilling and Nicolas Thiéry).

2. A new characterization for the m-quasiinvariants of S_n and explicit basis for two row hook shapes (with Gregg Musiker).

3. An elementary proof of the hook formula.

4. Combinatorics of Macdonald polynomials and extensions (doctoral dissertation under the direction of Adriano Garsia).

5. Quasiinvariants of S_3 (with Gregg Musiker).

6. A Weight Preserving Bijection Between Schroeder Paths and Schroeder Permutations (with Eric Egge and Kendra Killpatrick).

7. An Area-to-Inv Bijection Between Dyck Paths and 312-avoiding Permutations (with Kendra Killpatrick).