Here is my curriculum vitae (or PDF).

Teaching info: In Winter 2010, I am teaching MAT21A and MAT108.

Papers and preprints

Ehrhart polynomials of cyclic polytopes (arXiv) Fall 2004
A paper proving the conjecture made in math.CO/0402148 about the coefficients of the Ehrhart polynomials of cyclic polytopes.
Journal of Combinatorial Theory Ser. A 111 (2005), no. 1, 111-127.

(k,m)-Catalan numbers and hook length polynomials for plane trees, with Rosena Du (arXiv) Winter 2005
A short paper defining the hook length polynomials for m-ary trees and plane forests, and introducing a new generalization of Catalan numbers, by using which we prove our hook length polynomials have a simple binomial expression.
European Journal of Combinatorics 28 (2007), no. 4, 1312-1321.

Hook length polynomials for plane forests of a certain type (arXiv) Summer 2005
A short note defining the hook length polynomials for plane forests of a given degree sequence type. Some other enumerative results on trees are also given.
Annals of Combinatorics 13 (2009), no. 3, 315-322.

Ehrhart polynomials of lattice-face polytopes (arXiv) Fall 2005
A paper defining a new family of polytopes, lattice-face polytopes, which is a generalization of cyclic polytopes. We show that the Ehrhart polynomial of a lattice-polytope has the same simple form as cyclic polytopes.
Transactions of the American Mathematical Society 360 (2008), no. 6, 3041-3069.

The irreducibility of certain pure-cycle Hurwitz spaces, with Brian Osserman (arXiv) Fall 2006
We use a combination of geometric and group-theoretic techniques to prove that Hurwitz spaces of genus-0 covers of the projective line having a single ramified point over each branch point are irreducible.
American Journal of Mathematics 130 (2008), no. 6, 1687-1708.

A generating function for all semi-magic squares and the volume of the Birkhoff polytope, with Jesus A. De Loera and Ruriko Yoshida (arXiv) Fall 2006 - Winter 2007
We provide an explicit combinatorial formula for the volume of the polytope of n by n doubly-stochastic matrices, also known as the Birkhoff polytope. We do this through finding the multivariate generating function for the lattice points of the polytope.
Journal of Algebraic Combinatorics 30 (2009), no. 1, 113-139.

Combinatorial bases for multilinear parts of free algebras with two compatible brackets (arXiv) Spring - Summer 2008
We construct bases for Lie_2(n) and P_2(n) from combinatorial objects, the set of rooted trees, then prove the dimension formulas for these two algebras conjectured by B. Feigin. We also define a complementary space Eil_2(n) to Lie_2(n), give a pairing between them, and show that the pairing is perfect.
Journal of Algebra 323 (2010), no. 1, 132-166.

A note on lattice-face polytopes and their Ehrhart polynomials (arXiv) Summer - Fall 2008
We redefine lattice-face polytope by removing an unnecessary restriction in the old definition and show that the Ehrhart polynomial of a new lattice-face poltyope has the same simple form as the old ones. Furthermore, we show that the new family of lattice-face polytopes contains all possible combinatorial types of rational polytopes.
Proceedings of the American Mathematical Society 137 (2009), no. 10, 3247-3258.

Moduli of crude limit linear series (arXiv) Winter 2009
We answer a combinatorial question posed by Osserman, giving a description of the dimensions of the spaces of crude limit linear series that he introduced.
International Mathematics Research Notices 2009 (2009), no. 21, 4032-4050.

Higher integrality conditions, volumes and Ehrhart polynomials (arXiv) Fall 2009
We introduce the definition of k-integral polytopes, and show that the Ehrhart polynomial of a k-integral polytope P has the properties that the coefficients in degrees of less than or equal to k are determined by a projection of P, and the coefficients in higher degrees are determined by slices of P. A key step of the proof is that under certain generality conditions, the volume of a polytope is equal to the sum of volumes of slices of the polytope.