I was trained in algebraic geometry at the University of Chicago, where I received my PhD. in 1990 under the direction of Bill Fulton. A paper based on my dissertation was published as Curves in Grassmannians (Trans. Amer. Math. Soc. 347 (1995), no. 9, 3179-3246). Among other things, it contains a useful appendix summarizing the algebraic theory of principal parts/jet bundles.

I spent the academic year of 1993-1994 at the University of Oslo, Norway. Under the gentle prompting of Ragni Piene, I pursued an interest in toric varieties, which eventually led to two papers: Principal parts of line bundles on toric varieties, (Compositio Mathematica 104, 27-39, 1996) and Inflections of toric varieties, (Michigan Math. J. 48, 483-515, 2000).

The year 1998-1999 was spent at the University of Genoa, Italy. There, I was lucky enough to hang out with Tony Geramita and became involved with the research group on computational commutative algebra, COCOA, headed by Lorenzo Robbiano. I still maintain a (much too distant) connection with this wonderful group of people. I wrote and maintain the documentation of the computational commutative algebra system by the same name: CoCoA. As an outgrowth of the COCOA VI conference in Torino, Ezra Miller and I wrote Eight Lectures on Monomial Ideals (COCOA VI: Proceedings of the International School, Villa Gualino -- May-June, 1999, (Anthony V. Geramita, ed.), Queens Papers in Pure and Applied Mathematics, no. 120, Queen's Univ., Kingston, ON, 2001, 3-105) based on the lectures given there by Bernd Sturmfels. Ezra and Bernd have expanded these lectures into a book: Combinatorial Commutative Algebra.

My main research interest at the moment is studying polytopes generated by group representations. Recently, I have written a couple of papers with Reed students: Frobenius Polytopes (preprint) with John Collins, describing the structure of polytopes corresponding Frobenius groups; and Some facets of the polytope of even permutation matrices (Linear Algebra and its Applications, 381, 2004), with Jeff Hood, concerning the complexity of the face structure of the even permutation polytope. During the Summer of 2003, I led several undergraduates in research on representation theory and polytopes, and taught a course on polytopes in the Fall of 2003. I have recently written a paper with Robert Guralnick (to appear in the Journal of Combinatorial Theory, Series A). It relates the transitivity of a permutation group with geometric properties of its corresponding permutation polytope.

Most of my academic energy has gone into getting others, namely my students, to do research.