Writings

Pieri resolutions for classical groups (with Jerzy Weyman), preprint	arXiv (last updated 10/9/09) Slides
Positivity theorems for solid-angle polynomials (with Matthias Beck and Sinai Robins), to appear in Beiträge Algebra Geom..	arXiv (last updated 6/22/09)
A finite calculus approach to Ehrhart polynomials (with Kevin M. Woods), preprint	arXiv (last updated 4/3/09)
Computing inclusions of Schur modules, Journal of Software for Algebra and Geometry 1 (2009), 5–10	arXiv (last updated 7/29/09) Journal Macaulay2 package
A bijective proof for a theorem of Ehrhart, Amer. Math. Monthly 116 (2009), no. 8, 688–701.	arXiv (last updated 6/27/08) Journal
Grid graphs, Gorenstein polytopes, and domino stackings (with Matthias Beck and Christian Haase), to appear in Graphs Combin..	arXiv (last updated 4/28/09)
Maximal periods of (Ehrhart) quasi-polynomials (with Matthias Beck and Kevin M. Woods), J. Combin. Theory Ser. A 115 (2008), 517–525.	arXiv (last updated 8/17/07) Journal MathSciNet

The Caldero–Chapoton formula for cluster algebras (10 pages) — My final paper for 18.735 (quivers in representation theory). It proves the Caldero–Chapoton formula for writing down cluster variables in coefficient-free finite type cluster algebras using Euler characteristics of quiver Grassmannians. Last updated 5/1/09.
Computing syzygies with Gröbner bases (6 pages) — My report for my presentation for the University of Utah REU on computational algebraic geometry. Last updated 7/2/08.
Schur functors and equivariant resolutions (38 pages) — My undergraduate senior thesis. Written at Berkeley, spring 2008, under the supervision of David Eisenbud. It discusses Betti diagrams of finitely generated modules over polynomial rings and their relation to cohomology tables of vector bundles on projective space, as well as my implementation of SchurFunctors.m2 (see software section) which computes pure free resolutions in characteristic 0 via representations of the general linear group. Last updated 7/17/08.
Note: Some time after I wrote my thesis, my package has been renamed to PieriMaps, and SchurFunctors now refers to a different package. I have also been rewriting parts of the code and user interface for PieriMaps, so the user manual section in my thesis is deprecated. The user interested in using this code is pointed to my article "Computing inclusions of Schur modules" (see above). The paper "Pieri resolutions for classical groups" is a sort of sequel to my thesis.

Sometimes when I give a lecture, I prepare notes to organize my thoughts. I'll post these here.

Notes on algebraic K-theory (4 pages) — some notes I wrote up while preparing my lecture on Quillen's paper Higher algebraic K-theory I. in the graduate topology seminar 18.915 at MIT. Last updated 9/29/08.
Representability by sums of squares (2 pages) — A proof of Lagrange's four square theorem: every positive integer can be written as the sum of four squares. Notes for a talk I gave in the Many Cheerful Facts seminar at Berkeley. I got this proof from a summer mini-course taught by Christian Haase, but I do not know whose proof it is. Last updated 3/6/08.

Infinitude of primes (2 pages) — I am collecting interesting proofs of the fact that there are infinitely many primes. Last updated 4/2/08.
Period collapse list — A bunch of nonintegral polygons whose Ehrhart quasi-polynomial has smaller than expected period. I'm sure a lot of them are affinely equivalent. I reduced the fractions myself, so this might contain some typos.

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