Algebraic Unimodular Counting

We study algebraic algorithms for expressing the number of non-negative integer solutions to a unimodular system of linear equations as a function of the right hand side. Our methods include Todd classes of toric varieties via Gr\"obner bases, and rational generating functions as in Barvinok's algorithm. We report polyhedral and computational results for two special cases: counting contingency tables and Kostant's partition function.Comment: 21 page

Not all simplicial polytopes are weakly vertex-decomposable

In 1980 Provan and Billera defined the notion of weak $k$-decomposability for pure simplicial complexes. They showed the diameter of a weakly $k$-decomposable simplicial complex $\Delta$ is bounded above by a polynomial function of the number of $k$-faces in $\Delta$ and its dimension. For weakly 0-decomposable complexes, this bound is linear in the number of vertices and the dimension. In this paper we exhibit the first examples of non-weakly 0-decomposable simplicial polytopes

Stellar Populations in Spiral Galaxies

We report preliminary results of the characterization of bulge and inner disk stellar populations for 8 nearby spiral galaxies using Gemini/GMOS. The long-slit spectra extend out to 1-2 disk scale lengths with S/N/Ang > 50. Two different model fitting techniques, absorption-line indices and full spectral synthesis, are found to weigh age, metallicity, and abundance ratios differently, but with careful attention to the data/model matching (resolution and flux calibration), we are able constrain real signatures of age and metallicity gradients in star-forming galaxies.Comment: 4 pages, 3 figures. To appear in the proceedings for IAUS 241 "Stellar Populations as Building Blocks of Galaxies", Eds. R.F. Peletier and A. Vazdeki