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

Fermions in odd space-time dimensions: back to basics

It is a well known feature of odd space-time dimensions $d$ that there exist two inequivalent fundamental representations $A$ and $B$ of the Dirac gamma matrices. Moreover, the parity transformation swaps the fermion fields living in $A$ and $B$. As a consequence, a parity invariant Lagrangian can only be constructed by incorporating both the representations. Based upon these ideas and contrary to long held belief, we show that in addition to a discrete exchange symmetry for the massless case, we can also define chiral symmetry provided the Lagrangian contains fields corresponding to both the inequivalent representations. We also study the transformation properties of the corresponding chiral currents under parity and charge conjugation operations. We work explicitly in 2+1 dimensions and later show how some of these ideas generalize to an arbitrary number of odd dimensions.Comment: 8 pages, no figure

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

On causality violation in Lyra Geometry

In this paper the causality issues are discussed in a non-Riemannian geometry, called Lyra geometry. It is a non-Riemannian geometry originated from Weyl geometry. In order to compare this geometry with the Riemannian geometry, the Einstein field equations are considered. It is verified that the G\"{o}del and G\"{o}del-type metric are consistent with this non-Riemannian geometry. A non-trivial solution for G\"{o}del universe in the absence of matter sources is determined without analogue in general relativity. Different sources are considered and then different conditions for causal and non-causal solutions are discussed.Comment: 13 pages, accepted for publication in Int. J. Geom. Meth. Mod. Phy