On Poisson Structure and Curvature

We consider a curved space-time whose algebra of functions is the commutative limit of a noncommutative algebra and which has therefore an induced Poisson structure. In a simple example we determine a relation between this structure and the Riemann tensor.Comment: 8 pages, Late

Sigma One

We demonstrate that it is possible to calculate not only the mean of an underlying population but also its dispersion, given only a single observation and physically reasonable constraints (i.e., that the quantities under consideration are non-negative and bounded). We suggest that this counter-intuitive conclusion is in fact at the heart of most modeling of astronomical data.Comment: Accepted to the Astronomical Journal. 13 pages, 4 figure

Classical Gravity on Fuzzy Space-Time

A review is made of recent efforts to find relations between the commutation relations which define a noncommutative geometry and the gravitational field which remains as a shadow in the commutative limit.Comment: Lecture given at the 30th International Symposium Ahrenshoop on the Theory of Elementary Particles, Buckow, Germany, August 27-31, 1996; 11 Pages LaTe

Fuzzy Space-Time

A review is made of recent efforts to define linear connections and their corresponding curvature within the context of noncommutative geometry. As an application it is suggested that it is possible to identify the gravitational field as a phenomenological manifestation of space-time commutation relations and to thereby clarify its role as an ultraviolet regularizer.Comment: 17 pages LaTe

Two New Tests of the Metallicity Sensitivity of the Cepheid Period-Luminosity Relation (The Leavitt Law)

We undertake a new test of the metallicity sensitivity of the Leavitt Law for Classical Cepheids. We derive an empirical calibration of the apparent luminosities of Cepheids as measured from the optical through the mid-infrared (0.45-8.0um) as a function of spectroscopic [Fe/H] abundances of individual Cepheids in the Large Magellanic Cloud from Romaniello et al. (2008). The cumulative trend over the entire wavelength range shows a nearly monotonic behavior. The sense of the trend is consistent with differential line-blanketing in the optical, leading to stars of high metallicity being fainter in the optical. This is followed by a reversal in the trend at longer wavelengths, with the cross-over occurring near the K band at about 2.2um, consistent with a subsequent redistribution of energy resulting in a mild brightening of Cepheids (with increased metallicity) at mid-infrared wavelengths. This conclusion agrees with that of Romaniello et al. based on a differential comparison of the mean V- and K-band Leavitt Laws for the Galaxy, SMC and LMC, but is opposite in sign to most other empirical tests of the sensitivity of Cepheid distances to mean [O/H] HII region abundances. We also search for a correlation of Cepheid host-galaxy metallicity with deviations of the galaxy's Cepheid distance from that predicted from a pure Hubble flow. Based on Cepheid distances to 26 nearby galaxies in the local flow, only a very weak signal is detected giving Dmu_o = -0.17 (+/- 0.31) ([O/H] - 8.80) - 0.21 (+/-0.10). This is in agreement with previous determinations, but statistically inconclusive.Comment: Accepted to the Astrophysical Journal. 8 pages, 5 figures, 1 tabl

Connes' Model Building Kit

Alain Connes' applications of non-commutative geometry to interaction physics are described for the purpose of model building.Comment: 35 pages, LATeX, CPT-93/P.296

Fuzzy Surfaces of Genus Zero

A fuzzy version of the ordinary round 2-sphere has been constructed with an invariant curvature. We here consider linear connections on arbitrary fuzzy surfaces of genus zero. We shall find as before that they are more or less rigidly dependent on the differential calculus used but that a large number of the latter can be constructed which are not covariant under the action of the rotation group. For technical reasons we have been forced to limit our considerations to fuzzy surfaces which are small perturbations of the fuzzy sphere.Comment: 11 pages, Late