The Quantum McKay Correspondence for polyhedral singularities

Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity C^3/G. The classical McKay correspondence describes the classical geometry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over the positive roots of R. In terms of counts of BPS states (Gopakumar-Vafa invariants), our result can be stated as a correspondence: each positive root of R corresponds to one half of a genus zero BPS state. As an application, we use the crepant resolution conjecture to provide a full prediction for the orbifold Gromov-Witten invariants of [C^3/G].Comment: Introduction rewritten. Issue regarding non-uniqueness of conifold resolution clarified. Version to appear in Inventione

ALMA Thermal Observations of Europa

We present four daytime thermal images of Europa taken with the Atacama Large Millimeter Array. Together, these images comprise the first spatially resolved thermal dataset with complete coverage of Europa's surface. The resulting brightness temperatures correspond to a frequency of 233 GHz (1.3 mm) and a typical linear resolution of roughly 200 km. At this resolution, the images capture spatially localized thermal variations on the scale of geologic and compositional units. We use a global thermal model of Europa to simulate the ALMA observations in order to investigate the thermal structure visible in the data. Comparisons between the data and model images suggest that the large-scale daytime thermal structure on Europa largely results from bolometric albedo variations across the surface. Using bolometric albedos extrapolated from Voyager measurements, a homogenous model reproduces these patterns well, but localized discrepancies exist. These discrepancies can be largely explained by spatial inhomogeneity of the surface thermal properties. Thus, we use the four ALMA images to create maps of the surface thermal inertia and emissivity at our ALMA wavelength. From these maps, we identify a region of either particularly high thermal inertia or low emissivity near 90 degrees West and 23 degrees North, which appears anomalously cold in two of our images.Comment: 9 pages, 3 figures, accepted for publication in the Astronomical Journa