Heart and Minds: A Social Model of U.S. Productivity Growth

macroeconomics, product growth

Positive curvature and the elliptic genus

We prove several results about the vanishing of the elliptic genus on positively curved Spin manifolds with logarithmic symmetry rank. The proofs are based on the rigidity of the elliptic genus and Kennard's improvement of the Connectedness Lemma for transversely intersecting, totally geodesic submanifolds.Comment: 15 pages. Paper was rewritten. To appear in New York Journal of Mathematic

Non-Perturbative Mass and Charge Renormalization in Relativistic No-Photon Quantum Electrodynamics

Starting from a formal Hamiltonian as found in the physics literature -- omitting photons -- we define a renormalized Hamiltonian through charge and mass renormalization. We show that the restriction to the one-electron subspace is well-defined. Our construction is non-perturbative and does not use a cut-off. The Hamiltonian is relevant for the description of the Lamb shift in muonic atoms.Comment: Reformulation of main theorem, minor changes in the proo

Six Years of Chandra Observations of Supernova Remnants

We present a review of the first six years of Chandra X-ray Observatory observations of supernova remnants. From the official "first-light" observation of Cassiopeia A that revealed for the first time the compact remnant of the explosion, to the recent million-second spectrally-resolved observation that revealed new details of the stellar composition and dynamics of the original explosion, Chandra observations have provided new insights into the supernova phenomenon. We present an admittedly biased overview of six years of these observations, highlighting new discoveries made possible by Chandra's unique capabilities.Comment: 82 pages, 28 figures, for the book Astrophysics Update

The variability of the Crab Nebula in radio: No radio counterpart to gamma-ray flares

We present new Jansky Very Large Array (VLA) radio images of the Crab Nebula at 5.5 GHz, taken at two epochs separated by 6 days about two months after a gamma-ray flare in 2012 July. We find no significant change in the Crab's radio emission localized to a region of <2 light-months in radius, either over the 6-day interval between our present observations or between the present observations and ones from 2001. Any radio counterpart to the flare has a radio luminosity of <~ $2 \times 10^{-4}$ times that of the nebula. Comparing our images to one from 2001, we do however find changes in radio brightness, up to 10% in amplitude, which occur on decade timescales throughout the nebula. The morphology of the changes is complex suggesting both filamentary and knotty structures. The variability is stronger, and the timescales likely somewhat shorter, nearer the centre of the nebula. We further find that even with the excellent uv~coverage and signal-to-noise of the VLA, deconvolution errors are much larger than the noise, being up to 1.2% of peak brightness of the nebula in this particular case.Comment: Accepted to MNRAS; 13 pages, 6 figure