Computing Hilbert Class Polynomials

We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm which uses the class group action on CM-curves over finite fields. Our run time analysis gives tighter bounds for the complexity of all known algorithms for computing $H_D$, and we show that all methods have comparable run times

Oscillatory subglacial drainage in the absence of surface melt

The presence of strong diurnal cycling in basal water pressure records obtained during the melt season is well established for many glaciers. The behaviour of the drainage system outside the melt season is less well understood. Here we present borehole observations from a surge-type valley glacier in the St Elias Mountains, Yukon Territory, Canada. Our data indicate the onset of strongly correlated multi-day oscillations in water pressure in multiple boreholes straddling a main drainage axis, starting several weeks after the disappearance of a dominant diurnal mode in August 2011 and persisting until at least January 2012, when multiple data loggers suffered power failure. Jökulhlaups provide a template for understanding spontaneous water pressure oscillations not driven by external supply variability. Using a subglacial drainage model, we show that water pressure oscillations can also be driven on a much smaller scale by the interaction between conduit growth and distributed water storage in smaller water pockets, basal crevasses and moulins, and that oscillations can be triggered when water supply drops below a critical value. We suggest this in combination with a steady background supply of water from ground water or englacial drainage as a possible explanation for the observed wintertime pressure oscillations

Some genus 3 curves with many points

Using an explicit family of plane quartic curves, we prove the existence of a genus 3 curve over any finite field of characteristic 3 whose number of rational points stays within a fixed distance from the Hasse-Weil-Serre upper bound. We also provide an intrinsic characterization of so-called Legendre elliptic curves

Reducing the linewidth of a diode laser below 30 Hz by stabilization to a reference cavity with finesse above 10^5

An extended cavity diode laser operating in the Littrow configuration emitting near 657 nm is stabilized via its injection current to a reference cavity with a finesse of more than 10^5 and a corresponding resonance linewidth of 14 kHz. The laser linewidth is reduced from a few MHz to a value below 30 Hz. The compact and robust setup appears ideal for a portable optical frequency standard using the Calcium intercombination line.Comment: 8 pages, 4 figures on 3 additional pages, corrected version, submitted to Optics Letter

West Antarctic ice sheet and CO2 greenhouse effect: a threat of disaster

DIB's contribution to this work is from the DOMINOS project, a component of the International Thwaites Glacier Collaboration (ITGC). Support for DIB was provided by the Natural Environment Research Council (NERC: Grant NE/S006605/1). ITGC Contribution No. ITGC:025.Over 40 years ago, the glaciologist John Mercer warned that parts of the West Antarctic Ice Sheet were at risk of collapse due to the CO2 greenhouse effect. Mercer recognised the unique vulnerability of ice sheets resting on beds far below sea level (marine-based ice sheets), where an initial warming signal can initiate irreversible retreat. In this paper, we review recent work on evidence for ice sheet collapse in warmer periods of the recent geological past, the current behaviour of the ice sheet, and computer models used to predict future ice-sheet response to global warming. Much of this work points in the same direction: warming climates can indeed trigger collapse of marine-based portions of the West Antarctic Ice Sheet, and retreat in response to recent warming has brought parts of the ice sheet to the threshold of instability. Further retreat appears to be inevitable, but the rate of collapse depends critically on future emissions.Publisher PDFPeer reviewe