Tropical images of intersection points

A key issue in tropical geometry is the lifting of intersection points to a non-Archimedean field. Here, we ask: Where can classical intersection points of planar curves tropicalize to? An answer should have two parts: first, identifying constraints on the images of classical intersections, and, second, showing that all tropical configurations satisfying these constraints can be achieved. This paper provides the first part: images of intersection points must be linearly equivalent to the stable tropical intersection by a suitable rational function. Several examples provide evidence for the conjecture that our constraints may suffice for part two.Comment: 13 pages, 9 figure

Through the Looking Glass

It is frequently possible to produce new Calabi-Yau threefolds from old ones by a process of allowing the complex structure to degenerate to a singular one, and then performing a resolution of singularities. (Some care is needed to ensure that the Calabi-Yau condition be preserved.) There has been speculation that all Calabi-Yau threefolds could be linked in this way, and considerable evidence has been amassed in this direction. We propose here a natural way to relate this construction to the string-theoretic phenomenon known as ``mirror symmetry.'' We formulate a conjecture which in principle could predict mirror partners for all Calabi-Yau threefolds, provided that all were indeed linked by the degeneration/resolution process. The conjecture produces new mirrors from old, and so requires some initial mirror manifold construction---such as Greene-Plesser orbifolding---as a starting point. (Lecture given at the CIRM conference, Trento, June 1994, and at the Workshop on Complex Geometry and Mirror Symmetry, Montr\'eal, March 1995.)Comment: latex2e, 22 pages with 1 figur

Compactifications of moduli spaces inspired by mirror symmetry

We study moduli spaces of nonlinear sigma-models on Calabi-Yau manifolds, using the one-loop semiclassical approximation. The data being parameterized includes a choice of complex structure on the manifold, as well as some ``extra structure'' described by means of classes in H^2. The expectation that this moduli space is well-behaved in these ``extra structure'' directions leads us to formulate a simple and compelling conjecture about the action of the automorphism group on the K\"ahler cone. If true, it allows one to apply Looijenga's ``semi-toric'' technique to construct a partial compactification of the moduli space. We explore the implications which this construction has concerning the properties of the moduli space of complex structures on a ``mirror partner'' of the original Calabi-Yau manifold. We also discuss how a similarity which might have been noticed between certain work of Mumford and of Mori from the 1970's produces (with hindsight) evidence for mirror symmetry which was available in 1979. [The author is willing to mail hardcopy preprints upon request.]Comment: 25 pp., LaTeX 2.09 with AmS-Font

Heavy-duty staple remover operated by hand

To remove staples from thick reports, a rooter, bending hook and post are incorporated into a heavy duty hand tool. This makes possible one-step extraction of long staples

Suspension cell culture in microgravity and development of a space bioreactor

NASA has methodically developed unique suspension type cell and recovery apparatus culture systems for bioprocess technology experiments and production of biological products in microgravity. The first space bioreactor has been designed for microprocessor control, no gaseous headspace, circulation and resupply of culture medium, and slow mixing in very low shear regimes. Various ground based bioreactors are being used to test reactor vessel design, on-line sensors, effects of shear, nutrient supply, and waste removal from continuous culture of human cells attached to microcarriers. The small (500 ml) bioreactor is being constructed for flight experiments in the Shuttle middeck to verify systems operation under microgravity conditions and to measure the efficiencies of mass transport, gas transfer, oxygen consumption, and control of low shear stress on cells