The Strominger-Yau-Zaslow conjecture: From torus fibrations to degenerations

This survey article begins with a discussion of the original form of the Strominger-Yau-Zaslow conjecture, surveys the state of knowledge concering this conjecture, and explains how thinking about this conjecture naturally leads to the program initiated by the author and Bernd Siebert to study mirror symmetry via degenerations of Calabi-Yau manifolds and log structures.Comment: 44 pages, to appear in the Proceedings of the 2005 AMS Symposium on Algebraic Geometry, Seattl

Virus Reduction by the Stanford Onsite Wastewater Treatment System

A field study to examine the Stanford Onsite Wastewater Treatment System\u27s ability to remove bacteriophage from wastewater was conducted. MS2 Coliphage was Injected Into the low pressure pipe (LPP) distribution system to achieve an Influent concentration of 1.6 x 106 plague forming units per milliliter (PFU/ml). The bacteriophage was Injected Into the system three times during the day, and samples were taken from drainage tiles of the treatment system. Tile drainage was assayed on conform bacteria host cultures for MS2 phage. The treatment system removed two to three logs (99% to 99.9%) of the phage. During the past two years, the treatment system has also reduced total organic carbon from 55 mg/1 to 5 mg/1. The system also reduced the ammonium-nitrogen concentration from 41 mg/1 to 1 mg/1. The nitrate-nitrogen concentration rose from less than 1 mg/1 1n the Influent to 4 mg/1 1n the effluent. Over the past two years, the geometric mean fecal coliform concentration was 18 colony-forming units per ml (CFU/ml). The effluent water quality meets the Arkansas Department of Health, Standards for Outdoor Bathing Places

The moduli space of (1,11)-polarized abelian surfaces is unirational

We prove that the moduli space A_{11}^{lev} of (1,11) polarized abelian surfaces with level structure of canonical type is birational to Klein's cubic hypersurface: a^2b+b^2c+c^2d+d^2e+e^2a=0 in P^4. Therefore, A_{11}^{lev} is unirational but not rational, and there are no Gamma_{11}-cusp forms of weight 3. The same methods also provide an easy proof of the rationality of A_{9}^{lev}.Comment: 27 pages, TeX with diagrams.tex. Related Macaulay2 code and PostScript file available at http://www.math.columbia.edu/~psorin