Variations of Hodge Structure Considered as an Exterior Differential System: Old and New Results

This paper is a survey of the subject of variations of Hodge structure (VHS) considered as exterior differential systems (EDS). We review developments over the last twenty-six years, with an emphasis on some key examples. In the penultimate section we present some new results on the characteristic cohomology of a homogeneous Pfaffian system. In the last section we discuss how the integrability conditions of an EDS affect the expected dimension of an integral submanifold. The paper ends with some speculation on EDS and Hodge conjecture for Calabi-Yau manifolds

Extremal degenerations of polarized Hodge structures

We describe a Hodge theoretic approach to the question: In what ways can a smooth projective variety degenerate?Comment: v.2 (typos corrected), comments welcom

Underwater optical wireless communications : depth dependent variations in attenuation

Depth variations in the attenuation coefficient for light in the ocean were calculated using a one-parameter model based on the chlorophyll-a concentration Cc and experimentally-determined Gaussian chlorophyll-depth profiles. The depth profiles were related to surface chlorophyll levels for the range 0–4  mg/m2, representing clear, open ocean. The depth where Cc became negligible was calculated to be shallower for places of high surface chlorophyll; 111.5 m for surface chlorophyll 0.8<Cc<2.2  mg/m3 compared with 415.5 m for surface Cc<0.04  mg/m3. Below this depth is the absolute minimum attenuation for underwater ocean communication links, calculated to be 0.0092  m−1 at a wavelength of 430 nm. By combining this with satellite surface-chlorophyll data, it is possible to quantify the attenuation between any two locations in the ocean, with applications for low-noise or secure underwater communications and vertical links from the ocean surface

Liberty, National Security and the Big Society

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Period Mappings and Ampleness of the Hodge line bundle

We discuss progress towards a conjectural Hodge theoretic completion of a period map. The completion is defined, and we conjecture that it admits the structure of a compact complex analytic variety. The conjecture is proved when the image of the period map has dimension 1,2. Assuming the conjecture holds, we then prove that the augmented Hodge line bundle extends to an ample line bundle on the completion. In particular, the completion is a projective algebraic variety that compactifies the image, analogous to the Satake-Baily-Borel compactification.Comment: 62 pages. v2 significant revision of the initial submission (v1); v3 further improvements and new references adde