Companion forms for unitary and symplectic groups

We prove a companion forms theorem for ordinary n-dimensional automorphic Galois representations, by use of automorphy lifting theorems developed by the second author, and a technique for deducing companion forms theorems due to the first author. We deduce results about the possible Serre weights of mod l Galois representations corresponding to automorphic representations on unitary groups. We then use functoriality to prove similar results for automorphic representations of GSp4 over totally real fields.Comment: 40 page

Congruences between Hilbert modular forms: constructing ordinary lifts

Under mild hypotheses, we prove that if F is a totally real field, k is the algebraic closure of the finite field with l elements and r : G_F --> GL_2(k) is irreducible and modular, then there is a finite solvable totally real extension F'/F such that r|_{G_F'} has a modular lift which is ordinary at each place dividing l. We deduce a similar result for r itself, under the assumption that at places v|l the representation r|_{G_F_v} is reducible. This allows us to deduce improvements to results in the literature on modularity lifting theorems for potentially Barsotti-Tate representations and the Buzzard-Diamond-Jarvis conjecture. The proof makes use of a novel lifting technique, going via rank 4 unitary groups.Comment: 48 page

The Sato-Tate conjecture for Hilbert modular forms

We prove the Sato-Tate conjecture for Hilbert modular forms. More precisely, we prove the natural generalisation of the Sato-Tate conjecture for regular algebraic cuspidal automorphic representations of \GL_2(\A_F), $F$ a totally real field, which are not of CM type. The argument is based on the potential automorphy techniques developed by Taylor et. al., but makes use of automorphy lifting theorems over ramified fields, together with a 'topological' argument with local deformation rings. In particular, we give a new proof of the conjecture for modular forms, which does not make use of potential automorphy theorems for non-ordinary $n$-dimensional Galois representations.Comment: 59 pages. Essentially final version, to appear in Journal of the AMS. This version does not incorporate any minor changes (e.g. typographical changes) made in proo

Local-global compatibility for l=p, II

We prove the compatibility at places dividing l of the local and global Langlands correspondences for the l-adic Galois representations associated to regular algebraic essentially (conjugate) self-dual cuspidal automorphic representations of GL_n over an imaginary CM or totally real field. We prove this compatibility up to semisimplification in all cases, and up to Frobenius semisimplification in the case of Shin-regular weight.Comment: 13 page

Sufferers of the Revolution : the paper money movement in Brunswick County, Virginia, 1780-1787

The years following the American War for Independence were marked by economic decline and political uncertainty. In the mid-1780s, Virginia was mired in a depression that gave rise to a vocal movement that called for a return to a policy of emitting paper currency to augment scarce supplies of gold and silver coin. While historians have discussed Virginia\u27s monetary situation at length there has never been a satisfactory examination of the people who supported this particular movement. Petitions from Brunswick County residents who backed emissions of paper money provide an opportunity to develop a more accurate portrait of this group. Correlating petitioners with data such as their wealth in terms of real and personal property, voting patterns, and creditor/debtor status achieved this enhanced understanding. It is clear that Brunswick\u27s paper money movement drew support from a cross-section of the community and especially from those who struggled with debt

A review of bovine Johne's disease control activities in 6 endemically infected countries

Mycobacterium avium subspecies paratuberculosis (MAP) is endemic in the bovine populations of many countries and can cause a significant reduction in animal welfare and production efficiency making control desirable. Effective control has proved very difficult to achieve despite multiple regionally coordinated programmes being in existence since the 1920s. The international community increasingly recognises the value in learning from the collective experiences of existing programmes to improve the effectiveness of control. The aim of this review is to outline key aspects of bovine Johne's disease control activities across 6 endemically infected countries to facilitate comparison of current international practice. The background, control activities and monitoring components of programmes in Australia, Canada, Denmark, the Netherlands, the United Kingdom and the United States of America were individually reviewed. Factual accuracy of each review was checked by individuals involved in the respective programmes before the reviews were condensed and combined into a single document presented here, with the complete reviews of each programme available as supplementary material. There was considerable heterogeneity in key aspects of control activity design including goals, responses to declining participation, herd classification, recommended control measures and associated test requirements. The data presented will be of interest to organisations that are involved in developing new or existing regionally coordinated BJD control activities

Fabrication and Comprehensive Modeling of Ion-Exchanged Bragg Opitcal Add-Drop Multiplexers

Optical add–drop multiplexers (OADMs) based on asymmetric Y branches and tilted gratings offer excellent-performance in wavelength-division multiplexed systems. To simplify waveguide fabrication, ion-exchange techniques appear to be an important option in photosensitive glasses. Optimum OADM performance depends on how accurately the waveguide fabrication process and tilted Bragg grating operation are understood and modeled. Results from fabrication and comprehensive modeling are compared for ion-exchange processes that use different angles of the tilted grating. The transmission and reflection spectra for the fabricated and simulated OADMs show excellent agreement. The OADM’s performance is evaluated in terms of the measured characteristics of the Y branches and tilted gratings