On the notion of conductor in the local geometric Langlands correspondence

Under the local Langlands correspondence, the conductor of an irreducible representation of \Gl_n(F) is greater than the Swan conductor of the corresponding Galois representation. In this paper, we establish the geometric analogue of this statement by showing that the conductor of a categorical representation of the loop group is greater than the irregularity of the corresponding meromorphic connection.Comment: Minor report following referees report. To appear in Canadian Journal of Mat

Three Bands Concert Spring 2009

The School of Performing Arts submitted this proposal in September, but we need to resubmit the request because the guest conductor became unavailable. This is the exact same proposal, with two exceptions: substituting the original guest conductor (Tony Maiello) with a different conductor (Denton Stokes), and we are requesting a total of $1,000 rather than$2,000. Mr. Stokes, although well-noted (bio is on following page), does not have the same national ranking as did Mr. Maiello

Decohering d-dimensional quantum resistance

The Landauer scattering approach to 4-probe resistance is revisited for the case of a d-dimensional disordered resistor in the presence of decoherence. Our treatment is based on an invariant-embedding equation for the evolution of the coherent reflection amplitude coefficient in the length of a 1-dimensional disordered conductor, where decoherence is introduced at par with the disorder through an outcoupling, or stochastic absorption, of the wave amplitude into side (transverse) channels, and its subsequent incoherent re-injection into the conductor. This is essentially in the spirit of B{\"u}ttiker's reservoir-induced decoherence. The resulting evolution equation for the probability density of the 4-probe resistance in the presence of decoherence is then generalised from the 1-dimensional to the d-dimensional case following an anisotropic Migdal-Kadanoff-type procedure and analysed. The anisotropy, namely that the disorder evolves in one arbitrarily chosen direction only, is the main approximation here that makes the analytical treatment possible. A qualitatively new result is that arbitrarily small decoherence reduces the localisation-delocalisation transition to a crossover making resistance moments of all orders finite.Comment: 14 pages, 1 figure, revised version, to appear in Phys. Rev.

Frequency Following Imaging of Electric Fields from Resonant Superconducting Devices using a Scanning Near-Field Microwave Microscope

We have developed a scanning near-field microwave microscope that operates at cryogenic temperatures. Our system uses an open-ended coaxial probe with a 200 mm inner conductor diameter and operates from 77 to 300 K in the 0.01-20 GHz frequency range. In this paper, we present microwave images of the electric field distribution above a Tl2Ba2CaCu2O8 microstrip resonator at 77 K, measured at several heights. In addition, we describe the use of a frequency-following circuit to study the influence of the probe on the resonant frequency of the device.Comment: 4 pages, postscript file with 6 figures conference proceeding for the Applied Superconductivity Conference 199

On the bending effects of a copper-type down conductor

Down-conductor is part of critical component in the external Lightning Protection System (LPS) as to divert the lightning current from the air termination to the earth termination system of protected structure. In this paper, numerical analysis approach incorporating the effect of copper conductor bending angle under current transient and voltage is utilized. Various angles of copper conductor will be synthesized following a simplified and generic, but meticulous, model based on the manufacturer's datasheet specification which is normally used. The fields were analyzed and the results were discussed in comparison with the MS IEC 62305-3 standard accordingly. In this case, the cross-sectional area of down-conductor was selected based on the accessible type produced by various manufacturers as proposed by the MS IEC 62305-3 standard for a critical study. This study presents the optimum angle of down-conductor with a view to develop a practical approach and to set the down-conductors in a confined area locations of a building