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    <title><string language="fre"><![CDATA[Rod Gover - An introduction to conformal geometry and tractor calculus (Part 1)]]></string></title>
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        <string language="fre"><![CDATA[After recalling    some    features    (and    the    value    of)    the    invariant    ``Ricci calculus''    of    pseudo-­‐Riemannian    geometry,    we    look    at    conformal rescaling    from    an    elementary    perspective.    The    idea    of    conformal covariance    is    visited    and    some    covariant/invariant    equations    from physics    are    recovered    in    this    framework.    Motivated    by    the    need    to    develop a    more    effective    approach    to    such    problems    we    are    led    into    the    idea    of conformal    geometry    and    a conformally    invariant    calculus;    this``tractor    calculus''    is    then    developed    explicitly.    We    will    discuss    how to    calculate    using    this,    and    touch    on    applications    to    the    construction of    conformal    invariants    and    conformally    invariant    differential    operators. The    second    part    of    the    course    is    concerned    with    the    application    of conformal    geometry and    tractor    calculus    for    the    treatment    of    conformal compactification    and    the    geometry    of    conformal    infinity. The    link with    Friedrich’s    conformal    field    equations    will    be    made. As    part    of this    part    we    also    dedicate    some    time    to    the    general    problem    of treating    hypersurfaces    in    a    conformal    manifold,    and    in    particular arrive    at    a    conformal    Gauss    equation.    Finally    we    show    how    these    tools    maybe    applied    to    treat    aspects    of    the    asymptotic    analysis    of    boundary problems    on    conformally    compact    manifolds.]]></string></description>
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