Symmetry via Lie algebra cohomology

The Killing operator on a Riemannian manifold is a linear differential operator on vector fields whose kernel provides the infinitesimal Riemannian symmetries. The Killing operator is best understood in terms of its prolongation, which entails some simple tensor identities. These simple identities can be viewed as arising from the identification of certain Lie algebra cohomologies. The point is that this case provides a model for more complicated operators similarly concerned with symmetry.Comment: Conference proceedings: JARCS Sydney 2009 (The Australian-Japanese Workshop on Real and Complex Singularities held at the University of Sydney

Extensions of the coeffective complex

The coeffective differential complex on a symplectic manifold is extended both in length and in scope, unifying the constructions of various other authors.Comment: 9 page

Do higher solvency ratios reduce the costs of bailing out insured banks?

The relationship between solvency constraints and bank behaviour in the presence of fixed rate deposit insurance is investigated. A rise in the minimum solvency ratio does not necessarily reduce the adverse consequences of moral hazard: bank efficiency may fall and expected bailout costs may rise. Such outcomes are possible even if credit risk is purely systemic. Similar results obtain in respect of level increases in bank capital, tangible or intangible, although in this case purely systemic risk excludes perverse outcomes

Higher Order Connections

The purpose of this article is to present the theory of higher order connections on vector bundles from a viewpoint inspired by projective differential geometry