The diagrammatic cumulant expansion for the periodic Anderson model with infinite Coulomb repulsion (U = ∞) is considered here for an hypercubic lattice of infinite dimension (d = ∞). The nearest neighbour hopping of the uncorrelated electrons is described exactly by a conduction band, while two different models of hybridization are treated as a perturbation. The same type of simplifications obtained by Metzner for the cumulant expansion of the Hubbard model in the limit of d = ∞, are also shown to be valid for the periodic Anderson model. The derivation of these properties had to be modified because of the exact treatment of the conduction band. § Associate Member of ICTP,

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We consider the polarization of unstable type-IIB D0-branes in the presence of a background five-form field strength. This phenomenon is studied from the point of view of the leading terms in the non-abelian Born Infeld action of the unstable D0-branes. The equations have SO(4) invariant solutions describing a non-commutative 3-sphere, which becomes a classical 3-sphere in the large-N limit. We discuss the interpretation of these solutions as spherical D3-branes. The tachyon plays a tantalizingly geometrical role in relating the fuzzy S 3 geometry to that of a fuzzy S 4 .

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