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We make an imaginative comparison between the Minimal Supersymmetric Standard Model and the 24‐cell polytope in four dimensions, the Octacube.;
We outline the solution of the Killing spinor equations of the heterotic supergravity. In addition, we describe the classification of all half supersymmetric solutions.
We first review the notion of a G 2 —manifold, defined in terms of a principal ; G 2 (“gauge”) bundle over a 7—dimensional manifold, before discussing their relation to supergravity. In a second thread, we focus on associative submanifolds and present their deformation theory. In...
The spinorial geometry method is an effective method for constructing systematic classifications of supersymmetric supergravity solutions. Recent work on analysing highly supersymmetric solutions in type IIB supergravity using this method is reviewed 1, 2. It is shown that all supersymmetric...
We construct stable sheaves over K3 fibrations using a relative Fourier‐Mukai transform which describes the sheaves in terms of spectral data. This procedure is similar to the construction for elliptic fibrations, which we also describe. On K3 fibered Calabi‐Yau threefolds, we show that the...
A computer assisted approach is presented for the cohomological uniqueness of Kähler metrics conformal to Einstein metrics on the two point blow‐up of ; C P 2 .
The main result of 2 extends the Marsden‐Ratiu reduction theorem 4 in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof in 2. Further, we provide an alternative algebraic proof for the main...
We study the (generalized Dolbeault) cohomology of generalized complex manifolds in 4 real dimensions. We show that in 4 real dimensions, the first cohomology around a nondegenerate type change point is given by holomorphic (1,0) forms defined on the type change locus. We use this to compute the...
Four‐dimensional Osserman metrics are reviewed by focusing on their connection with Einstein self‐dual structures. Special attention is paid to the nondiagonalizability of the self‐dual Weyl curvature operator.;