Gauge gravity duality and new geometrical structures

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The project will focus on the implications of the gauge gravity correspondence for geometry. In particular, it implies a relationship between algebraic structures (such as Calabi-Yau algebras) on the one hand and new differential geometrical structures (extensions of Hitchin's notion of generalised geometry) on the other. One concrete conjecture is that the cyclic cohomology of the algebra is equal to a new generalisation of Dolbeault cohomololgy on the manifold. This will give new insight into topics ranging from Hilbert series of quiver theories, to topological strings, to black hole state counting, to new hyper-Kahler quotient constructions. The student will start by learning some of the basics of both sides of the physical correspondence, and the underlying mathematics, then focus on a number of new examples: these include marginal deformations of the general class of Ypq geometries, the Plich-Warner geometries and flows between Pilch-Warner and T11, and in particular, geometries dual to wrapped M5-brane theories.