Geometrical aspects of string theory and supergravity

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String theory provides a framework for investigating how quantum theory modifies the geometry of space-time. Very recently para-Hermitian geometry has been advocated as a way to unify older attempts at a genuine `string geometry', such as doubled geometry and generalized geometry. The project will aim to develop the para-Hermitian approach systematically and to combine it with other modern global approaches to the geometry of both space-time and moduli spaces. It will take into account other recent developments, such as the inclusion of exotic space-time phases which can be realized in string theory through duality transformations. One emphasis of the project will be to work out new explicit examples which allow to clarify to which extent proposed generalizations of geometrical concepts lead to new and interesting physics. Possible case studies include: (i) how do the effective field theories obtained by dimensional reduction on generalized spaces look like? (ii) does the use of doubled geometry makes sense if space-time is not a torus fibration? (iii) can exotic space-time phases where kinetic energy for some fields becomes negative, or which have multiple time-like directions be connected to conventional space-times by any physical process, and if yes, what are the implications for cosmology (dark energy, inflation)? (iv) what are the implications for the laws black hole thermodynamics and their information-theoretic interpretation?