Generalised Geometric Structures in String Theory

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In string theory, extra dimensions of spacetime are curled up in a small internal space. Physical predictions, such as the spectrum of particles, are largely determined by the choice of internal space, so that understanding the possible internal spaces that give consistent string backgrounds is an important question. Reasonable physical restrictions lead to a rich class of possible internal geometries with a deep mathematical structure that has led to a productive interplay between mathematics and physics that has led to important results and understanding on both sides. The aim of the research is to extend this to find and study a wider class of internal spaces, including those with fluxes and those which do not have conventional geometries, as recent developments suggest that there is a deep underlying structure that involves new ideas in mathematics. The non-conventional geometries may in fact be generic in string theory, and studying them will provide new insights into the nature of string theory that go beyond the field theory approximation that is often applied.