Research in string compactifications and mathematical string theory

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The PI proposes to investigate the properties of four dimensional theories with N = 1 supersymmetry which are obtained from compactifications of string theory. Another topic of investigation will be the connection between geometry and string theory. Another objective will be to study a particular generalization of "mirror symmetry," a duality between typically topologically distinct spaces. The PI also hopes to study heterotic string compactifications with fluxes which involve understanding manifolds that are not of the usual Kahler variety. Other directions of this research include studying a class of string vacua derived from "hybrid" Landau-Ginzburg models.The broader impacts of this proposal are that the PI proposes a series of intensive two-week summer schools for visiting grad students and postdocs to teach relevant advanced mathematics to young physicists. This series of summer schools will help to fill what the PI perceives as a significant pedagogical gap in the training of young persons in this field namely the lack of schools to teach the advanced mathematics needed to make progress in formal string theory. The research advocated in this proposal is multidisciplinary in nature involving collaboration with mathematicians with expertise in geometry