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Topological String Theory I

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In these two lectures I will present on overview of topological string theory, starting with the basic concepts and continuing to the most recent developments. Aspects that will be covered are: closed and open strings, Gromov-Witten theory, matrix models, quantum crystals, and special holonomy manifolds. I will end with some more speculative thoughts about the non-perturbative definition of (topological) string theory and quantum geometry.