Reflexive Polyhedra and their Applications in String and F-theory

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This is an informal introduction to the concept of reflexive polyhedra and some of their most important applications in perturbative and non-perturbative string physics. Following the historical development, topics like mirror symmetry, gauged linear sigma models, and the geometrical structures relevant to string and F-theory dualities are discussed. Finally some recent developments concerning the classification of reflexive polyhedra are mentioned.
Contribution to the proceedings of the TMR meeting "Quantum Aspects of Gauge Theories, Supersymmetry and Unification" held in Paris in September 1999; 8 pages

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