Mirror symmetry and moduli spaces of superconformal field theories

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We review the applications of mirror symmetry to the study of the moduli spaces of two-dimensional conformal field theories with $N{=}(2,2)$ supersymmetry, particularly those constructed from Calabi--Yau manifolds. (Lecture delivered at the Zurich ICM, section on mathematical physics.)
11 pages, AmS-TeX v2.1, no figures, author-supplied dvi file at ftp://ftp.math.duke.edu/preprints/94-06.dvi

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