Geometrical Structures of M-Theory

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N=(2,1) heterotic string theory provides clues about hidden structure in M-theory related to string duality; in effect it geometrizes some aspects of duality. The program whereby one may deduce this hidden structure is outlined, together with the results obtained to date. Speculations are made as to the eventual shape of the theory. Talk presented at Strings '96 (Santa Barbara, July 20-25, 1996).
19 pages, latex

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