Mathematical Sciences: Studies in Algebraic Geometry

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The investigator studies arithmetical group quotients of bounded Hermitian domains of exceptional types with the goal to find their geometric interpretation as the moduli spaces of some special Calabi-Yau manifolds. The cohomology of such varieties should carry additional special structures related to representation theory of Lie groups of exceptional type. Calabi-Yau manifolds have recently become notorious because of their important role in physics. New ten dimensional models of the space-time proposed in the string theory contain a Calabi-Yau manifold as an additional part to the usual four dimensional space-time. The special Calabi-Yau manifolds sought by the investigator may appear as the right candidates for the choice of the model of the space-time.