Mathematical Sciences: Studies in Algebraic Geometry

研究了例外类型有界Hermitian域的算术群商，目的是找到它们的几何解释为某些特殊的Calabi-Yau流形的模空间。这类簇的上同调应该带有与例外类型李群的表示理论有关的附加特殊结构。Calabi-Yau流形最近因其在物理学中的重要作用而臭名昭著。弦理论中提出的新的十维时空模型包含一个Calabi-Yau流形，作为通常的四维时空的附加部分。研究者所寻求的特殊的Calabi-Yau流形可能是选择时空模型的合适候选者。

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.