Mathematical Sciences: Hodge Theory

9404642 Cattani研究范围包括研究Hodge结构的极化变化及其在Calabi-Yau空间的镜像对称猜想中的应用。此外，还将探讨与Hodge结构的变化、模空间的紧致化和多维余数的计算有关的其他问题。这项研究对数学物理中的代数几何和超弦理论具有潜在的应用价值。***

9404642 Cattani The topics covered in the scope of research include the study of polarized variations of Hodge structures with applications to the mirror-symmetry conjecture for Calabi-Yau spaces. Further problems related to the variation of Hodge structure, compactification of moduli spaces and computation of multidimensional residues will also be pursued. The research has potential applications to algebraic geometry and superstring theory in mathematical physics. ***