US-India Cooperative Research: Geometric Invariants for Quotient Modules

0097044 Douglas描述：该奖项支持美国-印度合作研究：商模块的几何不变式。 美国PI罗纳德·道格拉斯（德克萨斯农工大学）和加达达尔·米斯拉（印度统计研究所，班加罗尔）将研究函数代数上的Hilbert模的几何不变量。 该项目将导致更好地理解多元算子理论和算子理论与埃尔米特代数几何的交叉施肥。 这是一个基本问题，其目标是通过几何不变量对商希尔伯特模进行分类。 朝着寻找完整的酉不变量和深化多变量算子理论与复杂几何之间的联系的目标取得进展将是一个重大的进步。范围：道格拉斯和米斯拉是著名的数学家与既定的研究记录。 道格拉斯是算子理论和数学的几个领域之间的相互作用的世界领导者;米斯拉是印度科学院院士。 他们在过去的工作中取得了成功，并通过电子联系维持了他们的大部分研究。 他们现在正处于需要直接接触以继续其开创性工作的阶段。 两位研究人员领导的小组将通过这种合作得到加强，其中还包括支持年轻科学家的交流。 该奖项由国际项目部和数学科学部共同支持。

0097044Douglas Description: This award supports US-India Cooperative Research: Geometric Invariants for Quotient Modules. US PI Ronald Douglas, Texas A&M University and Gadadhar Misra, Indian Statistical Institute, Bangalore will study geometric invariants of Hilbert modules over function algebras. The project will lead to a better understanding of multivariate operator theory and the cross-fertilization of operator theory with Hermitian algebraic geometry. It is a fundamental problem that has as its objective the classifying of quotient Hilbert modules via geometric invariants. Progress toward the goal of finding complete unitary invariants and deepening the connection between multivariable operator theory and complex geometry would be a significant advance. Scope: Douglas and Misra are distinguished mathematicians with established research records. Douglas is a world leader in the interaction between operator theory and several fields of mathematics; Misra is a Fellow of the Indian Academy of Sciences. They have worked successfully in the past and have sustained much of their research through electronic contact. They are now at a stage where direct contact is needed to proceed with their groundbreaking work. Both investigators lead groups that will be strengthened through this collaboration, which also includes support for an exchange of young scientists. This award is jointly supported by the Division of International Programs and the Division of Mathematical Sciences.