Mathematical Sciences: C*-Algebraic Deformation Quantization

Sheu将继续研究C*-代数与几何之间的相互作用，重点是C*-代数变形量化。这项研究的动机是最近世界范围内对有前途的量子群新理论的兴趣，它将数学的几个分支联系在一起，与数学物理密切相关。本研究的目的是促进对这一相对较新的数学领域的理解。本研究中使用的主要工具将来自各种数学分支，包括C*代数、李群、微分几何和伪微分算子。这个项目的一般数学领域在希尔伯特空间算子的代数理论中有其基础。运算符可以被认为是有限或无限的复数矩阵。特殊类型的运算符通常放在一个代数中，自然地称为运算符代数。这些抽象对象有各种各样的应用。例如，它们在结理论中发挥着关键作用，而结理论目前正被用于研究DNA的结构，它们在非交换几何中具有重要的基础意义，而非交换几何在物理学中正变得越来越重要。

Sheu will continue his research on the interaction between C*- algebras and geometry, with emphasis on the C*-algebraic deformation quantization. The motivation of this research is the recent worldwide interest in the promising new theory of quantum groups which links together several branches of mathematics and is closely related to mathematical physics. The objective of this research is to advance the understanding of this relatively new area of mathematics. The main tools to be used in this research will be from various mathematical branches including C*-algebras, Lie groups, differential geometry, and pseudodifferential operators. The general area of mathematics of this project has its basis in the theory of algebras of Hilbert space operators. Operators can be thought of as finite or infinite matrices of complex numbers. Special types of operators are often put together in an algebra, naturally called an operator algebra. These abstract objects have a surprising variety of applications. For example, they play a key role in knot theory, which in turn is currently being used to study the structure of DNA, and they are of fundamental importance in noncommutative geometry, which is becoming increasingly important in physics.