Research Training Group in Noncommutative Geometry

经典几何，如代数几何，可以通过交换代数来研究。非交换几何是通过算子代数研究“非交换空间”的几何和分析。非交换几何在数学的许多领域都有重要的应用，包括分析、流形的拓扑和几何、结理论、数学物理。最近，已经建立了与数论的深层联系。这个主题的广度和技术性质使得初学者很难导航到它的前沿。范德比尔特大学的非对易几何小组将建立一个培养非对易几何领域的博士生和博士后的项目。除了常规的培训计划（如课程和研讨会），该计划的一个重要组成部分是每年的非交换几何弹簧研究所。这个学校/会议的目的是培养学生和博士后在非交换几何和算子代数方面的知识。几门小型课程将由主要专家讲授，并将就该主题的最新进展进行额外的研究讨论。此外，春季研究所将为年轻研究人员提供一个论坛，让他们与资深科学家讨论他们的工作。

Classic geometry such as algebraic geometry can be studied through commutative algebra. Noncommutative geometry is the study of the geometry and analysis of ``noncommutative spaces'' through operator algebras. Noncommutative geometry has important applications to many areas of mathematics including analysis, topology and geometry of manifolds, knot theory, mathematical physics. More recently, deep connections to number theory have been established. The breadth and technical nature of this subject has made it difficult for beginners to navigate to its frontiers. The noncommutative geometry group at Vanderbilt will establish a program of training PhD students and postdoctoral associates in the area of noncommutative geometry. In addition to the regular training program (such as courses and seminars), an important component of the program is the annual noncommutative geometry spring institute. The purpose of this school/conference is to train students and postdocs in noncommutative geometry and operator algebras. Several mini-courses will be given by leading experts and there will be additional research talks on recent progress in the subject. In addition the spring institute will provide a forum for young researchers to discuss their work with senior scientists.