Mathematical Sciences: Structure of Operator Algebras

小行星9322675 琼斯将在分析的广泛领域进行研究， 代数，拓扑和数学物理，从工作在 群上同调的启发，由于不变量康纳斯冯 Neumann代数与低维域的统计 维（共形和其他）场论。的 在纽结理论和三维流形中， topology.统一的主题是一个子因素， 最终与所有这些主题有关。自同态到 次级因素也在发挥越来越大的作用。 在这个项目中的数学的一般领域有它的基础在量子力学的数学基础。在量子力学中，人们处理的是非对易的物体，可以通过考虑它们的代数结构作为一个 一个叫做冯·诺依曼代数的数学结构。这些 抽象对象具有令人惊讶的多种应用。在 这个项目，与这些代数相关的不变量将是 研究着眼于纽结理论的应用， 量子统计学 ***

9322675 Jones Jones will conduct research over broad areas in analysis, algebra, topology and mathematical physics, ranging from work in group cohomology inspired by an invariant due to Connes on von Neumann algebras to the statistics of fields in low dimensional(conformal and otherwise) field theory. The topological implications are in knot theory and 3-manifold topology. The unifying theme is that of a subfactor which is ultimately related to all these topics. Endomorphisms onto subfactors are also playing an increasing role. The general area of the mathematics in this project has its basis in the mathematical foundations of quantum mechanics. In quantum mechanics one deals with non-commutative objects that can be analyzed by considering their algebraic structure as a mathematical construct called a von Neumann algebra. These abstract objects have a surprising variety of applications. In this project, invariants associated with these algebras will be investigated with an eye towards applications in knot theory and quantum statistics. ***