Mathematical Sciences: Orbit Method C*-algebras and Applications

本文的研究将集中在谐波分析方面。重点将放在C(星)-代数的轨道方法上，包括这些代数在动力系统、拓扑学和流形几何中的应用。其中一个项目是发展关于轨道积分公式、对称空间和动力系统中的多重性问题的新结果。另一个项目是研究等变指标理论、算子代数不变量和离散群的表示。这项研究属于现代分析的一般领域，它考察了函数代数的表示理论。

This research will focus on harmonic analysis. The emphasis will be on the orbit method of C(star)-algebras, including applications of these algebras to dynamical systems, to topology, and to the geometry of manifolds. One project is to develop new results on orbital integral formulas, symmetric spaces, and multiplicity questions in dynamical systems. The other project is a study of equivariant index theory, operator algebra invariants, and representations of discrete groups. This research is in the general subarea of modern analysis which examines the representation theory of algebras of functions.