Lie Groups

9321285 Wolf将继续他在李群、谐波分析和表示理论方面的研究，并将其应用于复分析、黎曼几何、数值分析和控制理论。他将继续研究无限维李群，这是有限维群的直接极限，并将研究控制理论中的问题，这些问题本质上是表征理论的问题。李群理论是为了纪念挪威数学家索夫斯·李而命名的，它一直是20世纪数学的主要主题之一。作为利用系统中固有对称性的数学工具，李群表示理论对数学本身，特别是分析和数论，以及理论物理，特别是量子力学和基本粒子物理产生了深远的影响。＊＊＊

9321285 Wolf Wolf will continue his research on Lie groups, harmonic analysis and representation theory, with applications to complex analysis, riemannian geometry, numerical analysis and control theory. He will continue his work on infinite dimensional Lie groups that are direct limits of finite dimensional groups, and will investigate questions in control theory that are essentially questions of representation theory. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics. ***