Structure of Hermitian groups and Group C*-algebras

数学的两个重要领域是群论和泛函分析。这两个主题中的第一个，群论，最初起源于对称性的研究，并在过去的几个世纪中成为数学中最基本的结构之一。群论的应用是深远的，该理论经常应用于物理，化学，材料科学和其他领域。泛函分析是一个最近的创新，最初是在二十世纪发展起来的。一些应用泛函分析技术的领域包括图像处理、经济学、偏微分方程和量子物理学。本项目旨在了解两个功能分析结构产生的群体：群代数L1（G）和全群C*-代数C*（G），这是在巴拿赫代数，C*-代数和抽象调和分析领域的基本研究对象的结构特性。

Two important areas of mathematics are group theory and functional analysis. The first of these two topics, group theory, originally arose from the study of symmetries and has become one of the most fundamental structures in mathematics over the past couple of centuries. Group theory's applications are far reaching and the theory is frequently applied to physics, chemistry, materials science, and other areas. Functional analysis is a much more recent innovation, being initially developed in twentieth century. Some of the areas where functional analysis techniques are applied include image processing, economics, partial differential equations, and quantum physics. This project seeks to understand the structural properties of two functional analytic constructions arising from groups: the group algebra L1(G) and the full group C*-algebra C*(G), which are fundamental objects of study in the fields of Banach algebras, C*-algebras, and abstract harmonic analysis.