Locally compact groups and their C*-algebras

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My research revloves around the intersection of two important areas of mathematics: groups and C*-algebras. Groups are one of the most fundamental structures in all of mathematics and originally arose by studying symmetries, whereas C*-algebras were developed early in the twentieth century in order to model phenomena occuring in quantum mechanics. My research focuses around a class of C*-algebras which arise from groups. To every locally compact group G, there are two natural constructions of C*-algebras: the full group C*-algebra C*(G) and the reduced group C*-algebra C*r(G). The class of group C*-algebras has been essential in developing a modern theory of C*-algebras and remains a very active area of research. Despite the importance of group C*-algebras, only the C*-algebras of discrete groups are well understood. This project seeks to better understand group C*-algebras of locally compact groups as a whole by investigating C*-algebras of classes of locally compact groups which "behave like" discrete groups.