Operator spaces and harmonic analysis

群是最自然的数学对象之一，被用来模拟对称性。 无限群通常具有难以驾驭的代数行为，这通常可以通过检查它们的空间行为来驯服，即使用拓扑。 表示论是理解这些拓扑群的重要工具。 我感兴趣的是研究特定的数学对象，某些巴拿赫代数，这是与这些陈述。 这些代数，来自表示论，与算子（理解表示的自然框架）非常密切相关，这种联系允许在这些代数中观察非平凡的空间结构，因此我们称之为算子空间结构。 这是非对易调和分析。

Groups are amongst the most natural mathematical objects, developed to model symmetries. Infinite groups often have unruly algebraic behavior, which can frequently be tamed by examining their spatial behavior, i.e. using topology. Representation theory is is an important tool for understanding these topological groups. I am interested in studying particular mathematical objects, certain Banach algebras, which are associated with these representations. These algebras, coming from representation theory, are very closely related to operators (the natural framework in which representations are understood), and this connection allows for non-trivial spatial structures to be viewed in these algebras, which we hence call operator space structures. This is non-commutative harmonic analysis.