Cohomological properties of group algebras and Fourier algebras

我的主要研究领域是调和分析，重点是非交换群，如顺从群和李群。最初，谐波分析的引入是出于对波和信号的研究，这可以追溯到欧拉和后来的傅立叶。我目前正在解决的问题，从最近的观点在这一领域主要是在世纪发展，它被称为非交换谐波分析。这种发展的动机来自安德烈·韦尔的工作，他创建了一个领域，从不同的方法系统地研究谐波分析中的各种问题，将这个领域与代数和泛函分析联系起来。这些联系，沿着最近应用算子空间理论调和分析，使这一领域相当交叉和富有成效。

My main field of research is harmonic analysis with an emphasis on non- commutative groups such as amenable groups and Lie groups. Originally the introduction of harmonic analysis was motivated by studying waves and signals which goes back as far as Euler and later on Fourier. I am currently addressing problems from a recent point of view in this field developed mainly in 20th century; it is called non-commutative harmonic analysis. The motivation for such development came from the work of Andre Weil of creating an area that systematically studies various questions in harmonic analysis from different approaches, connecting this field to algebra and functional analysis. These connections, along with the recent applications of operator space theory to harmonic analysis, have made this area quite intersecting and fruitful.