Cohomological properties of group algebras and Fourier algebras

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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.