There is a website trying to explain some aspects, ideas, and concepts of the noncommutative phase space analysis: the pseudo-differential type analysis on groups and related noncommutative analysis on more general spaces (without group structure).
It is very much under construction but the information is gradually being added there. Please feel free to explore it:
This is the version of that website with more explanations:
Recent research grants:
EPSRC Grant EP/R003025: Regularity in affiliated von Neumann algebras and applications to partial differential equations
|Marie Curie Project H2020-MSCA-IF-2018 LieLowerBounds: Lower bounds for partial differential operators on compact Lie groups (2019-2021)|