Introducing abstract maths to the real world
The 'Modern methods of operator algebras for time-frequency analysis' (MOTIF) project conducted research into the frontiers of non-commutative geometry, quantum mechanics and time-frequency analysis. The main objective was to use modern methods of operator algebras to gain a deeper understanding of time-frequency analysis and quantum mechanics.Time-frequency analysis is an essential element of signal processing and a fundamental element in applications across areas such as information communication technologies (ICT) and medicine. Project partners used a wide set of tools from non-commutative geometry and translated and generalised the construction of projective modules over non-commutative tori into the framework of Gabor analysis. Efforts effectively produced a dictionary that relates notions from non-commutative geometry with ones in time-frequency analysis. This succeeded in connecting the very abstract theory of non-commutative geometry with real-world concepts and problems in a novel way. Project results led to further insights on quantum functions and the construction of projections in non-commutative tori. This can potentially contribute to a greater understanding of notions and objects in non-commutative geometry and operator algebras in general.
