Applications of generalised geometry to duality in quantum theory. This project will undertake research into mathematics at the forefront of modern physics. The aim of the project is to develop a mathematical theory of T-duality, a phenomenon in quantum physics, using generalised geometry.
Noncommutative analysis and geometry in interaction with quantum physics. Quantum theory has produced many advances in our understanding of the physical world for the last hundred years while mathematical breakthroughs have been made through exploiting innovative ideas from quantum physics. This project continues in this highly successful framework and will lead to advances in geometry both classical and noncommutative.