From topological Hochschild homology to algebraic K-theory. The project will use methods of algebraic topology, specifically topological Hochschild homology, to study algebraic K-theory. This will increase our understanding of algebraic geometry, number theory, and the geometry of manifolds.
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.
Geometric transforms and duality. This Proposal is fundamental, basic research at the forefront of modern differential geometry and its application to physics. It will ensure that Australia is involved in today's mathematical and physical advances and that we have Australian mathematicians trained to take advantage of the future benefits of these advances.