Dualities in String Theory and Conformal Field Theory in the context of the Geometric Langlands Program. The Langlands program ties together seemingly unrelated areas of Mathematics. Recently, in the context of the Geometric Langlands correspondence, novel connections with Theoretical Physics have emerged, thus becoming one of the most active areas of research in both Mathematics and Theoretical Physics. Australia has a number of world-renowned experts, including the two CI's, in various aspect ....Dualities in String Theory and Conformal Field Theory in the context of the Geometric Langlands Program. The Langlands program ties together seemingly unrelated areas of Mathematics. Recently, in the context of the Geometric Langlands correspondence, novel connections with Theoretical Physics have emerged, thus becoming one of the most active areas of research in both Mathematics and Theoretical Physics. Australia has a number of world-renowned experts, including the two CI's, in various aspects of the Langlands program, and is therefore well-placed to make seminal contributions. Being involved in these new developments is of crucial importance to the health of Mathematics and Theoretical Physics in Australia. An integral part of this proposal is student involvement and postgraduate training.Read moreRead less
Supersymmetric quantum field theory, topology and duality. Supersymmetry is universally considered as one of the most fundamental concepts in physics, playing an increasingly central role in recent studies of quantum field theory and string theory. There is a corresponding development of supersymmetry in mathematics and this project will make advances both in 'superphysics' and 'supermathematics'.
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.