Global aspects of dualities in String Theory in the presence of background fluxes. String Theory, known to the general public as the "Theory of Everything', is currently an extremely active area of research internationally. It has not only stimulated considerable interaction between mathematical physicists and mathematicians, but also increased public interest in science through television programs and books. Unfortunately, the majority of the Australian scientific community has not yet caught ....Global aspects of dualities in String Theory in the presence of background fluxes. String Theory, known to the general public as the "Theory of Everything', is currently an extremely active area of research internationally. It has not only stimulated considerable interaction between mathematical physicists and mathematicians, but also increased public interest in science through television programs and books. Unfortunately, the majority of the Australian scientific community has not yet caught up with these developments. Our recent papers, all published in premier journals in this field, have not only received widespread international attention but have also increased the profile of String Theory amongst Australia's mathematicians and mathematical physicists. The proposed project is expected to continue this trend.Read moreRead less
Stability conditions on triangulated categories and related aspects of homological mirror symmetry. The proposed research studies one of the deepest questions in nature through superstring theory and mathematics with leading experts around the world. So, the proposed project maintains the Australia's profile in science. Also, the proposed project fits within the the Research Priority: Frontier Technologies for Building and Transforming Australian Industries. We will have exciting mathematical di ....Stability conditions on triangulated categories and related aspects of homological mirror symmetry. The proposed research studies one of the deepest questions in nature through superstring theory and mathematics with leading experts around the world. So, the proposed project maintains the Australia's profile in science. Also, the proposed project fits within the the Research Priority: Frontier Technologies for Building and Transforming Australian Industries. We will have exciting mathematical discussions which stimulate Australian students. They will be able to take advantage of such experience, especially when they need innovation. Thus, it is an investment for future of Australian industries.Read moreRead less
Generalized Geometries and their Applications. Geometry is one of the pillars of both ancient and modern mathematics. It also plays a vital role in many scientific applications, in particular in physics. Progress on the mathematical aspects and the applications have often gone hand in hand, as for example with differential geometry and general relativity. Geometry is a very fruitful area for interdisciplinary research.
Australia has a long tradition and a recognized research strength in Mat ....Generalized Geometries and their Applications. Geometry is one of the pillars of both ancient and modern mathematics. It also plays a vital role in many scientific applications, in particular in physics. Progress on the mathematical aspects and the applications have often gone hand in hand, as for example with differential geometry and general relativity. Geometry is a very fruitful area for interdisciplinary research.
Australia has a long tradition and a recognized research strength in Mathematical Physics, and this project will contribute to maintaining that status. An integral part of this proposal is student involvement and postgraduate research training, for which the topic lends itself particularly well.Read moreRead less
Twisted K-theory and its application to String Theory and Conformal Field Theory. String Theory is, at present, the only consistent theory of quantum gravity. Recently, twisted K-theory was proposed as the algebraic structure underlying the classification of D-branes, i.e. solitonic extended objects, in certain closed string backgrounds. In this project we aim to advance our understanding of the properties of twisted K-theory in the context of String Theory and Conformal Field Theory. The ult ....Twisted K-theory and its application to String Theory and Conformal Field Theory. String Theory is, at present, the only consistent theory of quantum gravity. Recently, twisted K-theory was proposed as the algebraic structure underlying the classification of D-branes, i.e. solitonic extended objects, in certain closed string backgrounds. In this project we aim to advance our understanding of the properties of twisted K-theory in the context of String Theory and Conformal Field Theory. The ultimate goal is to find the appropriate K-theory classifying D-branes in arbitrary closed string backgrounds or, similarly, classifying boundary Conformal Field Theories. It has already emerged that the K-theory of C*-algebras will play an important role.Read moreRead less
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
Modular Index Theory. This project capitilises on Australian advances in mathematics, particularly noncommutative geometry. It will maintain and extend Australia's prominence in this subject, providing excellent opportunities for young researchers via the research networks this project will establish. Being at the interface of ideas in mathematics and physics, there is potential for future technological spin offs for Australia.