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Indecomposable Structure in Representation Theory and Logarithmic Conformal Field Theory. Logarithmic conformal field theory describes non-local observables in statistical models of important physical systems (eg. polymers, percolation). This realisation has led to a recent explosion of activity among physicists and mathematicians. Mathematical physics in Australia is well-placed to capitalise on this activity, having several experts working in the area, and this project will significantly aug ....Indecomposable Structure in Representation Theory and Logarithmic Conformal Field Theory. Logarithmic conformal field theory describes non-local observables in statistical models of important physical systems (eg. polymers, percolation). This realisation has led to a recent explosion of activity among physicists and mathematicians. Mathematical physics in Australia is well-placed to capitalise on this activity, having several experts working in the area, and this project will significantly augment Australia's reputation within the international community by bringing (and developing) mathematical tools and insights which complement current research strengths. Such augmentations are vital to the well-being of mathematics and physics in Australia.Read moreRead less
Algebraic Structures in Mathematical Physics and Their Applications. Algebraic structures such as affine (super)algebras, quantised algebras and vertex operator algebras are among the most important discoveries in mathematics. They provide a universal common algebraic framework underlying applications in a wide range of physics (eg. statistical mechanics, string theory, condensed matter physics etc.) leading to a high level of research activity worldwide. The project harnessess the high level ....Algebraic Structures in Mathematical Physics and Their Applications. Algebraic structures such as affine (super)algebras, quantised algebras and vertex operator algebras are among the most important discoveries in mathematics. They provide a universal common algebraic framework underlying applications in a wide range of physics (eg. statistical mechanics, string theory, condensed matter physics etc.) leading to a high level of research activity worldwide. The project harnessess the high level of expertise in mathematical physics across Australia to focus on exciting new developments in the theory of these algebraic structures and their application to physics, thus ensuring Australia plays a leading role in this rapidly expanding field.Read moreRead less