Macdonald polynomials: Combinatorics and representations. This proposal is part of the aim to build a world class research team in algebraic combinatorics and combinatorial representation theory at the University of Melbourne, led by the two CI.
These fields are currently experiencing very rapid growth and development, and a strong Australia based team will further enhance the country's strong reputation in combinatorics and algebra.
The project will also provide a perfect training ground fo ....Macdonald polynomials: Combinatorics and representations. This proposal is part of the aim to build a world class research team in algebraic combinatorics and combinatorial representation theory at the University of Melbourne, led by the two CI.
These fields are currently experiencing very rapid growth and development, and a strong Australia based team will further enhance the country's strong reputation in combinatorics and algebra.
The project will also provide a perfect training ground for Higher Degree Students with interests in pure mathematics as well as computer
algebra and symbolic computation.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
Algebraic approach to exactly soluble models for disordered systems. In nanoscience there are a diverse range of systems in which disorder, randomness, or noise can play a significant role. Examples range from quantum wires to qubits to unzipping DNA.
Even the simplest mathematical models for systems in the presence of disorder have a rich mathematical structure because they can be formulated in terms of Lie algrebras or diffusion on a curved surface.
The complementary physical and mathem ....Algebraic approach to exactly soluble models for disordered systems. In nanoscience there are a diverse range of systems in which disorder, randomness, or noise can play a significant role. Examples range from quantum wires to qubits to unzipping DNA.
Even the simplest mathematical models for systems in the presence of disorder have a rich mathematical structure because they can be formulated in terms of Lie algrebras or diffusion on a curved surface.
The complementary physical and mathematical expertise of the two Chief Investigators is crucial to this project.Read moreRead less