Problems of duality for semigroups and other algebras. The theory of natural dualities has emerged as a powerful tool in algebra and its applications, including logic, computer science and theoretical physics. The project aims to apply recently developed techniques to a particular class of mathematical objects of established application in areas such as automata and language theory; namely the class of semigroups. As well as the contribution to the theory of semigroups, the work will provide a ....Problems of duality for semigroups and other algebras. The theory of natural dualities has emerged as a powerful tool in algebra and its applications, including logic, computer science and theoretical physics. The project aims to apply recently developed techniques to a particular class of mathematical objects of established application in areas such as automata and language theory; namely the class of semigroups. As well as the contribution to the theory of semigroups, the work will provide an understanding of the limits and full potential of application of the general theory of natural dualities.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
Generalized group characters. With its numerous international visitors, Ganter's program will be a significant gain for Melbourne as a centre of science and research. Students at all levels will benefit from training in a scientific environment of world-rank.
Ganter plans to build a research community in her field, involving individuals across the nation; this will be a good addition to the Australian research landscape. Finally, she hopes that her past experience in working with minority stud ....Generalized group characters. With its numerous international visitors, Ganter's program will be a significant gain for Melbourne as a centre of science and research. Students at all levels will benefit from training in a scientific environment of world-rank.
Ganter plans to build a research community in her field, involving individuals across the nation; this will be a good addition to the Australian research landscape. Finally, she hopes that her past experience in working with minority students will enable her to contribute to creating a more diverse research community in pure mathematics in Melbourne and across Australia.Read moreRead less