Fundamental mathematical structures in statistical and quantum systems. Mathematics is playing a key role in modern science and technology. This project will bring together world leading experts from Australia and the USA to unravel the most fundamental mathematical structures in of statistical and quantum systems arising in settings ranging from physics of tiny quantum dots to string theory in high energy physics. This research will ensure Australia's involvement in cutting-edge international d ....Fundamental mathematical structures in statistical and quantum systems. Mathematics is playing a key role in modern science and technology. This project will bring together world leading experts from Australia and the USA to unravel the most fundamental mathematical structures in of statistical and quantum systems arising in settings ranging from physics of tiny quantum dots to string theory in high energy physics. This research will ensure Australia's involvement in cutting-edge international developments in mathematical sciences poised to deliver new significant results in the fundamental quantum theory of matter. The project will also contribute to training young researchers to maintain Australia's international standing in fundamental science.Read moreRead less
Quantization of polyhedral surfaces. Recent developments in the theory of discrete surfaces have revealed their fascinating links to many other areas of mathematics including integrable systems and quantum geometry. Rapid progress in this field is motivated by applications in pure mathematics, mathematical physics, computer graphics and engineering. Australian researchers are world recognized experts in integrable systems and this project will link them together with German experts in discrete d ....Quantization of polyhedral surfaces. Recent developments in the theory of discrete surfaces have revealed their fascinating links to many other areas of mathematics including integrable systems and quantum geometry. Rapid progress in this field is motivated by applications in pure mathematics, mathematical physics, computer graphics and engineering. Australian researchers are world recognized experts in integrable systems and this project will link them together with German experts in discrete differential geometry. The project will advance our knowledge base in fundamental and applied sciences and offer a unique research training opportunity for students in contemporary areas of pure and applied mathematics.Read moreRead less
Diffusion driven pattern formation and signal propagation in spatially complex excitable media. A basic understanding of the mechanisms for pattern formation, from the spots on leopards to electrical signalling of neurons, has been achieved through reaction-diffusion equations. However to obtain a complete understanding, which is vital for many applications, it is necessary to modify this mathematical model to incorporate spatial complexities in the underlying media. This project will develop ....Diffusion driven pattern formation and signal propagation in spatially complex excitable media. A basic understanding of the mechanisms for pattern formation, from the spots on leopards to electrical signalling of neurons, has been achieved through reaction-diffusion equations. However to obtain a complete understanding, which is vital for many applications, it is necessary to modify this mathematical model to incorporate spatial complexities in the underlying media. This project will develop a fractional calculus framework for pattern formation, including signal propagation, in spatially complex and excitable media. In a particular application we will model the way in which the signalling properties of neurons depend critically on their spatial complexity.Read moreRead less
Quantum many-body systems with higher mathematical symmetries. Ongoing developments in the experimental realisation of ultracold quantum systems play a leading role in the international effort towards the eventual realisation of quantum technology. This project brings together Australian and US researchers with complementary strengths to develop the mathematical study of fundamental systems of interacting quantum particles of relevance to experiments. The project will ensure that Australian rese ....Quantum many-body systems with higher mathematical symmetries. Ongoing developments in the experimental realisation of ultracold quantum systems play a leading role in the international effort towards the eventual realisation of quantum technology. This project brings together Australian and US researchers with complementary strengths to develop the mathematical study of fundamental systems of interacting quantum particles of relevance to experiments. The project will ensure that Australian researchers participate in and benefit from international developments in a leading edge area of fundamental research. It will also contribute to training students in rapidly advancing areas with the capacity to contribute to a wide range of problems, including the emerging technology of quantum devices.Read moreRead less
Elliptic Schubert Calculus. We are well placed to become one of the world's leading centers in the emerging discipline of elliptic representation theory. This proposal describes our plan of establishing a cohesive research program spanning all the different aspects of this multi-disciplinary field, which applies elliptic cohomology to geometric representation theory, enumerative geometry, integrable systems and invariants of singular varieties.
Our mathematically diverse team all have played key ....Elliptic Schubert Calculus. We are well placed to become one of the world's leading centers in the emerging discipline of elliptic representation theory. This proposal describes our plan of establishing a cohesive research program spanning all the different aspects of this multi-disciplinary field, which applies elliptic cohomology to geometric representation theory, enumerative geometry, integrable systems and invariants of singular varieties.
Our mathematically diverse team all have played key roles in the recent developments surrounding the field, and in very different capacities. This is a unique moment, where we have the chance to transform our individual research programs into a cohesive and powerful collaboration with a strong
international presence.Read moreRead less
The mathematical analysis of ultracold quantum gases. Ongoing developments in the experimental realisation of ultracold quantum
gases play a leading role in the international effort towards the
eventual realisation of quantum technology. This project brings together Australian
researchers with complementary strengths to develop a sophisticated range of innovative
mathematical tools for understanding these fundamental quantum systems. The expected
outcomes will thus include potentially far r ....The mathematical analysis of ultracold quantum gases. Ongoing developments in the experimental realisation of ultracold quantum
gases play a leading role in the international effort towards the
eventual realisation of quantum technology. This project brings together Australian
researchers with complementary strengths to develop a sophisticated range of innovative
mathematical tools for understanding these fundamental quantum systems. The expected
outcomes will thus include potentially far reaching impacts on downstream quantum technology.
The project will contribute to training mathematically talented students and thus take essential
steps to establish the long term future of mathematical physics in Australia. It will also establish enduring key international research links.Read moreRead less
Polynomial representations of the Hecke algebra. This project will offer a great opportunity for talented students to engage in internationally competitive research in mathematics. In addition, through international collaboration, this project will be able to deliver an online database with software libraries which will be a world benchmark for computation with multivariate polynomials.
Statistical Topology and its Application to Deriving New Geometric Invariants. This project will offer a great opportunity for talented students to engage in internationally competitive research. Statistical topology, which combines ideas in topology, geometry and statistical mechanics is becoming a rapidly increasing branch of mathematics, with many emerging applications in bio-informatics, computer science and theoretical physics.
New mathematics of fractional diffusion for understanding cognitive impairment at the neuronal level. As Australia's population ages, cognitive impairment due to cortical ageing and neurodegeneration is looming as the nation's greatest health problem. The project will deliver new, more realistic, mathematical models for a mechanistic understanding of cognitive impairment at the neuronal level. This understanding is a vital first step in targeting drugs, e.g., to influence neuronal spine proper ....New mathematics of fractional diffusion for understanding cognitive impairment at the neuronal level. As Australia's population ages, cognitive impairment due to cortical ageing and neurodegeneration is looming as the nation's greatest health problem. The project will deliver new, more realistic, mathematical models for a mechanistic understanding of cognitive impairment at the neuronal level. This understanding is a vital first step in targeting drugs, e.g., to influence neuronal spine properties, for preventative health care. The project will maintain international collaborations, between applied mathematicians at UNSW, Sydney and biomathematicians and neuroscientists at Mount Sinai School of Medicine, New York, providing ongoing training opportunities for Australian scientists in this cutting edge biomathematical research.Read moreRead less