Elliptic special functions. Although elliptic functions and special functions are both classical areas of mathematics, the field of elliptic special functions was only established in the last two decades. It combines ideas from analysis, modular forms and statistical mechanics to tackle problems in number theory (elliptic curves), algebra (elliptic quantum groups), mathematical physics (Seiberg duality) and more. This project aims to settle two important problems in the field of elliptic special ....Elliptic special functions. Although elliptic functions and special functions are both classical areas of mathematics, the field of elliptic special functions was only established in the last two decades. It combines ideas from analysis, modular forms and statistical mechanics to tackle problems in number theory (elliptic curves), algebra (elliptic quantum groups), mathematical physics (Seiberg duality) and more. This project aims to settle two important problems in the field of elliptic special functions: the resolution of Boyd's conjectures concerning Mahler measures and L-values of elliptic curves, and the construction of an Askey-Wilson-Koorwinder theory of elliptic biorthogonal functions for the A-type root system.Read moreRead less
ROBUST SOLID OXIDE FUEL CELL TECHNOLOGY FOR SMALL-SCALE APPLICATIONS. The project aims to develop nano-materials for the next generation planar Solid Oxide Fuel Cell (SOFC) that will operate at temperatures between 600 and 800°C. The goal is to identify and demonstrate materials that meet the robust requirements for small scale power generators at the 3-5kW scale. It is expected that these will be used in stationary power generation applications, in remote area power supplies, and for providing ....ROBUST SOLID OXIDE FUEL CELL TECHNOLOGY FOR SMALL-SCALE APPLICATIONS. The project aims to develop nano-materials for the next generation planar Solid Oxide Fuel Cell (SOFC) that will operate at temperatures between 600 and 800°C. The goal is to identify and demonstrate materials that meet the robust requirements for small scale power generators at the 3-5kW scale. It is expected that these will be used in stationary power generation applications, in remote area power supplies, and for providing auxiliary power in vehicles. The work builds on the world-leading position that Ceramic Fuel Cells Ltd. has in planar SOFC technology, utilising micro-analysis and fuel cell expertise at the University of Queensland.Read moreRead less
Variational methods in partial differential equations. Research in partial differential equations is a very active area of modern mathematics linking nonlinear functional analysis, calculus of variations and differential geometry to applied sciences. This project will enable Australia-based researchers to participate in the forefront of mathematical research with leading international mathematicians by establishing new collaborations, strengthening on-going collaborations and providing internat ....Variational methods in partial differential equations. Research in partial differential equations is a very active area of modern mathematics linking nonlinear functional analysis, calculus of variations and differential geometry to applied sciences. This project will enable Australia-based researchers to participate in the forefront of mathematical research with leading international mathematicians by establishing new collaborations, strengthening on-going collaborations and providing international research experience for early career researchers. As a result, this proposal will enhance Australia's distinguished reputation in analysis and further link the UQ group with a number of mathematical institutes in USA and China.Read moreRead less
Geometric partial differential systems and their applications. This proposal addresses questions central to the understanding of nonlinear partial differential systems from classical, quantum field theory and liquid crystals. Applications to physical problems such as the Yang-Mills flow, Faddeev's model and liquid crystal systems are of great interest and importance in the broader scientific community. The project will yield internationally significant results in theoretical mathematics, with ....Geometric partial differential systems and their applications. This proposal addresses questions central to the understanding of nonlinear partial differential systems from classical, quantum field theory and liquid crystals. Applications to physical problems such as the Yang-Mills flow, Faddeev's model and liquid crystal systems are of great interest and importance in the broader scientific community. The project will yield internationally significant results in theoretical mathematics, with applications in physics and and other sciences. Specialist training will be provided for Australia's next generation of mathematicians. This project will enable Australian researchers to stay at the forefront of research in this area, strengthening links with a number of world-leading mathematicians.Read moreRead less
Geometric variational problems and nonlinear partial differential systems. We will investigate several important problems on non-linear partial differential systems, bridging analysis, differential geometry and mathematical physics. Harmonic maps are the prototype of maps minimizing the Dirichlet energy. The liquid crystal configuration generalizes the harmonic map with values into two dimensional spheres. The Yang-Mills equations originated from particle physics. We will make fundamental contri ....Geometric variational problems and nonlinear partial differential systems. We will investigate several important problems on non-linear partial differential systems, bridging analysis, differential geometry and mathematical physics. Harmonic maps are the prototype of maps minimizing the Dirichlet energy. The liquid crystal configuration generalizes the harmonic map with values into two dimensional spheres. The Yang-Mills equations originated from particle physics. We will make fundamental contributions to these topics: Regularity problem and energy minimality of weakly harmonic maps, Weak solutions of the liquid crystal equilibrium system, Yang-Mills heat flow and singular Yang-Mills connections.
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Categorical symmetries in representation theory. This project aims to develop categorical symmetries of central objects in mathematics such as braid groups, the Hilbert scheme of points, and the Virasoro algebra. The concept of symmetry is an important organising principle in science. Representation theory is the field of mathematics concerned with studying symmetries. The problems proposed have connections to many different areas including algebra, geometry, topology, and mathematical physics. ....Categorical symmetries in representation theory. This project aims to develop categorical symmetries of central objects in mathematics such as braid groups, the Hilbert scheme of points, and the Virasoro algebra. The concept of symmetry is an important organising principle in science. Representation theory is the field of mathematics concerned with studying symmetries. The problems proposed have connections to many different areas including algebra, geometry, topology, and mathematical physics. This project expects to advance pure mathematics and provide potential benefit in many related fields.Read moreRead less
The Mukhin-Varchenko and Rogers-Ramanujan conjectures. This project is aimed at proving two deep conjectures in pure mathematics. The conjectures are linked to many areas of mathematics, and success in proving either conjecture will signify a fundamental breakthrough in the fields of algebra, combinatorics and number theory.
Pathways To Mental Health And Obesity In Young Adults: A Longitudinal Study
Funder
National Health and Medical Research Council
Funding Amount
$698,510.00
Summary
While the health of the population has been gradually improving, there are some health problems which are increasing. The mental health of young people is one such area. Based on data relating to youth suicide, substance abuse, cigarette smoking by females and behavioural or mental health problems in the young, there has been evidence of a marked increase in some important health problems faced by the young. Little is known about the causes of these problems and even less is known about the reas ....While the health of the population has been gradually improving, there are some health problems which are increasing. The mental health of young people is one such area. Based on data relating to youth suicide, substance abuse, cigarette smoking by females and behavioural or mental health problems in the young, there has been evidence of a marked increase in some important health problems faced by the young. Little is known about the causes of these problems and even less is known about the reasons for the increase. Based on the available evidence, 20-25% of young persons manifest a mental health problem. A second area of marked health deterioration concerns youth (and adult) obesity. Existing research points to the accumulation of cardiovascular risk factors associated with obesity from a very early age. Over 10% of youth are obese and a substantially higher proportion are overweight. There is evidence that the rate of obesity has been substantially increasing. Again little is known about the factors that contribute to obesity or the causes of the increase in the rates of obesity in the population. This proposal is for a 21-year follow-up of a sample of youth first enrolled when their mothers attended for their first obstetrical visit. Using a substantial body of existing data, we propose to examine the changes in levels of mental health and obesity and to identify the factors which contribute to these changes. This study involves the largest Australian cohort ever assembled for such research. The main questions asked in this study concern the impact of the mother's social and economic circumstances, her physical health and well-being, her use of addictive substances (including alcohol, cigarettes, illicit drugs) on the youth's health. We will also examine the association between early indicators of mental health and well-being and subsequent youth health and development.Read moreRead less
Population-level Epidemiological Trends In Hepatocellular Carcinoma In Queensland 1996 - 2010.
Funder
National Health and Medical Research Council
Funding Amount
$251,695.00
Summary
Incidence and mortality of hepatocellular carcinoma (HCC, the most common form of liver cancer) is increasing in Australia, driven by viral hepatitis infections. Disease burden is not defined in Queensland, particularly for Indigenous, migrant and regional and remote communities. Such factors may influence risk of viral hepatitis, access to treatment, and incidence and survival of HCC. Defining disease burdens will enable clinical programs targeted at groups most at risk in order to impact HCC t ....Incidence and mortality of hepatocellular carcinoma (HCC, the most common form of liver cancer) is increasing in Australia, driven by viral hepatitis infections. Disease burden is not defined in Queensland, particularly for Indigenous, migrant and regional and remote communities. Such factors may influence risk of viral hepatitis, access to treatment, and incidence and survival of HCC. Defining disease burdens will enable clinical programs targeted at groups most at risk in order to impact HCC trends.Read moreRead less
The fundamental equations for inversion of operator pencils. This project seeks to deepen understanding of how complex systems may be significantly changed by incremental changes to ambient conditions. Mathematical models of complex systems (climate change processes, optimal driving strategies, efficient distribution policies, effective search routines) often depend on key parameters. If small perturbations to the parameters cause large changes to the solution, then the perturbations are said to ....The fundamental equations for inversion of operator pencils. This project seeks to deepen understanding of how complex systems may be significantly changed by incremental changes to ambient conditions. Mathematical models of complex systems (climate change processes, optimal driving strategies, efficient distribution policies, effective search routines) often depend on key parameters. If small perturbations to the parameters cause large changes to the solution, then the perturbations are said to be singular. This project aims to reveal the underlying mathematical structures and develop new computational algorithms to analyse a general class of perturbed systems both locally near an isolated singularity and globally. It plans to use these algorithms to solve systems of equations, calculate generalised inverse operators, examine perturbed Markov processes, and estimate exit times from meta-stable states in stochastic population dynamics.Read moreRead less