Defining Genetic And Epigenetic Variation During Early Development
Funder
National Health and Medical Research Council
Funding Amount
$996,075.00
Summary
We all began life with a set of genes inherited from our parents. However, it's now known that from the time we were in the womb onwards that genes can be turned off and on by the environment or even completely lost or gained. Even what your mother ate or how she behaved while she was pregnant could have influenced your future health. Because people are so different, we are studying the subtle differences between twins to tease out the factors that may influence our genes and our health.
Modelling The Effects Of Immunity On Influenza Transmission - Implications For Prevention And Vaccine Development
Funder
National Health and Medical Research Council
Funding Amount
$275,767.00
Summary
There is uncertainty about how many people can be infected by a single person with influenza at the start of an outbreak. Some data suggest that a single generation of transmission can infect 10-20 other people. With such a rate of growth (ie 10-20 fold every 3 days) the spread of an influenza outbreak is virtually unstoppable. Other data suggest that each person with influenza infects less than 2 other people on average. With such a lower rate of growth, control would be more feasible. Our proj ....There is uncertainty about how many people can be infected by a single person with influenza at the start of an outbreak. Some data suggest that a single generation of transmission can infect 10-20 other people. With such a rate of growth (ie 10-20 fold every 3 days) the spread of an influenza outbreak is virtually unstoppable. Other data suggest that each person with influenza infects less than 2 other people on average. With such a lower rate of growth, control would be more feasible. Our project will use data from historic and contemporary outbreaks of influenza and build mathematical models to explain the rate of growth of an influenza outbreak in terms of: 1. The proportion of people exposed to influenza who do not become ill (although there can be evidence of infection if careful studies are made). This proportion is about 33%. 2. The proportion of people who are protected from influenza by immunity, whether induced by vaccination or by past exposure to natural influenza infection (this can vary from 0% in isolated populations which have not seen influenza for many years up to 80 or 90% in urbanised populations that are exposed to influenza almost every season). 3. Different rates of contact between different people and groups of people - some may be exposed so often that their immunity is boosted regularly without them becoming severely ill; others, living in more isolated circumstances, may be rarely exposed, but when they are, they are more likely to become severely ill. 4. The effects of influenza vaccine in inducing protective immunity - it is well known that there is good protection if the vaccine is well matched to the circulating virus. 5. The effects of live virus infection in inducing (short-lived) protection against a wider range of influenza viruses. Our model results will be used to guide vaccine design and pandemic planning.Read moreRead less
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
Homotopy theory: interactions with representation theory and moduli spaces. This proposal will involve young researchers and train them for problem solving in many fields, including management, the sciences, the financial industries, and the development of technologies. Furthermore, many of the projects in this proposal are collaborative and interdisciplinary. It is the CI's sincere hope that this proposal can help bolster communication amongst the wealth of topology, number theory, and mathe ....Homotopy theory: interactions with representation theory and moduli spaces. This proposal will involve young researchers and train them for problem solving in many fields, including management, the sciences, the financial industries, and the development of technologies. Furthermore, many of the projects in this proposal are collaborative and interdisciplinary. It is the CI's sincere hope that this proposal can help bolster communication amongst the wealth of topology, number theory, and mathematical physics experts in Australia. The research in these exciting areas of mathematics will contribute to maintaining Australia's position as a research leader in pure mathematics.
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Discovery Early Career Researcher Award - Grant ID: DE160100975
Funder
Australian Research Council
Funding Amount
$307,536.00
Summary
Algebraic groups and Springer theory. This project aims to explore representation theory, which is a study of the basic symmetries that occur in nature. By its nature, representation theory has applications to number theory, physics, national security and internet security, and other sciences. Generalised Springer theory plays an important role in representations of finite groups of Lie type. The project aims to develop an analogous theory in a more general setting that includes symmetric spaces ....Algebraic groups and Springer theory. This project aims to explore representation theory, which is a study of the basic symmetries that occur in nature. By its nature, representation theory has applications to number theory, physics, national security and internet security, and other sciences. Generalised Springer theory plays an important role in representations of finite groups of Lie type. The project aims to develop an analogous theory in a more general setting that includes symmetric spaces. Moreover, the project aims to address various outstanding problems in algebraic groups. The project also plans to explore the connection between the geometry of certain null-cones and deformations of Galois representations.Read moreRead less
Theory and Applications of Hypergeometric Series. Techniques based on hypergeometric series lie at the heart of an exciting and rapidly developing class of mathematical methods, with applications to many areas of science and engineering, such as computer science, statistics, physics, chemistry and biology.
In the past decades Australia has been at the forefront of important developments in the field, and this proposal serves to further strengthen the country's leading reputation.
Many of th ....Theory and Applications of Hypergeometric Series. Techniques based on hypergeometric series lie at the heart of an exciting and rapidly developing class of mathematical methods, with applications to many areas of science and engineering, such as computer science, statistics, physics, chemistry and biology.
In the past decades Australia has been at the forefront of important developments in the field, and this proposal serves to further strengthen the country's leading reputation.
Many of the modern methods in the theory require expertise in mathematics as well as a high level of programming skills. This combination provides a unique training ground for higher degree students aiming at careers in financial mathematics, weather/climate forecasting and internet security.
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Coset spaces and Hecke algebra actions. This project will develop fundamental models and their mechanics as tools for studying subtle geometry and hidden symmetry in number systems and systems of equations. These powerful new models will provide an elementary and tractable approach for exploiting patterns that are naturally embedded in complex systems.
Geometric methods in representation theory and the Langlands program. This research project aims to study questions in representation theory of groups using geometric methods. A central role is played by Langlands program which, broadly understood, can be viewed as a grand unified theory of mathematics. One setting for the work is modular representation theory with the aim of understanding irreducible characters. The project also aims to work on combinatorics and geometry in algebraic groups in ....Geometric methods in representation theory and the Langlands program. This research project aims to study questions in representation theory of groups using geometric methods. A central role is played by Langlands program which, broadly understood, can be viewed as a grand unified theory of mathematics. One setting for the work is modular representation theory with the aim of understanding irreducible characters. The project also aims to work on combinatorics and geometry in algebraic groups in small characteristics and one goal is to obtain a more uniform geometric understanding across all characteristics. The project also aims to work in the context of real groups and with the Gukov-Witten "fix of the orbit method" via branes. Finally, the project expects to begin a study of deformations of Galois representations in a general context.Read moreRead less
Tantalizer algebras and generalized lattice models. This project exploits underlying symmetry to characterise components and flow patterns in network configurations. The project will develop tools for analysis and optimisation of systems of interacting nodes which can arise in materials, computing networks, and any social or industrial contexts with communication or product transfer between nodes.
The arithmetic of supersingular elliptic curves. The proposed research will have substantial benefits both in the area of pure mathematics, and to the standing of number theory within Australia generally. If successful, the investigators envisage: - fundamental advances in the study of both elliptic curves and modular forms; - key progress in our understanding of the final Millenium Prize Problem in Mathematics; - academic software to compute special values of L-functions; - applications to com ....The arithmetic of supersingular elliptic curves. The proposed research will have substantial benefits both in the area of pure mathematics, and to the standing of number theory within Australia generally. If successful, the investigators envisage: - fundamental advances in the study of both elliptic curves and modular forms; - key progress in our understanding of the final Millenium Prize Problem in Mathematics; - academic software to compute special values of L-functions; - applications to computational mathematics, particularly elliptic curve cryptosystems; - a huge boost to the development of number theory Australia-wide.
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