There and back again: operator algebras, algebras and dynamical systems. The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then ....There and back again: operator algebras, algebras and dynamical systems. The aim of this project is to develop mathematics that enables us to transfer information back and forth between dynamical systems and algebras, including operator algebras. Dynamical systems - systems that change over time - are ubiquitous, and central to modern mathematics and its applications. In mathematics, dualities allow us to translate questions from one context to another in which they are easier to solve and then translate the answer back again. Expected outcomes include increased understanding of the relationship between operator algebras and the dynamical systems that they represent. Benefits include enhanced international collaboration, and increased Australian capacity in pure mathematics, particularly operator algebras.Read moreRead less
Australian Laureate Fellowships - Grant ID: FL170100020
Funder
Australian Research Council
Funding Amount
$1,638,060.00
Summary
Advances in index theory and applications. The project aims to develop novel techniques to investigate Geometric analysis on infinite dimensional bundles, as well as Geometric analysis of pathological spaces with Cantor set as fibre, that arise in models for the fractional quantum Hall effect and topological matter, areas recognised with the 1998 and 2016 Nobel Prizes. Building on the applicant’s expertise in the area, the project will involve postgraduate and postdoctoral training in order to e ....Advances in index theory and applications. The project aims to develop novel techniques to investigate Geometric analysis on infinite dimensional bundles, as well as Geometric analysis of pathological spaces with Cantor set as fibre, that arise in models for the fractional quantum Hall effect and topological matter, areas recognised with the 1998 and 2016 Nobel Prizes. Building on the applicant’s expertise in the area, the project will involve postgraduate and postdoctoral training in order to enhance Australia’s position at the forefront of international research in Geometric Analysis. Ultimately, the project will enhance Australia's leading position in the area of Index Theory by developing novel techniques to solve challenging conjectures, and mentoring HDR students and ECRs.Read moreRead less
Twisted K-theory, higher geometry and operator algebras. This project aims to develop new theory and techniques linking twisted K-theory, higher-geometry and operator algebras. These are all fundamental areas of mathematics with applications both within mathematics itself and to mathematical physics, particularly in string theory. Anticipated outcomes are fundamental advances in knowledge in mathematics and mathematical physics, enhancement of Australia's international mathematical reputation an ....Twisted K-theory, higher geometry and operator algebras. This project aims to develop new theory and techniques linking twisted K-theory, higher-geometry and operator algebras. These are all fundamental areas of mathematics with applications both within mathematics itself and to mathematical physics, particularly in string theory. Anticipated outcomes are fundamental advances in knowledge in mathematics and mathematical physics, enhancement of Australia's international mathematical reputation and collaborative linkages, and the training of the next generation of Australian mathematicians.Read moreRead less
Coarse Geometry: a novel approach to the Callias index & topological matter. Coarse geometry is the study of the large-scale structure of metric spaces, in terms of operator algebras. This project aims to use coarse geometry to develop novel approaches to Callias index theory and its applications, and to topological phases of matter, where the Nobel Prize in physics in 2016 was awarded. This will yield new techniques in index theory and other areas, and solutions to several important problems. O ....Coarse Geometry: a novel approach to the Callias index & topological matter. Coarse geometry is the study of the large-scale structure of metric spaces, in terms of operator algebras. This project aims to use coarse geometry to develop novel approaches to Callias index theory and its applications, and to topological phases of matter, where the Nobel Prize in physics in 2016 was awarded. This will yield new techniques in index theory and other areas, and solutions to several important problems. Outcomes include a noncompact generalisation of the famous Guillemin-Sternberg conjecture that quantisation commutes with reduction, and new models of topological phases of matter in terms of K-theory of operator algebras. This project will benefit Australia by reinforcing its position in these highly active areas in science.Read moreRead less
Early Career Industry Fellowships - Grant ID: IE230100048
Funder
Australian Research Council
Funding Amount
$466,097.00
Summary
Ammonium-selective membranes to shift water industry into circular economy. The project aims to develop ammonium-selective membranes which are urgently needed in Australian key industries for sustainable ammonia recovery. The project expects to construct the membranes to achieve desirable pore size and surface functionality for fast and selective ammonia transport. The developed membranes should make ammonia recovery from wastewater more effective and sustainable, leading to the healthy waterway ....Ammonium-selective membranes to shift water industry into circular economy. The project aims to develop ammonium-selective membranes which are urgently needed in Australian key industries for sustainable ammonia recovery. The project expects to construct the membranes to achieve desirable pore size and surface functionality for fast and selective ammonia transport. The developed membranes should make ammonia recovery from wastewater more effective and sustainable, leading to the healthy waterway and reduced energy for both ammonia production and removal. Recovered ammonia expects to produce valuable products, supporting agriculture industry and hydrogen economy. The developed membranes should enable water industry's shift into circular economy, providing significant economic and environmental benefits to Australia.Read moreRead less
Sustainable Hydrogen Production from Used Water. The project aims to address the pressing challenge of water scarcity in hydrogen production by developing an innovative approach of using used water as the feed for water electrolysis. The project will result in an in-depth understanding of the impacts of water impurities in used water on the performance and durability of water electrolysers, and develop guidelines for the design of highly durable water electrolysers and the operation and upgrade ....Sustainable Hydrogen Production from Used Water. The project aims to address the pressing challenge of water scarcity in hydrogen production by developing an innovative approach of using used water as the feed for water electrolysis. The project will result in an in-depth understanding of the impacts of water impurities in used water on the performance and durability of water electrolysers, and develop guidelines for the design of highly durable water electrolysers and the operation and upgrade of existing wastewater treatment plants. The project will advance the practical applications of water electrolysis for scalable and sustainable hydrogen production and help Australia secure a leading position in the global emerging hydrogen economy.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE230101044
Funder
Australian Research Council
Funding Amount
$444,318.00
Summary
Bio-inspired nanomaterials with tunable drug loading and controlled release. This project aims to develop new platform technologies for making bio-inspired nanomaterials with tunable drug loading and controlled release. This project will revolutionise current approaches to make lipid nanoparticles camouflaged with natural cell membranes for delivery of both insoluble and soluble drugs. Significant outcomes will include a novel commercially relevant salt-induced nanoprecipitation platform technol ....Bio-inspired nanomaterials with tunable drug loading and controlled release. This project aims to develop new platform technologies for making bio-inspired nanomaterials with tunable drug loading and controlled release. This project will revolutionise current approaches to make lipid nanoparticles camouflaged with natural cell membranes for delivery of both insoluble and soluble drugs. Significant outcomes will include a novel commercially relevant salt-induced nanoprecipitation platform technology for making precisely engineered nanomaterials with tailored functions for applications in controlled release and targeted delivery. Benefits include securing a sustainable future for Australia, with new nanotechnology strategies for advanced manufacturing.Read moreRead less