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Multiparameter Harmonic Analysis: Weighted Estimates for Singular Integrals. This project aims to study advanced harmonic analysis concerning multiparameter theory and related topics. Harmonic analysis lies at the intersection of the frontiers of many branches of mathematics. It is fundamental to the study of operator theory and partial differential equations which has wide applications in many fields such as mathematical modelling, probability and number theory. This project aims to solve a num ....Multiparameter Harmonic Analysis: Weighted Estimates for Singular Integrals. This project aims to study advanced harmonic analysis concerning multiparameter theory and related topics. Harmonic analysis lies at the intersection of the frontiers of many branches of mathematics. It is fundamental to the study of operator theory and partial differential equations which has wide applications in many fields such as mathematical modelling, probability and number theory. This project aims to solve a number of open problems at the frontier of research in modern harmonic analysis including estimates on multilinear operators with nonsmooth kernels and advanced multiparameter theory on product spaces.Read moreRead less
Harmonic analysis: function spaces and singular integral operators. This project advances knowledge in harmonic analysis to new settings such as dyadic and multiparameter theories, Laplacian-like operators, and rough singular integrals. Outcomes will be solutions to long-standing problems, training of researchers, strong links with international researchers and enhancement of Australia's reputation in mathematics.
Bundle gerbes: generalisations and applications. This project is fundamental, basic research at the forefront of modern differential geometry and its application to physics. It will ensure that Australia is involved in today's mathematical and physical advances and that we have Australian mathematicians trained to take advantage of the future benefits of these advances.
Geometric transforms and duality. This Proposal is fundamental, basic research at the forefront of modern differential geometry and its application to physics. It will ensure that Australia is involved in today's mathematical and physical advances and that we have Australian mathematicians trained to take advantage of the future benefits of these advances.
Discovery Early Career Researcher Award - Grant ID: DE160100525
Funder
Australian Research Council
Funding Amount
$392,053.00
Summary
Index Theory for Spaces with Symmetries. This project aims to study spaces with symmetries, which are important geometric models in topology and representation theory. The project plans to conduct research into geometric approaches to the representation theory of groups using KK theory and index theory from the perspective of operator algebra. The expected outcomes of this project are constructions of new topological invariants and their geometric formulas for spaces with symmetries and applicat ....Index Theory for Spaces with Symmetries. This project aims to study spaces with symmetries, which are important geometric models in topology and representation theory. The project plans to conduct research into geometric approaches to the representation theory of groups using KK theory and index theory from the perspective of operator algebra. The expected outcomes of this project are constructions of new topological invariants and their geometric formulas for spaces with symmetries and applications in representation theory.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE120100901
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Deformation quantisation and index theory for semi-simple groups. Deformation quantisation is a mathematical technique for describing the counter-intuitive geometry of quantum physics as a small variation of classical geometry as Newton would have known it. This project will apply the same techniques to solve fundamental mathematical problems in the study of symmetries.
Symmetries in real and complex geometry. This project concerns an important area of abstract modern geometry. The results and techniques of the project will lead to significant progress in this area. It will benefit the national scientific reputation, strengthen the research profile of the home institutions, and provide training to young researchers.
Discovery Early Career Researcher Award - Grant ID: DE120102657
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Group actions and K-theory: a new direction. This project investigates cutting-edge research in the mathematics of symmetries arising in nature. The aim is to significantly advance the frontiers of our knowledge by introducing new examples, original methods and a modern perspective.
Holonomy groups in Lorentzian geometry. The project studies mathematical models used in physical theories, such as general relativity and string theory, to create a global picture of the universe. The outcomes will enhance the role Australia plays in these developments and contribute to the mathematical knowledge which lies at the foundations of modern technologies.
Holonomy groups and special structures in pseudo-Riemannian geometry. The project studies mathematical models used in physical theories, such as general relativity and string theory, to create a global picture of the universe. The outcomes will enhance the role that Australia plays in these developments and contribute to the mathematical knowledge which lies at the foundations of modern technologies.