Forecasting and management using imperfect models, with a focus on weather and climate. Research into complex systems is predicted to be the focus of twenty-first century science, since most of the problems of simple systems are solved. Examples include the weather and climate, economies, argriculture, ecologies, the mind and brain, genetics, biochemistry. Confidence in the reliability and usefulness of models will have significant bearing on how these models are used by decision making and how ....Forecasting and management using imperfect models, with a focus on weather and climate. Research into complex systems is predicted to be the focus of twenty-first century science, since most of the problems of simple systems are solved. Examples include the weather and climate, economies, argriculture, ecologies, the mind and brain, genetics, biochemistry. Confidence in the reliability and usefulness of models will have significant bearing on how these models are used by decision making and how the community perceives the value of this science. Specific immediate benefits of the project include better policy and management responses to climate change and servere weather events.Read moreRead less
Synthesis of dynamics, stochastics and information in forecasting and management of complex systems. Research into complex systems is predicted to be the focus of twenty-first century science, since most of the problems of simple systems are solved. Examples include the weather and climate, economies, agriculture, ecologies, the mind and brain, genetics, biochemistry. Confidence in the reliability and usefulness of models will have significant bearing on how these models are used by decision ma ....Synthesis of dynamics, stochastics and information in forecasting and management of complex systems. Research into complex systems is predicted to be the focus of twenty-first century science, since most of the problems of simple systems are solved. Examples include the weather and climate, economies, agriculture, ecologies, the mind and brain, genetics, biochemistry. Confidence in the reliability and usefulness of models will have significant bearing on how these models are used by decision making and how the community perceives the value of this science. Specific immediate benefits of the project include better policy and management responses to climate change and severe weather events.Read moreRead less
Super Duality and Deformations in the Representation Theory of Lie Superalgebras. Supersymmetry has remained in a central stage of fundamental research in both physics and mathematics for the last forty years. It is currently being tested by experiments of massive scales conducted on the Large Hadron Collider at CERN in Geneva. The present project aims to create new mathematical concepts and techniques for addressing fundamental issues of supersymmetry. Expected outcomes include new types of Bos ....Super Duality and Deformations in the Representation Theory of Lie Superalgebras. Supersymmetry has remained in a central stage of fundamental research in both physics and mathematics for the last forty years. It is currently being tested by experiments of massive scales conducted on the Large Hadron Collider at CERN in Geneva. The present project aims to create new mathematical concepts and techniques for addressing fundamental issues of supersymmetry. Expected outcomes include new types of Bose-Fermi correspondence, a deformation theory of Lie superalgebra representations, algebraic and geometric treatments of Jantzen filtration of parabolic Verma modules of Lie superalgebras, and quantum field theoretical models for the topological invariants of knots and 3-manifolds arising from quantum supergroups. Read moreRead less
Geometric themes in the theory of Lie supergroups and their quantisations. This project aims to develop mathematics on the geometry of super spaces and the algebra of super transformations, which are the cornerstones of the mathematical foundation of supersymmetry. The Large Hadron Collider at the European Organization for Nuclear Research is investigating supersymmetry as a possible symmetry of fundamental physics. Its empirical verification would confirm the existence of new constituents of ma ....Geometric themes in the theory of Lie supergroups and their quantisations. This project aims to develop mathematics on the geometry of super spaces and the algebra of super transformations, which are the cornerstones of the mathematical foundation of supersymmetry. The Large Hadron Collider at the European Organization for Nuclear Research is investigating supersymmetry as a possible symmetry of fundamental physics. Its empirical verification would confirm the existence of new constituents of matter, and reveal deep structures of space-time beyond the framework of Einstein's general relativity. Results of the project are expected to be directly applicable to high energy physics.Read moreRead less
Quantised algebras, supersymmetry and invariant theory. The discriminant of a quadratic equation is an invariant which most high school students learn about; it does not change under linear substitution of the variables. This project will develop new theorems about quantum invariants, which occur in quantum and super symmetry. Links will be forged with physics and quantum computing.
A new approach to compressed sensing. Compressed sensing is an exciting new paradigm promising vastly improved signal sampling and reconstruction in a wide variety of applications including digital cameras, mobile phones and MRI machines. This project will explore a newly discovered approach to compressed sensing which uses mathematical arrays known as hash families.
Constructive representation theory of classical and quantum Lie superalgebras. Classical and quantum Lie superalgebras lie at the heart of many recent theoretical developments in the fields of integrable models and conformal field theory. Based on results published in 2013 by the Chief Investigators, it is evident that the time is right to further develop these ideas into a coherent and canonical framework. This ambitious and thorough proposal is focussed on solving sophisticated, contemporary p ....Constructive representation theory of classical and quantum Lie superalgebras. Classical and quantum Lie superalgebras lie at the heart of many recent theoretical developments in the fields of integrable models and conformal field theory. Based on results published in 2013 by the Chief Investigators, it is evident that the time is right to further develop these ideas into a coherent and canonical framework. This ambitious and thorough proposal is focussed on solving sophisticated, contemporary problems in representation theory related to classical and quantum Lie superalgebras that will have immediate consequences in these burgeoning fields.Read moreRead less
Symmetry via braiding, diagrammatics and cellularity. Symmetry is a basic organising tool for humans to understand their environment. Invariants are the mathematical embodiment of symmetry, and their study is as ancient as thought itself. This project aims to use the tools of braided tensor categories and cellular structure, to analyse the invariants occurring in several fundamental areas of mathematics, particularly relating to physics. The endomorphism algebras in certain tensor categories, pa ....Symmetry via braiding, diagrammatics and cellularity. Symmetry is a basic organising tool for humans to understand their environment. Invariants are the mathematical embodiment of symmetry, and their study is as ancient as thought itself. This project aims to use the tools of braided tensor categories and cellular structure, to analyse the invariants occurring in several fundamental areas of mathematics, particularly relating to physics. The endomorphism algebras in certain tensor categories, particularly those for quantised superalgebras, will be realised as diagram algebras, and analysed using cellular theory. The intended output include criteria for semisimplicity, a new theory of diagram algebras, and decomposition theory which are expected to permit the determination of multiplicities of composition factors.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE120100040
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Partitioning and ordering Steiner triple systems. Steiner triple systems are fundamental mathematical objects with many real-world applications. This project will develop deep new insights into these objects, resulting in systems allowing many users to simultaneously use a communication channel, and in schemes for preventing the loss of computer data due to hard disk failures.
Quantum vertex algebras. The project aims to address major mathematical problems on the structure and representations of the families of quantum groups and vertex algebras associated with Lie algebras. Originating from solvable lattice models in statistical mechanics, the theory of quantum groups has important connections with, and applications to, a wide range of subjects in mathematics and physics. The project will extend and develop explicit theory of both the classical and quantum versions o ....Quantum vertex algebras. The project aims to address major mathematical problems on the structure and representations of the families of quantum groups and vertex algebras associated with Lie algebras. Originating from solvable lattice models in statistical mechanics, the theory of quantum groups has important connections with, and applications to, a wide range of subjects in mathematics and physics. The project will extend and develop explicit theory of both the classical and quantum versions of the vertex algebras which are of importance to conformal field theory and soliton spin-chain models.Read moreRead less