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Discovery Early Career Researcher Award - Grant ID: DE210100180
Funder
Australian Research Council
Funding Amount
$400,475.00
Summary
Effective classification of closed vertex-transitive groups acting on trees. Symmetry is a fundamental organising principle in mathematics and human endeavour. This project aims to advance our knowledge of zero-dimensional symmetry, a frontier in symmetry research. In the longer term, advancements in fundamental knowledge in this area have the potential to inform the usage and development of digital structures in more practical contexts, such as data networks and information processing. The proj ....Effective classification of closed vertex-transitive groups acting on trees. Symmetry is a fundamental organising principle in mathematics and human endeavour. This project aims to advance our knowledge of zero-dimensional symmetry, a frontier in symmetry research. In the longer term, advancements in fundamental knowledge in this area have the potential to inform the usage and development of digital structures in more practical contexts, such as data networks and information processing. The project is expected to develop new tools of both theoretical and computational nature that will accelerate ongoing research across the field and enable new approaches. This will cement Australia's position at the forefront of research in symmetry and its use in the digital age.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE150100308
Funder
Australian Research Council
Funding Amount
$283,536.00
Summary
Branching and self-similarity in group actions. This project aims to develop the theory of groups of symmetries that have self-similarity (part of the object has the same structure as the whole) and branching (transformations may be performed on parts of the object independently of one another while preserving the overall structure). The focus will be on a class of topological groups in which these properties frequently occur, building on methods recently developed and their actions on trees and ....Branching and self-similarity in group actions. This project aims to develop the theory of groups of symmetries that have self-similarity (part of the object has the same structure as the whole) and branching (transformations may be performed on parts of the object independently of one another while preserving the overall structure). The focus will be on a class of topological groups in which these properties frequently occur, building on methods recently developed and their actions on trees and on the Cantor set. The project aims to significantly advance the theory of locally compact groups, as well as giving insights into the phenomena of self-similarity and branching as they occur in group theory and dynamical systems.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE140100088
Funder
Australian Research Council
Funding Amount
$378,628.00
Summary
Computing with matrix groups and Lie algebras: new concepts and applications. Computational algebra combines symbolic computation and pure research in algebra, and is concerned with the design of algorithms for solving mathematical problems endowed with algebraic structure. Matrix groups and Lie algebras are prominent algebraic objects describing the natural concept of symmetry. Despite being very common and important in science, there is a paucity of algorithms to study their structure. This pr ....Computing with matrix groups and Lie algebras: new concepts and applications. Computational algebra combines symbolic computation and pure research in algebra, and is concerned with the design of algorithms for solving mathematical problems endowed with algebraic structure. Matrix groups and Lie algebras are prominent algebraic objects describing the natural concept of symmetry. Despite being very common and important in science, there is a paucity of algorithms to study their structure. This project will develop deep new mathematical theories for computing with these objects, leading to ground-breaking advances in computational algebra, and providing powerful tools facilitating new research, including in other sciences. The new functionality will be used to solve two classification problems in group and Lie theory.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE140101137
Funder
Australian Research Council
Funding Amount
$389,470.00
Summary
Synthesis, Structure and Utility of Novel P-chiral and C-chiral Organophosphido Metal Complexes . The formation of new molecules requires original methods to achieve their synthesis with greatest efficiency. Organometallic chemistry remains crucial for establishing novel reagents and processes. Driven by advances in organo-multi-metallic chemistry this project will build upon fundamental concepts in main group and transition metal chemistry to establish the area of phosphorous-chiral and carbon- ....Synthesis, Structure and Utility of Novel P-chiral and C-chiral Organophosphido Metal Complexes . The formation of new molecules requires original methods to achieve their synthesis with greatest efficiency. Organometallic chemistry remains crucial for establishing novel reagents and processes. Driven by advances in organo-multi-metallic chemistry this project will build upon fundamental concepts in main group and transition metal chemistry to establish the area of phosphorous-chiral and carbon-chiral organophosphido metal chemistry. By rationally designing and integrating new chiral phosphido ligands into mono- and mixed-metal organometallic complexes, chemists will have access to a suite of new tools for application in asymmetric synthesis and catalysis, all relevant to the fields of structural, sustainable and biological chemistry.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE230100579
Funder
Australian Research Council
Funding Amount
$445,754.00
Summary
The existence and abundance of small bases of permutation groups. This project aims to study bases for permutation groups, which are the mathematical formalisation of symmetry. Bases are crucial to encoding and computing with groups in diverse areas of science. Small bases are desirable for efficiency, but can be hard to find. This project expects to combine techniques from areas of algebra and probability to determine the existence and abundance of bases. Expected outcomes of this project inclu ....The existence and abundance of small bases of permutation groups. This project aims to study bases for permutation groups, which are the mathematical formalisation of symmetry. Bases are crucial to encoding and computing with groups in diverse areas of science. Small bases are desirable for efficiency, but can be hard to find. This project expects to combine techniques from areas of algebra and probability to determine the existence and abundance of bases. Expected outcomes of this project include new methods to address enduring open problems in the study of bases, as well as novel applications of existing techniques. This should provide significant benefits, such as creating and strengthening international collaborations, and building on Australia’s reputation as a powerhouse of finite group theory.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE160100081
Funder
Australian Research Council
Funding Amount
$306,000.00
Summary
Structure theory for permutation groups and local graph theory conjectures. The focus of this project is on graphs, which are mathematical descriptions of networks, and it seeks to answer fundamental questions about how many symmetries such objects possess. This question is important since the symmetries of an object reveal its deepest structure. One of the main aims of this project it to convert local information into global properties of graphs. To make progress on the investigation of graphs, ....Structure theory for permutation groups and local graph theory conjectures. The focus of this project is on graphs, which are mathematical descriptions of networks, and it seeks to answer fundamental questions about how many symmetries such objects possess. This question is important since the symmetries of an object reveal its deepest structure. One of the main aims of this project it to convert local information into global properties of graphs. To make progress on the investigation of graphs, this project aims to classify the symmetry groups which arise from the local viewpoint. This classification is expected to provide new insight into symmetrical structures and have further impact on other areas of group theory.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE130101521
Funder
Australian Research Council
Funding Amount
$302,845.00
Summary
Permutation groups with finite subdegrees and the structure of totally disconnected locally compact groups. Understanding the symmetries of a structure is one way of determining its nature. Our lack of knowledge of these symmetries is holding back research in combinatorics and topological group theory. This project aims to understand the symmetries of an important collection of infinite structures that arise naturally in other areas of mathematics.
Discovery Early Career Researcher Award - Grant ID: DE130101001
Funder
Australian Research Council
Funding Amount
$300,000.00
Summary
Enumeration of vertex-transitive graphs. Graphs that are very symmetrical are very useful in constructing and describing large networks in a compact and understandable form. This project will involve high quality mathematical research on symmetrical graphs, which are also central to the mathematical field of algebraic graph theory.
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
Discovery Early Career Researcher Award - Grant ID: DE190100524
Funder
Australian Research Council
Funding Amount
$422,574.00
Summary
Heterometallic iron-molybdenum complexes for nitrogen activation. This project aims to develop a range of bio-inspired, mixed metal iron-molybdenum complexes that are capable of activating molecular nitrogen, N2, at ambient pressure and temperature. The activation of atmospheric N2 is performed on a multi-million tonne scale each year and is key to a number of industrial processes. The project expects to generate new knowledge in the area of organometallic chemistry, specifically with regards to ....Heterometallic iron-molybdenum complexes for nitrogen activation. This project aims to develop a range of bio-inspired, mixed metal iron-molybdenum complexes that are capable of activating molecular nitrogen, N2, at ambient pressure and temperature. The activation of atmospheric N2 is performed on a multi-million tonne scale each year and is key to a number of industrial processes. The project expects to generate new knowledge in the area of organometallic chemistry, specifically with regards to molecular metal-metal bonding and subsequent reactivity towards the activation of N2. Expected outcomes include new and improved catalysts, which will provide significant financial benefits to industry, as well as benefiting the environment by reducing energy demand.Read moreRead less