The Australian Research Data Commons (ARDC) invites you to participate in a short survey about your
interaction with the ARDC and use of our national research infrastructure and services. The survey will take
approximately 5 minutes and is anonymous. It’s open to anyone who uses our digital research infrastructure
services including Reasearch Link Australia.
We will use the information you provide to improve the national research infrastructure and services we
deliver and to report on user satisfaction to the Australian Government’s National Collaborative Research
Infrastructure Strategy (NCRIS) program.
Please take a few minutes to provide your input. The survey closes COB Friday 29 May 2026.
Complete the 5 min survey now by clicking on the link below.
Graded semisimple deformations. Recent advances in representation theory have revealed beautiful new structures in the classical representation theory of the symmetric groups and Hecke algebras. These discoveries have provided us with new algebras, the cyclotomic KLR algebras, that encode deep properties of fundamental objects in algebraic combinatorics and geometric representation theory. The cyclotomic quiver Hecke algebras are central to several open problems in mathematics but they are still ....Graded semisimple deformations. Recent advances in representation theory have revealed beautiful new structures in the classical representation theory of the symmetric groups and Hecke algebras. These discoveries have provided us with new algebras, the cyclotomic KLR algebras, that encode deep properties of fundamental objects in algebraic combinatorics and geometric representation theory. The cyclotomic quiver Hecke algebras are central to several open problems in mathematics but they are still poorly understood, with even basic properties like their dimensions being unknown. This project will establish a new framework for studying these algebras that will remove the current obstacles in this field and alllow us to prove substantial new results that advance the theory.Read moreRead less
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
Mitochondrial targeting by a new class of gadolinium agents. This research project will lead to the development of new molecular agents containing the element gadolinium which can selectively accumulate within cell mitochondria, with a long-term application in cutting-edge therapies involving X-rays or neutrons. The lanthanoid element gadolinium offers many unique opportunities for medicinal chemistry and this project will generate new knowledge in bioinorganic chemistry and synchrotron science. ....Mitochondrial targeting by a new class of gadolinium agents. This research project will lead to the development of new molecular agents containing the element gadolinium which can selectively accumulate within cell mitochondria, with a long-term application in cutting-edge therapies involving X-rays or neutrons. The lanthanoid element gadolinium offers many unique opportunities for medicinal chemistry and this project will generate new knowledge in bioinorganic chemistry and synchrotron science. The expected outcomes of this research will address many of the unresolved questions regarding mitochondrially-targeted gadolinium complexes, the first such agents specifically designed for potential long-term application in binary therapies and imaging.Read moreRead less
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
Diagram categories and transformation semigroups. A structural understanding of diagram categories is essential in many branches of mathematics and science. Despite this, very few methods for studying such categories are available, a fact this pure mathematics project seeks to rectify. By building strong bridges between diagram categories and semigroup theory, a field of abstract algebra that models transformation and change, the structure of diagram categories may be unlocked with powerful semi ....Diagram categories and transformation semigroups. A structural understanding of diagram categories is essential in many branches of mathematics and science. Despite this, very few methods for studying such categories are available, a fact this pure mathematics project seeks to rectify. By building strong bridges between diagram categories and semigroup theory, a field of abstract algebra that models transformation and change, the structure of diagram categories may be unlocked with powerful semigroup tools developed by the applicant investigator. Diagrammatic insights will also yield new ways to study semigroups, and the many other mathematical structures they interact with. Outcomes will have a lasting impact on both theories as well as the many fields influenced by them.Read moreRead less
A safety-preserving ecosystem for autonomous driving. In this project, Macquarie University will collaborate with UTS and SilverQuest to develop an innovative safety-preserving ecosystem for autonomous driving. This system will not only be adopted by SilverQuest’s customers (automotive companies) to secure their latest autonomous driving models, but also be commercialised as a toolset that can be plugged into existing autonomous vehicles to detect and prevent malicious attacks on autonomous driv ....A safety-preserving ecosystem for autonomous driving. In this project, Macquarie University will collaborate with UTS and SilverQuest to develop an innovative safety-preserving ecosystem for autonomous driving. This system will not only be adopted by SilverQuest’s customers (automotive companies) to secure their latest autonomous driving models, but also be commercialised as a toolset that can be plugged into existing autonomous vehicles to detect and prevent malicious attacks on autonomous driving models. The project will lead to two innovations: in theory design an attack detection and prevention ecosystem for autonomous driving and in application implement a safety analysis toolset for industry-scale autonomous systems.Read moreRead less
Categorical representation theory and applications. Symmetry is everywhere, and nature is designed symmetrically: Snails make their shells, spiders design their webs, and bees build hexagonal honeycombs, all based on the concept of symmetry. Symmetry is a general principle which plays an important role in various areas of knowledge and perception, ranging from arts to natural sciences and mathematics.
The 21th century way of the study of symmetries is categorical representation theory. The proj ....Categorical representation theory and applications. Symmetry is everywhere, and nature is designed symmetrically: Snails make their shells, spiders design their webs, and bees build hexagonal honeycombs, all based on the concept of symmetry. Symmetry is a general principle which plays an important role in various areas of knowledge and perception, ranging from arts to natural sciences and mathematics.
The 21th century way of the study of symmetries is categorical representation theory. The project aims are to strengthen this young field by advancing the theory and by finding applications from where its significance arises. The outcome will be new results on categorical representations and this will have benefits within mathematics, cryptography and also in physics/chemistry in the long run.Read moreRead less
Machine learning, group theory and combinatorics. This project aims to investigate group theory and combinatorics using machine learning techniques. This project expects to generate new knowledge concerning symmetric groups and symmetric functions, using an innovative approach from reinforcement learning. Expected outcomes of this project include a clarification of the types of difficult problems in pure mathematics that can be gainfully attacked via machine learning, and an understanding of the ....Machine learning, group theory and combinatorics. This project aims to investigate group theory and combinatorics using machine learning techniques. This project expects to generate new knowledge concerning symmetric groups and symmetric functions, using an innovative approach from reinforcement learning. Expected outcomes of this project include a clarification of the types of difficult problems in pure mathematics that can be gainfully attacked via machine learning, and an understanding of the role of group theory in machine learning. This should provide significant benefits, such as progress on long standing open problems, the development of an emerging technology with significant implications for mathematics, and the training of Australian scientists in a vital area of research.Read moreRead less
New constructions and techniques for tensor categories. The goal of this project is to make fundamental advances in the structure theory of tensor categories. Such categories play crucial roles in numerous fields of mathematics, physics and beyond. New methods, theory and examples will be developed, inspired by algebra, representation theory and geometry. These will then be applied in the foundational study of tensor categories for (dis)proving several of the most important open conjectures in t ....New constructions and techniques for tensor categories. The goal of this project is to make fundamental advances in the structure theory of tensor categories. Such categories play crucial roles in numerous fields of mathematics, physics and beyond. New methods, theory and examples will be developed, inspired by algebra, representation theory and geometry. These will then be applied in the foundational study of tensor categories for (dis)proving several of the most important open conjectures in the field. This will open new perspectives for applications in other areas, most notably in representation theory. Other benefits include enhanced international collaboration and scientific capacity in Australia.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE190101099
Funder
Australian Research Council
Funding Amount
$420,256.00
Summary
Representation theory: studies of symmetry shadows. This project aims to solve fundamental problems in representation theory by combining cutting-edge techniques and developing novel higher level structures. Representation theory is the mathematical study of symmetry, an essential concept in science. Since the 1990s, mathematicians have been observing shadows of a more general notion of symmetry but so far have failed to explain it. Expected outcomes include a structural explanation of these sh ....Representation theory: studies of symmetry shadows. This project aims to solve fundamental problems in representation theory by combining cutting-edge techniques and developing novel higher level structures. Representation theory is the mathematical study of symmetry, an essential concept in science. Since the 1990s, mathematicians have been observing shadows of a more general notion of symmetry but so far have failed to explain it. Expected outcomes include a structural explanation of these shadows, new mathematical software to understand them and solutions to important conjectures. This project will make a significant contribution to the field of representation theory, with ramifications in mathematical physics and computer science.Read moreRead less