Gravity and quantum-limited measurements with a fundamental minimum length. This project aims to investigate the effects of a fundamental minimum length on the nature of gravity and on how accurately we can make measurements in our world. The key challenge is to combine our best theories of fundamental physics to model what happens at ultra-short distances. This project will generate new knowledge at this interface by using a novel approach inspired by information theory. The expected outcomes a ....Gravity and quantum-limited measurements with a fundamental minimum length. This project aims to investigate the effects of a fundamental minimum length on the nature of gravity and on how accurately we can make measurements in our world. The key challenge is to combine our best theories of fundamental physics to model what happens at ultra-short distances. This project will generate new knowledge at this interface by using a novel approach inspired by information theory. The expected outcomes are new connections between fundamental limitations on measurements, the nature of gravitation, and ultra-small-scale quantum physics. The benefit of this work is breaking the logjam in answering the most important open question in all of physics: how to unite quantum theory and gravitation.Read moreRead less
Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected ou ....Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected outcomes will include innovative techniques that will greatly enhance and interconnect our knowledge of field theories and quantum gravity, together with new discoveries in quantum-corrected geometries. A new network of domestic and international experts will largely benefit the fields of theoretical and mathematical physics.Read moreRead less
Physical realisation of enriched quantum symmetries. This project aims to investigate fundamental mathematical structures in modern category theory, providing an algebraic description of physical systems including topological order and conformal field theory. The project will study quantum symmetry, and classify and construct new classes of conformal field theories, using novel tools from enriched category theory, modular forms, and lattice gauge theory.
The main goal is to understand the lands ....Physical realisation of enriched quantum symmetries. This project aims to investigate fundamental mathematical structures in modern category theory, providing an algebraic description of physical systems including topological order and conformal field theory. The project will study quantum symmetry, and classify and construct new classes of conformal field theories, using novel tools from enriched category theory, modular forms, and lattice gauge theory.
The main goal is to understand the landscape of topological and conformal field theories, laying the foundation for new technologies based on topological order. This timely project capitalises on the recent arrival of subfactor experts in Australia, and builds capacity in mathematical research and international links in a cutting edge field.Read moreRead less
Engineering one dimensional quantum phases with nanostructured Josephson junction arrays. This project aims to engineer novel quantum electronic devices based on strongly-coupled, one-dimensional superconducting microcircuits. These will be realised using chains of nanoscale superconducting islands fabricated on a chip. The project expects to achieve a special type of insulating state, where individual charges can be transported one by one. This would be significant as a primary standard that pr ....Engineering one dimensional quantum phases with nanostructured Josephson junction arrays. This project aims to engineer novel quantum electronic devices based on strongly-coupled, one-dimensional superconducting microcircuits. These will be realised using chains of nanoscale superconducting islands fabricated on a chip. The project expects to achieve a special type of insulating state, where individual charges can be transported one by one. This would be significant as a primary standard that precisely links time (or frequency) to charge. The project also aims to create a current mirror device, in which a supercurrent sent down one chain induces a reflected supercurrent in the other, forming the basis of a new superconducting quantum bit. Other devices will be used to study a simplified model related to high temperature superconductors.Read moreRead less
Symmetry and geometric partial differential equations. This project aims to develop tools to assist the study of partial differential equations, which are fundamental to our understanding of the physical world. Symmetries of the Laplace equation are fundamental in both finding and interpreting its solutions and can be traced to the conformal symmetries of the underlying space. Only for the most symmetric of spaces, Euclidean space and the sphere, is this correspondence well understood. Using pow ....Symmetry and geometric partial differential equations. This project aims to develop tools to assist the study of partial differential equations, which are fundamental to our understanding of the physical world. Symmetries of the Laplace equation are fundamental in both finding and interpreting its solutions and can be traced to the conformal symmetries of the underlying space. Only for the most symmetric of spaces, Euclidean space and the sphere, is this correspondence well understood. Using powerful geometric tools from conformal geometry, the project will extend this to less symmetric spaces. The knowledge generated from this project will extend to more general geometric contexts providing a concrete setting for the study of the associated natural equations in curved spaces.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
Rank-dependent choice equilibrium. This project aims to develop and test a new statistical theory of games, Rank-Dependent Choice Equilibrium (RDCE), which has the potential to unify and improve on existing approaches where the extreme reliance on perfect decision making and perfect foresight has raised doubts about their empirical relevance. The project intends to develop the theoretical foundations of RDCE, explore its relation with various parametric approaches, and evaluate RDCE via meta stu ....Rank-dependent choice equilibrium. This project aims to develop and test a new statistical theory of games, Rank-Dependent Choice Equilibrium (RDCE), which has the potential to unify and improve on existing approaches where the extreme reliance on perfect decision making and perfect foresight has raised doubts about their empirical relevance. The project intends to develop the theoretical foundations of RDCE, explore its relation with various parametric approaches, and evaluate RDCE via meta studies and stress tests. Expected outcomes of RDCE include a paradigm shift in game theory, resulting in broader acceptance and adoption of statistical game theory and to more robust policy recommendations.Read moreRead less
Designing Efficient and Equitable Voting Mechanisms. The most commonly used method for collective decision making, majority voting, is generally not efficient as it does not allow voters to express the intensity of their preferences. In addition, majority voting suffers from the tyranny of the majority, i.e. the risk of repeatedly excluding minority groups from representation. A final downside of majority voting is its winner-take-all nature, i.e. it provides no compensation for losing voters. T ....Designing Efficient and Equitable Voting Mechanisms. The most commonly used method for collective decision making, majority voting, is generally not efficient as it does not allow voters to express the intensity of their preferences. In addition, majority voting suffers from the tyranny of the majority, i.e. the risk of repeatedly excluding minority groups from representation. A final downside of majority voting is its winner-take-all nature, i.e. it provides no compensation for losing voters. This project concerns the design of alternative mechanisms that avoid these shortcomings and robustly deliver efficient and equitable outcomes. The project develops the theory underlying these novel mechanisms, tests them in a range of environments, and delivers an implementation for practical use.
Read moreRead less
Broadening Choice and Increasing Diversity in Public Schools. Currently, most families are limited to the public school in their catchment area, meaning the area in which they can afford to live. This leads to socio-economically and ethnically homogenous schools and entrenches disadvantage, as well as denying students the crucial life lessons that flow from being part of a diverse student body. This project aims to investigate a model for allocating public school places that integrates catchment ....Broadening Choice and Increasing Diversity in Public Schools. Currently, most families are limited to the public school in their catchment area, meaning the area in which they can afford to live. This leads to socio-economically and ethnically homogenous schools and entrenches disadvantage, as well as denying students the crucial life lessons that flow from being part of a diverse student body. This project aims to investigate a model for allocating public school places that integrates catchment areas. The expected outcome would be a system that gives families a wider choice, enabling them to enrol in out-of-area schools, while ensuring that allocations remain fair, equitable and balanced, and also delivering benefits such as achieving a desired level of diversity in student populations within schoolsRead moreRead less