Discovery Early Career Researcher Award - Grant ID: DE200100896
Funder
Australian Research Council
Funding Amount
$427,008.00
Summary
How to beat model uncertainty with more information. Experience of the 2008 financial crisis exposed a weakness in our over-reliance on mathematical models. The main aim of this project is to develop mathematical tools to investigate the role of information in reducing model uncertainty. The project will undertake pressing research in robust finance, which is now one of the most active and dynamic topics in financial mathematics. It expects to quantify the value of information under uncertainty ....How to beat model uncertainty with more information. Experience of the 2008 financial crisis exposed a weakness in our over-reliance on mathematical models. The main aim of this project is to develop mathematical tools to investigate the role of information in reducing model uncertainty. The project will undertake pressing research in robust finance, which is now one of the most active and dynamic topics in financial mathematics. It expects to quantify the value of information under uncertainty in mathematical modelling. It will generate new knowledge in probability theory and stochastic processes providing a significant mathematical contribution in its own right.Read moreRead less
Hypergraph models for complex discrete systems. This project aims to better understand the structure and properties of very large hypergraphs of various kinds. Hypergraphs are very general mathematical objects which can be used to model complex discrete systems. They arise naturally in many areas such as ecology, chemistry and computer science. Despite this, our theoretical understanding of very large, or random, hypergraphs lags far behind the intensely-studied special case of graphs. This proj ....Hypergraph models for complex discrete systems. This project aims to better understand the structure and properties of very large hypergraphs of various kinds. Hypergraphs are very general mathematical objects which can be used to model complex discrete systems. They arise naturally in many areas such as ecology, chemistry and computer science. Despite this, our theoretical understanding of very large, or random, hypergraphs lags far behind the intensely-studied special case of graphs. This project will answer many fundamental questions about large, random hypergraphs. The expected outcomes of the project also include new tools for working with hypergraphs, such as efficient algorithms for sampling hypergraphs. These outcomes will benefit researchers who use hypergraphs in their work and will enhance Australia's reputation for research in this area.Read moreRead less
New universality in stochastic systems. This project aims to uncover new analyses and effects in the complex behaviour of non-linear systems with random noise. Many systems originate near an unstable equilibrium. This project will develop a new mathematical theory that establishes a universality in the way the long term effect of noise expresses itself as random initial conditions in the dynamics. It will fill gaps in Mathematics and make refinements to existing fundamental scientific laws by in ....New universality in stochastic systems. This project aims to uncover new analyses and effects in the complex behaviour of non-linear systems with random noise. Many systems originate near an unstable equilibrium. This project will develop a new mathematical theory that establishes a universality in the way the long term effect of noise expresses itself as random initial conditions in the dynamics. It will fill gaps in Mathematics and make refinements to existing fundamental scientific laws by including random initial conditions as predicted by our theory. This will advance our understanding of complex systems subjected to noise and will provide significant benefits in the scientific discoveries in Biology, Ecology, Physics and other Sciences where such systems are frequently met.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
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
The economics of (mis)information in the age of social media. New media technologies allow anyone to broadcast their views, leading to a “cacophony of voices” where misinformation flourishes. Tools from information economics are tailor-made for understanding information consumption in settings with many biased news sources. We develop economic models where many sources compete to attract and influence heterogenous listeners. We then study how misinformation spreads and amplifies when consumers ....The economics of (mis)information in the age of social media. New media technologies allow anyone to broadcast their views, leading to a “cacophony of voices” where misinformation flourishes. Tools from information economics are tailor-made for understanding information consumption in settings with many biased news sources. We develop economic models where many sources compete to attract and influence heterogenous listeners. We then study how misinformation spreads and amplifies when consumers of information communicate with many others through a social network. Finally, we study how to design simple and robust rules to foster informative discourse and filter misinformation. The results will shape economic policy recommendations for regulating misinformation in media platforms and social media.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.
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Productivity, growth and unemployment in economies with frictions. This project aims to examine decisions driving productivity, growth, and unemployment in macroeconomies with frictions. It examines how government (fiscal, monetary, and education) policies determine these decisions, and identifies the best configurations of these policies. It will construct dynamic general equilibrium models of economies to analyse the causal structure behind productivity changes, growth and unemployment. It wil ....Productivity, growth and unemployment in economies with frictions. This project aims to examine decisions driving productivity, growth, and unemployment in macroeconomies with frictions. It examines how government (fiscal, monetary, and education) policies determine these decisions, and identifies the best configurations of these policies. It will construct dynamic general equilibrium models of economies to analyse the causal structure behind productivity changes, growth and unemployment. It will conduct quantitative experiments using simulations, to estimate optimal government policy design settings. This project expects to identify policies that promote productivity, growth and employment.Read moreRead less