Rare Event Simulation with Heavy Tails. The project provides a rigorous way to enhance our understanding of the mechanisms that bring about catastrophic rare events such as urban flooding, electricity shortages and financial bankrupcy. Australia is at the forefront of exciting recent developments in rare event simulation. The advancement of the knowledge in this area will generate a competitive advantage for various sections of the Australian industry, including the areas of industrial reliabili ....Rare Event Simulation with Heavy Tails. The project provides a rigorous way to enhance our understanding of the mechanisms that bring about catastrophic rare events such as urban flooding, electricity shortages and financial bankrupcy. Australia is at the forefront of exciting recent developments in rare event simulation. The advancement of the knowledge in this area will generate a competitive advantage for various sections of the Australian industry, including the areas of industrial reliability, finance and insurance, were accurate simulation techniques are becoming increasingly important.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE130100819
Funder
Australian Research Council
Funding Amount
$281,600.00
Summary
Measuring the improbable: optimal Monte Carlo methods for rare event simulation of maxima of dependent random variables. Some events occurring with low frequency can have dramatic consequences: natural catastrophes, economic crises, system malfunctions. Estimating their probabilities is a very difficult problem. This project will develop new simulation methods capable of delivering the most precise and efficient estimators for the probabilities of such events.
Random network models with applications in biology. Complex biological systems consist of a large number of interacting agents or components, and so can be studied using mathematical random network models. We aim to gain deeper insights into the laws emerging as the random networks evolve in time. This can help us to deal with dangerous disease epidemics and better understand the human brain.
Random Discrete Structures: Approximations and Applications. The behaviour of many real world systems can be modelled by random discrete structures evolving over time. For example, the sizes of populations of frogs in some close patches of forests can be modelled as interacting random processes. The aim of the project is to investigate large discrete random structures that arise from real world application in areas such as biology, complex networks and insurance. The proposed project is at the i ....Random Discrete Structures: Approximations and Applications. The behaviour of many real world systems can be modelled by random discrete structures evolving over time. For example, the sizes of populations of frogs in some close patches of forests can be modelled as interacting random processes. The aim of the project is to investigate large discrete random structures that arise from real world application in areas such as biology, complex networks and insurance. The proposed project is at the interface of mathematics and 'big data' applications and so the work of the project aims to provide theoretical and heuristic underpinnings useful in the algorithms and techniques of practitioners. Understanding the applications in the project requires new, broadly applicable methods and developing such is a complementary aim.Read moreRead less
Games and decisions with bounded rationality: theory and economic implications. This project will develop concepts and tools for decision making in complex environments, where it is impossible to fully characterise the possible outcomes and factors that may affect them. A central goal will be to integrate heuristic rules such as the precautionary principle with the more formal approach adopted in benefit-cost analysis.
Discovery Early Career Researcher Award - Grant ID: DE140100633
Funder
Australian Research Council
Funding Amount
$395,169.00
Summary
Problems in the Langlands Program. The Langlands program is an international research program sitting at the interface of number theory, representation theory, algebraic geometry, and mathematical physics. The aim of this project is to prove three conjectures in this program. Settling these conjectures would lead to significant advances in the Langlands program by strengthening connections between this program and the geometry of loop groups, representations of finite groups, and representations ....Problems in the Langlands Program. The Langlands program is an international research program sitting at the interface of number theory, representation theory, algebraic geometry, and mathematical physics. The aim of this project is to prove three conjectures in this program. Settling these conjectures would lead to significant advances in the Langlands program by strengthening connections between this program and the geometry of loop groups, representations of finite groups, and representations of affine Kac-Moody algebras at the critical level.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
Heterogeneity, Wage Inequality, Unemployment, and Economic Growth. This project would provide the first internally consistent theory of wage inequality, unemployment and economic growth - and the roles that government policy variables play in determining them. It would use and extend frontier developments in theory, and identify the settings of policy variables (unemployment insurance, tax structures, education policies) that maximise social welfare, given that governments must satisfy their bud ....Heterogeneity, Wage Inequality, Unemployment, and Economic Growth. This project would provide the first internally consistent theory of wage inequality, unemployment and economic growth - and the roles that government policy variables play in determining them. It would use and extend frontier developments in theory, and identify the settings of policy variables (unemployment insurance, tax structures, education policies) that maximise social welfare, given that governments must satisfy their budget constraints. It also aims to uncover the relationship between the innate abilities of workers and their education choices - and the consequences for macro economies and public policy.Read moreRead less
Categorical symmetries in representation theory. This project aims to develop categorical symmetries of central objects in mathematics such as braid groups, the Hilbert scheme of points, and the Virasoro algebra. The concept of symmetry is an important organising principle in science. Representation theory is the field of mathematics concerned with studying symmetries. The problems proposed have connections to many different areas including algebra, geometry, topology, and mathematical physics. ....Categorical symmetries in representation theory. This project aims to develop categorical symmetries of central objects in mathematics such as braid groups, the Hilbert scheme of points, and the Virasoro algebra. The concept of symmetry is an important organising principle in science. Representation theory is the field of mathematics concerned with studying symmetries. The problems proposed have connections to many different areas including algebra, geometry, topology, and mathematical physics. This project expects to advance pure mathematics and provide potential benefit in many related fields.Read moreRead less
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