Integral transforms and moduli theory. This project is in algebraic geometry, a branch of pure
mathematics. An overarching goal is a better understanding of the
algebra underlying the sophisticated geometries that arise in the
classification problems that are pervasive in mathematics and its
applications to physics. This new knowledge will then be applied to
further elucidate the geometry of these spaces.
Expected outcomes of this project include major progress in our
understanding of derived ....Integral transforms and moduli theory. This project is in algebraic geometry, a branch of pure
mathematics. An overarching goal is a better understanding of the
algebra underlying the sophisticated geometries that arise in the
classification problems that are pervasive in mathematics and its
applications to physics. This new knowledge will then be applied to
further elucidate the geometry of these spaces.
Expected outcomes of this project include major progress in our
understanding of derived categories of algebraic stacks via the
Fourier-Mukai transform.
The benefit will be to enhance the international stature of Australian
science.Read moreRead less
Topology through applications: geometry, number theory and physics. Topology is the part of geometry that remains invariant under deformation (as in the inflation of a balloon). We will apply this flexibility to investigate deep problems in several disciplines as diverse as number theory, geometry and the mathematics of string theory.
Using Abstract Networks to Study Symmetry. An operad is a mathematical tool for packaging the connection between discrete blocks of information. In other words, an operad is a type of network, particularly suited for approaching complex problems by breaking them into smaller, manageable packets. This project aims to reimagine classical objects in geometry and topology such as Teichmüller space as variations of infinity operads. This reimagining will ensure new insights into key objects across th ....Using Abstract Networks to Study Symmetry. An operad is a mathematical tool for packaging the connection between discrete blocks of information. In other words, an operad is a type of network, particularly suited for approaching complex problems by breaking them into smaller, manageable packets. This project aims to reimagine classical objects in geometry and topology such as Teichmüller space as variations of infinity operads. This reimagining will ensure new insights into key objects across three areas of mathematics: algebraic number theory (the mathematics of modern encryption), the representation theory of quantum groups and topological quantum field theories. Read moreRead less
Universal structures in stringy extra dimensions. The project aims to study properties of extra dimensions in string theory by means of techniques from supersymmetric gauge theory. This new approach makes it possible to study areas in the landscape of stringy extra dimensions that have not been accessible before. The project expects to uncover new universal features. This will have significant impact on string theory and mathematics. Expected outcomes of this project include answers to conceptua ....Universal structures in stringy extra dimensions. The project aims to study properties of extra dimensions in string theory by means of techniques from supersymmetric gauge theory. This new approach makes it possible to study areas in the landscape of stringy extra dimensions that have not been accessible before. The project expects to uncover new universal features. This will have significant impact on string theory and mathematics. Expected outcomes of this project include answers to conceptual questions in string theory, new types of extra dimensions, and new methods to compute quantum corrections in string theory. This should provide significant benefits, such as interdisciplinary collaborations at the national and international level and a strengthening of string theory in Australia.Read moreRead less
Quasi-subtractive varieties: a unified framework for substructural, modal and quantum logic. An algebraic theory is proposed that provides a common umbrella for a plethora of non-classical logics. At the same time, it identifies a core that these logics share with classical algebras.
Structure of relations: algebra and applications. Relations and relational structures form the fundamental mathematical essence required for studying computational problems and computational systems. This project will provide new algebraic methods for solving old problems in the theory of relations, informing our understanding of computational complexity and the nature of computing.
Monetary and Fiscal Policy under Imperfect Knowledge. This project lays out an agenda exploring the consequences of imperfect knowledge for macroeconomic dynamics and stabilisation policy. Learning dynamics are central to understanding aggregate fluctuations in periods during which agents have limited information about their environment, as has been the case during and after the Global Financial Crisis. The agenda comprises two lines of inquiry. The first develops theoretical issues relating to ....Monetary and Fiscal Policy under Imperfect Knowledge. This project lays out an agenda exploring the consequences of imperfect knowledge for macroeconomic dynamics and stabilisation policy. Learning dynamics are central to understanding aggregate fluctuations in periods during which agents have limited information about their environment, as has been the case during and after the Global Financial Crisis. The agenda comprises two lines of inquiry. The first develops theoretical issues relating to the design and implementation of monetary and fiscal policy under imperfect knowledge. The second adduces empirical evidence on the classes of possible beliefs that any macroeconomic model should account for.Read moreRead less
Modelling, Identification and Control of Complex Networks. Australia has been well known for its leading research in systems and control and many real-world applications in, for instance, telecommunications, defence, power grids and life sciences. This project will further promote Australia's leading position in the emerging new research field - complex networks by theoretical breakthrough in modelling, identification and control of complex networks, and cutting-edge platform technology that can ....Modelling, Identification and Control of Complex Networks. Australia has been well known for its leading research in systems and control and many real-world applications in, for instance, telecommunications, defence, power grids and life sciences. This project will further promote Australia's leading position in the emerging new research field - complex networks by theoretical breakthrough in modelling, identification and control of complex networks, and cutting-edge platform technology that can help Australian energy industry to reduce greenhouse emissions. It will also result in education of the next generation research leaders in this emerging field.Read moreRead less
Logarithmic conformal field theory and the 4D/2D correspondence. Conformal field theory provides powerful methods for attacking problems in theoretical physics and furnishes beautiful connections between seemingly disparate branches of pure mathematics. This proposal aims to greatly expand our knowledge of the logarithmic conformal field theories that have recently witnessed a resurgence of interest in physics. Advancing these theories is crucial to progress in high-energy physics and pure mathe ....Logarithmic conformal field theory and the 4D/2D correspondence. Conformal field theory provides powerful methods for attacking problems in theoretical physics and furnishes beautiful connections between seemingly disparate branches of pure mathematics. This proposal aims to greatly expand our knowledge of the logarithmic conformal field theories that have recently witnessed a resurgence of interest in physics. Advancing these theories is crucial to progress in high-energy physics and pure mathematics. Expected outcomes include a completely new understanding of the mathematical structure of these theories which will, in turn, facilitate applications in 4D gauge theory. This will boost research capacity and further cement Australia's reputation as an international leader in mathematical physics research.Read moreRead less
In Public / In Focus: Photography, Testimony and the Public Sphere. Photography plays an important but little understood role in the public sphere. Photographs invite viewers to identify with stories, events and others, and the ease with which photographs circulate in print and online makes them ideal for fostering discourse and debate. However, the increasing focus on testimony and witness in contemporary culture has recently altered the way that photography operates in public and raised some s ....In Public / In Focus: Photography, Testimony and the Public Sphere. Photography plays an important but little understood role in the public sphere. Photographs invite viewers to identify with stories, events and others, and the ease with which photographs circulate in print and online makes them ideal for fostering discourse and debate. However, the increasing focus on testimony and witness in contemporary culture has recently altered the way that photography operates in public and raised some significant problems for photography historians regarding the representation of events, others and the past. This project will respond to these problems, and produce a new understanding of the historical, social, cultural and political links between photography and the public sphere today.Read moreRead less