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
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
Frobenius manifolds from a geometrical and categorical viewpoint. This project aims to provide connections between Frobenius manifolds obtained from algebraic curves in diverse ways. The different constructions, using complex geometry on the one hand and category theory on the other, provide, respectively, a quantitative and qualitative view on the same Frobenius manifold. Together, these distinct points of view allow for the calculation of previously inaccessible physical quantities, and point ....Frobenius manifolds from a geometrical and categorical viewpoint. This project aims to provide connections between Frobenius manifolds obtained from algebraic curves in diverse ways. The different constructions, using complex geometry on the one hand and category theory on the other, provide, respectively, a quantitative and qualitative view on the same Frobenius manifold. Together, these distinct points of view allow for the calculation of previously inaccessible physical quantities, and point to deep new relations between algebraic, complex and differential geometry. These relations are expected to guide new fundamental research on the border of mathematics and physics.Read moreRead less
Proving the Landau-Ginzburg/Conformal Field Theory correspondence. This project aims to provide the first precise mathematical statement and geometric proof of the Landau-Ginzburg/Conformal Field Theory (LG/CFT) correspondence for simple singularities, a physically motivated principle that relates hypersurface singularities in algebraic geometry to representations of vertex algebras in conformal field theory. The formalism developed here is expected to clarify the nature of the correspondence an ....Proving the Landau-Ginzburg/Conformal Field Theory correspondence. This project aims to provide the first precise mathematical statement and geometric proof of the Landau-Ginzburg/Conformal Field Theory (LG/CFT) correspondence for simple singularities, a physically motivated principle that relates hypersurface singularities in algebraic geometry to representations of vertex algebras in conformal field theory. The formalism developed here is expected to clarify the nature of the correspondence and lead directly to generalisations beyond simple singularities, as well as provide a dictionary to translate methods of CFT into singularity theory and vice versa. These results will further cement Australia's reputation as an international leader in pure mathematics and mathematical physics research.Read moreRead less
Classical and quantum invariants of low-dimensional manifolds. This project aims to advance our understanding of knots and 3-dimensional spaces, which arise naturally in fields as diverse as physics, computer graphics, chemistry and biology. Recent ideas from quantum field theory link physics to topology in dimensions 3 and 4, leading to powerful invariants of knots and 3-dimensional manifolds that include the Jones polynomial and the 3D-index. This project aims to resolve key questions relating ....Classical and quantum invariants of low-dimensional manifolds. This project aims to advance our understanding of knots and 3-dimensional spaces, which arise naturally in fields as diverse as physics, computer graphics, chemistry and biology. Recent ideas from quantum field theory link physics to topology in dimensions 3 and 4, leading to powerful invariants of knots and 3-dimensional manifolds that include the Jones polynomial and the 3D-index. This project aims to resolve key questions relating these quantum invariants to classical topology and geometry. The project will have a major impact in low-dimensional topology, and lead to deep and unexpected connections between mathematics and mathematical physics.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
Discovery Early Career Researcher Award - Grant ID: DE230100829
Funder
Australian Research Council
Funding Amount
$425,100.00
Summary
Geometric approaches to quantum many body problems. The project aims to utilise results from differential geometry and related areas to investigate the physics of interacting many-body quantum systems. This project expects to generate new knowledge in the area of mathematical physics with broad applications in quantum information, condensed matter physics and statistical mechanics. The key focus will lie on the development of variational methods for the efficient simulation of quantum evolution ....Geometric approaches to quantum many body problems. The project aims to utilise results from differential geometry and related areas to investigate the physics of interacting many-body quantum systems. This project expects to generate new knowledge in the area of mathematical physics with broad applications in quantum information, condensed matter physics and statistical mechanics. The key focus will lie on the development of variational methods for the efficient simulation of quantum evolution and the characterisation of suitable quantum state families by their correlation structures.Read moreRead less
Social Network Analysis: Social Media, Peer Effects and the Environment. The aims of this proposal are to better understand the role of networks in different activities such as social media, education, crime and environment-friendly behaviour. The project expects to help inform the design and practice of policies for education and environmental authorities, police and media markets. Social networks are pervasive in Australia. The project tackles issues of criminal gangs in Australian cities, the ....Social Network Analysis: Social Media, Peer Effects and the Environment. The aims of this proposal are to better understand the role of networks in different activities such as social media, education, crime and environment-friendly behaviour. The project expects to help inform the design and practice of policies for education and environmental authorities, police and media markets. Social networks are pervasive in Australia. The project tackles issues of criminal gangs in Australian cities, the political system and environment-friendly behaviours. This project is at the frontier of work in the economics of networks, with expected outcomes to include new models and methods to better understand the impact of social networks. Benefits include clear policy recommendations to improve welfare in Australian society.Read moreRead less
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
Moduli, invariants, and algebraisation. This project is in pure mathematics. It aims to address gaps in our
knowledge in the modern geometries and their associated algebraic structures that arise in classification problems that pervade mathematics and its applications.
This project expects to generate new knowledge in modern algebra and geometry.
Expected outcomes of this project include major progress in our
understanding of invariants of derived categories of algebraic stacks and the
relat ....Moduli, invariants, and algebraisation. This project is in pure mathematics. It aims to address gaps in our
knowledge in the modern geometries and their associated algebraic structures that arise in classification problems that pervade mathematics and its applications.
This project expects to generate new knowledge in modern algebra and geometry.
Expected outcomes of this project include major progress in our
understanding of invariants of derived categories of algebraic stacks and the
relationship between algebraic and other geometries.
The benefit will be to enhance the international stature of Australian science.Read moreRead less