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
Discovery Early Career Researcher Award - Grant ID: DE120102204
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
Quantum computation and relativistic quantum information. Quantum information theory has profound implications both for practical computing and for our fundamental understanding of the universe. This project will determine the viability of one particular quantum computing platform and also develop theoretical and experimental tools to probe the interface between quantum theory and relativity.
Quantum invariants and hyperbolic manifolds in three-dimensional topology. The project aims to broaden our understanding of three-dimensional (3-D) spaces, including spaces that arise in engineering, microbiology and physics. It is known that all 3-D spaces can be decomposed into geometric pieces. The most common type of geometry is hyperbolic. It is also known that such spaces have algebraic structures arising from quantum physics, known as quantum invariants. Several important conjectures, bas ....Quantum invariants and hyperbolic manifolds in three-dimensional topology. The project aims to broaden our understanding of three-dimensional (3-D) spaces, including spaces that arise in engineering, microbiology and physics. It is known that all 3-D spaces can be decomposed into geometric pieces. The most common type of geometry is hyperbolic. It is also known that such spaces have algebraic structures arising from quantum physics, known as quantum invariants. Several important conjectures, based on developments in physics, assert that hyperbolic geometry and quantum invariants are deeply related, but they remain unproved. The project aims to find new relationships between hyperbolic geometry and quantum invariants, advancing our understanding of both areas.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
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.
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
Integrable Systems in Gauge and String Theories. Gauge theory describes all quantum forces except gravity. String theory aims to describe quantum gravity. Both theories are widely believed to be different limits of one unknown theory. Discoveries of integrable nonlinear partial differential equations and integrable quantum systems in gauge/string theories are among the most remarkable recent developments in mathematical physics. They have led to deep results in known gauge/string theories, as we ....Integrable Systems in Gauge and String Theories. Gauge theory describes all quantum forces except gravity. String theory aims to describe quantum gravity. Both theories are widely believed to be different limits of one unknown theory. Discoveries of integrable nonlinear partial differential equations and integrable quantum systems in gauge/string theories are among the most remarkable recent developments in mathematical physics. They have led to deep results in known gauge/string theories, as well as to viable paths towards the unknown theory that interpolates them. This project contributes to these developments by adapting and developing sophisticated technical tools and insights from integrable models to shed light on that unknown theory that transcends the gauge/string gap. 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
Integrable models and topological strings. This project aims to develop advanced methods to compute n-point correlation functions in two-dimensional integrable models. The project expects to use recently discovered connections with topological strings to compute currently-inaccessible conformal blocks in conformal field theories, and their analogues in integrable massive field theories and statistical mechanical models. Expected outcomes include explicit expressions for the n-point correlation ....Integrable models and topological strings. This project aims to develop advanced methods to compute n-point correlation functions in two-dimensional integrable models. The project expects to use recently discovered connections with topological strings to compute currently-inaccessible conformal blocks in conformal field theories, and their analogues in integrable massive field theories and statistical mechanical models. Expected outcomes include explicit expressions for the n-point correlation functions, advances in the theory of topological vertices and the related representation theory, and new solutions of the Yang-Baxter equations. This should provide benefits that include a better understanding of two-dimensional integrable models and their deep connections with topological strings.Read moreRead less