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
Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected ou ....Reaching new frontiers of quantum fields and gravity through deformations. This project aims to reach new frontiers in quantum field and gravity theories. These underpin systems ranging from semi-conductors to particle collisions and the quantum behavior of black holes. An obstacle is that these theories are notoriously hard to solve. This project proposes to tackle this longstanding problem by using new deformations, symmetries and dualities that have attracted widespread attention. Expected outcomes will include innovative techniques that will greatly enhance and interconnect our knowledge of field theories and quantum gravity, together with new discoveries in quantum-corrected geometries. A new network of domestic and international experts will largely benefit the fields of theoretical and mathematical physics.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.
Physical realisation of enriched quantum symmetries. This project aims to investigate fundamental mathematical structures in modern category theory, providing an algebraic description of physical systems including topological order and conformal field theory. The project will study quantum symmetry, and classify and construct new classes of conformal field theories, using novel tools from enriched category theory, modular forms, and lattice gauge theory.
The main goal is to understand the lands ....Physical realisation of enriched quantum symmetries. This project aims to investigate fundamental mathematical structures in modern category theory, providing an algebraic description of physical systems including topological order and conformal field theory. The project will study quantum symmetry, and classify and construct new classes of conformal field theories, using novel tools from enriched category theory, modular forms, and lattice gauge theory.
The main goal is to understand the landscape of topological and conformal field theories, laying the foundation for new technologies based on topological order. This timely project capitalises on the recent arrival of subfactor experts in Australia, and builds capacity in mathematical research and international links in a cutting edge field.Read moreRead less
p-Adic Methods in Arithmetic Geometry. This project concerns algorithms for determining the number of
solutions to systems of polynomial equations over finite fields
by p-adic methods. Our goal is to determine a fundamental
invariant, the zeta function, appearing in arithmetic geometry,
whose characterization was the subject of the famous Weil
conjectures.
....p-Adic Methods in Arithmetic Geometry. This project concerns algorithms for determining the number of
solutions to systems of polynomial equations over finite fields
by p-adic methods. Our goal is to determine a fundamental
invariant, the zeta function, appearing in arithmetic geometry,
whose characterization was the subject of the famous Weil
conjectures.
We seek to understand and develop p-adic methods for determining
zeta functions, taking as point of departure the methods of Satoh
and Mestre for elliptic curves. Applications of this work include
public key cryptography and coding theory, having direct impact
in e-commerce and telecommunications.
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Bulk-boundary correspondence in quantum many-body systems. This project will develop theoretical and numerical methods to explore how the bulk properties of quantum materials at low temperature are manifested on the edge of the material. Characterising this bulk-boundary correspondence will uncover new regimes of physics and underpin the development of powerful quantum technologies in the laboratory.
Explicit Construction of Global Function Fields with Many Rational Places. The use of error-correcting codes and cryptosystems is fundamental to the secure and reliable operation of many technological devices that we depend upon in our everyday lives. Essentially invisible, both coding theory and cryptography are essential for banking (ATM machines, e-banking), commerce (e-commerce), defense (cryptography) and entertainment (digital TV and radio, music CDs, DVDs). While certain families of "goo ....Explicit Construction of Global Function Fields with Many Rational Places. The use of error-correcting codes and cryptosystems is fundamental to the secure and reliable operation of many technological devices that we depend upon in our everyday lives. Essentially invisible, both coding theory and cryptography are essential for banking (ATM machines, e-banking), commerce (e-commerce), defense (cryptography) and entertainment (digital TV and radio, music CDs, DVDs). While certain families of "good" codes and cryptosystems can be constructed from specific function fields whose existence is guaranteed by abstract theory, often no actual construction for the function field is currently known. We aim to close this gap, making a greater range of "good" codes and cryptosystems available for practical applications.
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Noncommutative analysis and geometry in interaction with quantum physics. Quantum theory has produced many advances in our understanding of the physical world for the last hundred years while mathematical breakthroughs have been made through exploiting innovative ideas from quantum physics. This project continues in this highly successful framework and will lead to advances in geometry both classical and noncommutative.
Algebraic methods for Markov Chain Monte Carlo and quasi-Monte Carlo. In an increasingly complex world, the requirements on computational methods for solving real world problems from areas like statistics, finance, economics, physics and others are also constantly increasing. The results from this project will significantly improve existing computational methods, thereby helping to solve existing computational challenges and further strengthening Australia's reputation as a leading scientific lo ....Algebraic methods for Markov Chain Monte Carlo and quasi-Monte Carlo. In an increasingly complex world, the requirements on computational methods for solving real world problems from areas like statistics, finance, economics, physics and others are also constantly increasing. The results from this project will significantly improve existing computational methods, thereby helping to solve existing computational challenges and further strengthening Australia's reputation as a leading scientific location. The research carried out will be in collaboration with international experts, creating and strengthening existing ties of Australian research institutions with other world class research institutes overseas.Read moreRead less
Integral lattices and their theta series. Lattice algorithms play a very important role in solving problems in algebra, number theory, combinatorics, optimisation and cryptography. Our proposed work will fill a major hole in current capabilities for computing with lattices. The enhanced ability to enumerate short vectors will have important applications to Diophantine equations, linear optimisation and also to understanding the security of cryptosystems based on the difficulty of finding a short ....Integral lattices and their theta series. Lattice algorithms play a very important role in solving problems in algebra, number theory, combinatorics, optimisation and cryptography. Our proposed work will fill a major hole in current capabilities for computing with lattices. The enhanced ability to enumerate short vectors will have important applications to Diophantine equations, linear optimisation and also to understanding the security of cryptosystems based on the difficulty of finding a shortest vector. The work on theta series should result in the first algorithm for this problem. This will also find many applications including to the construction of spherical codes and designs.Read moreRead less