Defining Genetic And Epigenetic Variation During Early Development
Funder
National Health and Medical Research Council
Funding Amount
$996,075.00
Summary
We all began life with a set of genes inherited from our parents. However, it's now known that from the time we were in the womb onwards that genes can be turned off and on by the environment or even completely lost or gained. Even what your mother ate or how she behaved while she was pregnant could have influenced your future health. Because people are so different, we are studying the subtle differences between twins to tease out the factors that may influence our genes and our health.
Discovery Early Career Researcher Award - Grant ID: DE120100173
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
A new upper bound for the Riemann zeta-function and applications to the distribution of prime numbers. Prime numbers are known to every schoolchild and are ubiquitous in modern cryptography; some of their deepest properties relate to a function called the Riemann zeta-function. This project aims at better estimating this function, thereby improving current knowledge on the distribution of prime numbers.
Verifying the Riemann hypothesis to large heights: theory and applications. This project aims to verify the Riemann hypothesis to a record height and apply this verification to the distribution of prime numbers. The Riemann hypothesis (an open problem for 150 years) is ubiquitous in analytic number theory and prevalent in many other areas of mathematics. This project plans to use state-of-the-art computational hardware and the mathematical and algorithmic expertise of the investigators to verify ....Verifying the Riemann hypothesis to large heights: theory and applications. This project aims to verify the Riemann hypothesis to a record height and apply this verification to the distribution of prime numbers. The Riemann hypothesis (an open problem for 150 years) is ubiquitous in analytic number theory and prevalent in many other areas of mathematics. This project plans to use state-of-the-art computational hardware and the mathematical and algorithmic expertise of the investigators to verify the Riemann hypothesis several orders of magnitude further than what is currently known. A secondary aim is to apply this new verification to a multitude of results in analytic number theory: this would provide future researchers with vastly superior results.Read moreRead less
Representations of arithmetic groups and their associated zeta functions. This project aims to investigate deep connections between number theory and group theory by studying linear actions of arithmetic groups. Arithmetic groups are used in geometry, dynamics, number theory and other areas of pure mathematics. This project will study their representations from two perspectives. First, it will establish properties of the associated zeta functions to resolve open problems about the asymptotic beh ....Representations of arithmetic groups and their associated zeta functions. This project aims to investigate deep connections between number theory and group theory by studying linear actions of arithmetic groups. Arithmetic groups are used in geometry, dynamics, number theory and other areas of pure mathematics. This project will study their representations from two perspectives. First, it will establish properties of the associated zeta functions to resolve open problems about the asymptotic behaviour of the dimensions of the irreducible representations. Second, it will explore the evolution of representations across families of groups under new induction and restriction functors, in analogy with creation and annihilation operators in physics. The project will enhance Australia's capacity in representation theory and group theory, the mathematics that underline symmetry in nature.Read moreRead less
Braid groups and higher representation theory. Symmetry is a central notion in classical representation theory. In higher representation theory the symmetries of classical representation theory are replaced by higher symmetries. These higher symmetries contain new structure not present at the classical level. The proposed research will develop the higher representation theory of fundamental objects from classical representation theory and geometric group theory, focusing on braid groups and quan ....Braid groups and higher representation theory. Symmetry is a central notion in classical representation theory. In higher representation theory the symmetries of classical representation theory are replaced by higher symmetries. These higher symmetries contain new structure not present at the classical level. The proposed research will develop the higher representation theory of fundamental objects from classical representation theory and geometric group theory, focusing on braid groups and quantum groups.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE140101519
Funder
Australian Research Council
Funding Amount
$393,979.00
Summary
Advances in algebraic stacks and applications. Algebraic stacks are a geometric manifestation of algebraic and physical phenomena. Stacks provide a fundamental mathematical structure to study questions in geometry, topology and number theory having deep applications to string theory and complexity theory. This project will prove new fundamental theorems about algebraic stacks that will have broad implications. In particular, the new results obtained on algebraic stacks will be applied in order t ....Advances in algebraic stacks and applications. Algebraic stacks are a geometric manifestation of algebraic and physical phenomena. Stacks provide a fundamental mathematical structure to study questions in geometry, topology and number theory having deep applications to string theory and complexity theory. This project will prove new fundamental theorems about algebraic stacks that will have broad implications. In particular, the new results obtained on algebraic stacks will be applied in order to resolve a long-standing open problem in algebraic geometry. Specifically, the project will provide a new description of the birational geometry of one of the most interesting and studied algebraic varieties, the moduli space of smooth curves.Read moreRead less
Equations of Monge-Ampere type and applications. Many fundamental problems in geometry, physics and applied sciences are related to equations of Monge-Ampere type. In recent years there have been rapid developments in the study of these equations with major breakthroughs made by the proposers. This project aims at new discoveries and findings in theory and applications by resolving outstanding open problems, and enhance Australian leadership, expertise, and training in key areas of mathematics a ....Equations of Monge-Ampere type and applications. Many fundamental problems in geometry, physics and applied sciences are related to equations of Monge-Ampere type. In recent years there have been rapid developments in the study of these equations with major breakthroughs made by the proposers. This project aims at new discoveries and findings in theory and applications by resolving outstanding open problems, and enhance Australian leadership, expertise, and training in key areas of mathematics and its applications.Read moreRead less
Stabilisation of nonlinear quantum feedback control systems. One of the most exciting technological developments of this century promises to be the development of quantum technology. Quantum feedback systems will play a key part of this technology and this project will develop the underlying fundamental theory which will be crucial to the systematic design of quantum feedback control systems.
Coherent Feedback Synchronisation and Stabilisation of Quantum Systems. The aim of this project is to address a range of fundamental problems of stabilisation and coherent synchronisation in quantum feedback control systems, leading to new systematic methods of designing controllers for the interacting quantum systems arising in emerging areas of quantum technology. Quantum feedback control systems will be at the heart of emerging areas of quantum technology and stability is essential for their ....Coherent Feedback Synchronisation and Stabilisation of Quantum Systems. The aim of this project is to address a range of fundamental problems of stabilisation and coherent synchronisation in quantum feedback control systems, leading to new systematic methods of designing controllers for the interacting quantum systems arising in emerging areas of quantum technology. Quantum feedback control systems will be at the heart of emerging areas of quantum technology and stability is essential for their operation. Standard control system methods do not take into account the special features of quantum systems and there is a need for new control theories that deal with stabilisation and synchronisation as quantum technologies become more advanced. Read moreRead less
Nonlinear elliptic partial differential equations and applications. Many fundamental advances in modern technology, science and economics are driven by the analysis of nonlinear models based on nonlinear partial differential equations. In recent years there has been increasing use in applications of partial differential equations of elliptic type with major discoveries made and longstanding problems resolved by the two Chief Investigators, who have in return received many international accolades ....Nonlinear elliptic partial differential equations and applications. Many fundamental advances in modern technology, science and economics are driven by the analysis of nonlinear models based on nonlinear partial differential equations. In recent years there has been increasing use in applications of partial differential equations of elliptic type with major discoveries made and longstanding problems resolved by the two Chief Investigators, who have in return received many international accolades. This project provides for the continuation of Australian leadership in key strategic areas of international science, such as optimal transportation, as well as the continued building of related expertise and training.Read moreRead less