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.
Breast Cancer is a very common disease in women and although huge progress has been made in the last two decades, much remains to be done to improve our understanding of different types of breast cancer and its management. This program brings together the expertise of three senior researchers: 2scientists and 1 medical scientist. Dr Trench has an interest in identifying genes involved in cancers arising in patients who have a strong family history. She will use molecular methods and cohorts of p ....Breast Cancer is a very common disease in women and although huge progress has been made in the last two decades, much remains to be done to improve our understanding of different types of breast cancer and its management. This program brings together the expertise of three senior researchers: 2scientists and 1 medical scientist. Dr Trench has an interest in identifying genes involved in cancers arising in patients who have a strong family history. She will use molecular methods and cohorts of patients enrolled with Kathleen Cunningham Foundation for Research into Familial Breast and Ovarian Cancer to identify the genes responsible, assess their distribution in the population and determine whether these genes also play a role in non-familial cancers. Dr Khanna's work examines the complex array of enzymes that are responsible for maintaining the integrity of the DNA, and investigates how failure of these mechanisms leads to damage of the genetic material which ultimately results in cancer. It is known that genes involved in familial predisposition code for proteins that work as DNA repair enzymes. It is also known that different types of breast cancer exist, each with differing behaviour and response to treatment and that they are associated with specific genetic changes, including those associated with a familial predisposition. Prof Lakhani's interest lies in using microscopy and the latest molecular tools to refine the classification of these different types of breast tumour so that they can be managed appropriately by his surgical and oncological colleagues. A better understanding of the genetic changes and underlying biology of different types of breast cancer will lead to individualised and specific therapy for patients. This program brings together a unique combination, nationally and internationally, that investigates cancers at the level of genes and cells and translates the information to the clinic for the benefit of patient management.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.
Read moreRead less
Counting points on algebraic surfaces. This project aims to develop algorithms for calculating the number of solutions to polynomial equations and to compute zeta functions of certain types of algebraic varieties. Existing algorithms cannot solve these problems. The new algorithms will enable researchers in number theory to test and refine conjectures on generalisations of many famous problems, such as the Sato-Tate conjecture, the Lang-Trotter conjecture and the Birch-Swinnerton-Dyer conjecture ....Counting points on algebraic surfaces. This project aims to develop algorithms for calculating the number of solutions to polynomial equations and to compute zeta functions of certain types of algebraic varieties. Existing algorithms cannot solve these problems. The new algorithms will enable researchers in number theory to test and refine conjectures on generalisations of many famous problems, such as the Sato-Tate conjecture, the Lang-Trotter conjecture and the Birch-Swinnerton-Dyer conjecture. The project will also have a flow-on effect in other areas of mathematics and computer science where zeta functions play a central role, including cryptography, coding theory and mathematical physics.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE220100859
Funder
Australian Research Council
Funding Amount
$354,000.00
Summary
New techniques for exponential sums over low degree polynomials. This project aims to obtain new quantitative estimates for Weyl sums over low degree polynomials. Such estimates are fundamental to several areas of number theory. By interfacing techniques from diverse areas of mathematics, including algebraic geometry, analytic number theory, the geometry of numbers and harmonic analysis, this project will provide the first progress on estimating Weyl sums over low degree polynomials in over a ce ....New techniques for exponential sums over low degree polynomials. This project aims to obtain new quantitative estimates for Weyl sums over low degree polynomials. Such estimates are fundamental to several areas of number theory. By interfacing techniques from diverse areas of mathematics, including algebraic geometry, analytic number theory, the geometry of numbers and harmonic analysis, this project will provide the first progress on estimating Weyl sums over low degree polynomials in over a century. The expected outcomes include a deeper understanding of Weyl sums and enhanced international collaborations. Such progress will place Australia at the forefront of this important branch of number theory.Read moreRead less