Discovery Early Career Researcher Award - Grant ID: DE230100579
Funder
Australian Research Council
Funding Amount
$445,754.00
Summary
The existence and abundance of small bases of permutation groups. This project aims to study bases for permutation groups, which are the mathematical formalisation of symmetry. Bases are crucial to encoding and computing with groups in diverse areas of science. Small bases are desirable for efficiency, but can be hard to find. This project expects to combine techniques from areas of algebra and probability to determine the existence and abundance of bases. Expected outcomes of this project inclu ....The existence and abundance of small bases of permutation groups. This project aims to study bases for permutation groups, which are the mathematical formalisation of symmetry. Bases are crucial to encoding and computing with groups in diverse areas of science. Small bases are desirable for efficiency, but can be hard to find. This project expects to combine techniques from areas of algebra and probability to determine the existence and abundance of bases. Expected outcomes of this project include new methods to address enduring open problems in the study of bases, as well as novel applications of existing techniques. This should provide significant benefits, such as creating and strengthening international collaborations, and building on Australia’s reputation as a powerhouse of finite group theory.Read moreRead less
Symmetry: Groups, Graphs, Number Fields and Loops. Exploiting symmetry can greatly simplify complex mathematical problems. This project aims to apply the powerful Classification of Finite Simple Groups to advance our understanding of the internal structure of number fields, highly symmetric graphs, and algebraic structures associated with Latin squares. The project expects to generate new constructions and classifications utilising group theory. Expected outcomes include resolutions of major ope ....Symmetry: Groups, Graphs, Number Fields and Loops. Exploiting symmetry can greatly simplify complex mathematical problems. This project aims to apply the powerful Classification of Finite Simple Groups to advance our understanding of the internal structure of number fields, highly symmetric graphs, and algebraic structures associated with Latin squares. The project expects to generate new constructions and classifications utilising group theory. Expected outcomes include resolutions of major open problems in each area as well as innovative methods for studying algebraic and combinatorial structures based on group actions. Expected benefits include enhanced international collaboration, and highly trained mathematicians to strengthen Australia’s research standing in fundamental science.Read moreRead less
Categorification and KLR algebras. AIMS This project will solve three problems at the forefront of representation theory: the centre conjecture for graded Hecke algebras, concretely connecting crystals with KLR algebras and describing the grading and radical filtrations Specht modules.
SIGNIFICANCE Solving any of these problems will represent a serious advance in the field and have a lasting impact and creating new areas of research.
EXPECTED OUTCOMES We will remove major bottlenecks in our u ....Categorification and KLR algebras. AIMS This project will solve three problems at the forefront of representation theory: the centre conjecture for graded Hecke algebras, concretely connecting crystals with KLR algebras and describing the grading and radical filtrations Specht modules.
SIGNIFICANCE Solving any of these problems will represent a serious advance in the field and have a lasting impact and creating new areas of research.
EXPECTED OUTCOMES We will remove major bottlenecks in our understanding of KLR algebras.
BENEFITS In addition to the mathematical benefits, the skills and expertise that are required for, and will be enhanced by, this project are readily transferable and highly sought after by industry, including the financial, IT and education sectors.Read moreRead less