Computing with Lie groups and algebras: nilpotent orbits and applications. This project aims to advance knowledge of an important class of Lie algebras, for which recent work has shown that a deeper mathematical theory, and better computational tools are required. Lie theory is a mathematical area with rich applications in the physical sciences. Expected outcomes from this project include the first systematic treatment of these algebras, new powerful algorithms to compute with them, and explicit ....Computing with Lie groups and algebras: nilpotent orbits and applications. This project aims to advance knowledge of an important class of Lie algebras, for which recent work has shown that a deeper mathematical theory, and better computational tools are required. Lie theory is a mathematical area with rich applications in the physical sciences. Expected outcomes from this project include the first systematic treatment of these algebras, new powerful algorithms to compute with them, and explicit nilpotent orbit classifications that will solve open problems in black hole theory. This should significantly enhance fundamental mathematical research and the Lie functionality of leading computer algebra systems, and is expected to strengthen international linkages.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE190101231
Funder
Australian Research Council
Funding Amount
$390,000.00
Summary
Integrable systems from gauge theories. This project aims to construct and describe three important integrable systems and to produce new significant results in representation theory and mathematical physics. The focus of the project is the theory of integrable systems, a breakthrough area in modern mathematics, and it will use tools from geometric representation theory to study the interrelation between geometry and mathematical physics. Originating from string theory, the project will not only ....Integrable systems from gauge theories. This project aims to construct and describe three important integrable systems and to produce new significant results in representation theory and mathematical physics. The focus of the project is the theory of integrable systems, a breakthrough area in modern mathematics, and it will use tools from geometric representation theory to study the interrelation between geometry and mathematical physics. Originating from string theory, the project will not only provide a deeper understanding of the universe, it will also train young mathematicians and other highly qualified individuals with the potential to make a significant impact to technology, security, and the economy though their specialised skills.Read moreRead less