Discovery Early Career Researcher Award - Grant ID: DE210101323
Funder
Australian Research Council
Funding Amount
$345,448.00
Summary
Random tensors and random matrices: interactions and applications. This project aims at improving knowledge on probabilistic objects having applications in, for instance, mathematical-physics, statistical physics, quantum gravity and data science. In doing so, we expect to produce new mathematical results by building upon both classical approaches and innovative ones. In particular, on one hand, the extension of classical graphical methods will be developed and, on another hand, generalized prob ....Random tensors and random matrices: interactions and applications. This project aims at improving knowledge on probabilistic objects having applications in, for instance, mathematical-physics, statistical physics, quantum gravity and data science. In doing so, we expect to produce new mathematical results by building upon both classical approaches and innovative ones. In particular, on one hand, the extension of classical graphical methods will be developed and, on another hand, generalized probability theories will be used to provide new insights. The expected outcomes include a better understanding of the generic properties of quantum states. This should significantly benefit to mathematicians and physicists whose models use those objects and may impact the broader community of engineers and technicians.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE120101375
Funder
Australian Research Council
Funding Amount
$375,000.00
Summary
The Tutte polynomial of a graph: correlations, approximations and applications. The Tutte polynomial is a mathematical function of central importance to diverse fields of research, such as network reliability and statistical mechanics, that involve natural (and often difficult) counting problems. This project aims to obtain useful close approximations of this function with immediate applications in all these research fields.