Five ARC DECRAs awarded to our School
Congratulations to Stephane Dartois, Alexandr Garbali, Xi Geng, Mingming Gong and Jesper Ipsen for their successful applications.
Stephane Dartois: 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.
Alexandr Garbali: Toroidal quantum groups, integrable models and applications. Modelling systems of quantum and classical mechanics usually relies on computationally expensive numerical methods. Such methods typically provide raw answers and give little insight. In contrast, a special class of modelling based on quantum integrability provides us with a variety of analytic tools thanks to connections with algebra, geometry and combinatorics. The project aims to study quantum integrability with the help of new exciting developments in toroidal quantum groups. The anticipated outcomes include constructions of new models, developing analytic methods and computer algebra packages. These results are expected to facilitate challenging computational problems in modelling of quantum and classical systems.
Xi Geng: Inverting the Signature Transform for Rough Paths and Random Processes. The signature transform provides an effective summary of the essential information encoded in multidimensional paths that are highly oscillatory and involve complicated randomness. The main goal of this project is to develop new algorithmic methods to reconstruct rough paths and random processes from the signature transform at various quantitative levels. This project expects to make theoretical breakthrough on the significant open problem of signature inversion, thereby advancing knowledge in the areas of rough path theory and stochastic analysis. The newly developed methods will be utilised in combination with the emerging signature-based approach to study important problems in financial data analysis and visual speech recognition.
Mingming Gong: Causal Discovery from Unstructured Data. This Project aims to enable machines to discover causal relations from various kinds of unstructured data, such as images, text files, and sensor data. The project expects to promote causal revolution of data-centric intelligence and science – construct machines that can communicate in the language of cause and effect and answer ‘why’ questions by inferring from unstructured data. Expected outcomes of this project include theoretical foundations for causal discovery from unstructured data and practical algorithms that drive intelligent machines to make rational decisions in real-world scenarios. This should benefit society and the economy nationally and internationally through the applications of artificial intelligence and data science.
Jesper Ipsen: Stability and Complexity: New insights from Random Matrix Theory. Complexity is a rule of nature: large ecosystems, the human brain, and turbulent fluids are merely a few examples of complex systems. This project aims to study and classify criteria of stability in large complex systems based on universal probabilistic models. This project expects to generate new important understanding of stability using cutting-edge techniques from random matrix theory. Expected outcomes of this project include development and expansion of an innovative mathematical framework and techniques which allow a unified and universal approach to the question of stability in large complex systems.