The Australian Research Council released its Discovery Early Career Researcher Awards for 2020, and two ACEMS researchers from The University of Melbourne are on that list. They are Dr Jesper Ipsen and Dr Sasha Garbali.
Here is a look at their projects:
Dr 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.
Dr Alexandr "Sasha" 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.