Listed on this page are current research projects being offered for the Vacation Scholarship Program.
For more information on this research group see: Mathematical Physics
Lattice models of polymer systems
Long chain polymers like DNA can be modelled by walks, polygons, trees, and various other combinatorial structures embedded in lattices. This project aims to investigate new polymer models. This can be approached using exact solution techniques or computational methods like series enumeration and random sampling.
Contact: Nick Beaton nrbeaton@unimelb.edu.au
Quantum groups and integrable lattice models
In this project the student will learn about some algebraic constructions behind solvable physical models.
Contact: Sasha Garbali alexandr.garbali@unimelb.edu.au
Mathematical Quantum Information: From Quantum Chaos to Black Holes
My research is at the interface of quantum information and fundamental theory, which includes the study of correlations and chaos in many-body quantum systems and of quantum processing in relativistic settings, such as curved spacetime. Potential projects for a vacation scholar could study what typical quantum correlations can teach us about the dynamics of a quantum system, how Hawking radiation seems to imply that information is lost in a black hole and other questions on mathematical quantum information. Such a project may provide an opportunity to learn some techniques from differential geometry, Lie theory, random matrix theory and representation theory. While some physics background could be helpful, it is not required. Please contact me if you want to discuss specific directions.
Contact: Lucas Hackl lucas.hackl@unimelb.edu.au