I have held several management positions at the University of Melbourne in the past 20 years. I was Dean of the Faculty of Science 2019-2020, Head of School/Department of Mathematics and Statistics between 2011-2016 and Deputy Dean between 2017-2018. I was also Director of the Melbourne Graduate School of Science/Associate Dean (Graduate Program) between 2009 and 2016. I held an Australian Research Council Discovery Program grant on the Interplay of Topology and Geometry in Polymeric Critical Phenomena 2016-2019 and am a Fellow of the Australian Mathematical Society. I am on the Advisory Panel of senior referees for the Journal of Physics A: Mathematical and Theoretical.
My area of expertise is mathematical statistical mechanics and, in particular, the area of phase transitions and critical phenomena of model polymer systems, namely lattice walk models, which lies within the discipline of mathematical physics. My work endeavours to uncover the universal geometric and topological features of long chain molecules, such as DNA, in a variety of generic conditions. The models I study arise naturally in “Discrete Mathematics and Combinatorics” and in “Stochastic Processes”. I am part of a `Mathematical Physics Group‘ and the `Discrete Mathematics Group‘ working on these topics. I have several projects in the general area of the statistical mechanics of lattice polymer and vesicle models where there is scope for Master of Science and PhD projects, and some where post-doctoral collaboration would be fruitful. Please contact me if you are interested.
My School web profile is here, where information about past and present students and grant funding can be found.
Lattice Polymers, also known as lattice random walks, are a rich set of models describing the universal geometric and topological behaviour of long chain polymers which are ubiquitous in the world around us, from paints and plastics to the DNA in our cells. These models provide key insights into the behaviour of such polymers, but they also have deep connections to a variety of other models in mathematical physics, combinatorics and probability theory. Their study allows us to uncover both new physical phenomena and new mathematical structures.
My major programs of work are
Integrable lattice polymer models at the interface of algebra, analysis and combinatorics
Lattice paths, which model the geometry of polymers, play an important role in modern combinatorics and mathematical physics, and the resolution of these models has drawn on such diverse fields as algebra, probability theory and complex analysis. The projects I conduct aim to use a range of sophisticated techniques to expand the diversity and utility of solvable polymer models, which interface with the rich topic of integrable lattice models in statistical mechanics. The fundamental aim of these projects is to push forward the frontier of exactly solvable lattice path polymer models by:
1. Generalising the types of lattice path models to new, more diverse, polymer systems.
2. Applying sophisticated techniques to develop new methods for solving these models, and analysing their universal critical behaviour and phase diagrams.
3. Developing principles for understanding the scope of the methods by studying the relationship between the symmetries of the models and their solvability.
Expected outcomes include powerful new mathematical and computational tools in combinatorics and statistical physics.
Next generation simulation of polymer systems in complex environments
Elucidating the behaviour of long chain polymers using computer simulations, in various environments and experiencing physical and chemical interactions, has yielded a growing bank of results and insights over decades. The suite of projects here aims to apply next generation computational techniques to tackle the new frontier of polymer simulations, and in particular polymers with complex interactions and those with complicated topologies like stars, knots and links which have hitherto been inaccessible. Expected outcomes include new simulation methods designed to make use of modern computational clusters, and numerical estimates for the fundamental quantities driving polymer behaviour. The aims are to further develop Monte Carlo algorithms for long chain polymers which run in highly parallel systems, making use of modern computational clusters with many CPU cores.
These will lead to a greater understanding of complex polymer systems, which are widespread in chemistry, biology, and manufacturing.
Information about past and present students and grant funding can be found here, which is my School profile page.
Lattice walks at the Interface of Algebra, Analysis and Combinatorics, Banff International Research Station, Canada, September 2017.
Means, methods and results in the statistical mechanics of polymeric systems: a special issue in honour of Stuart Whittington’s 75th birthday.
Combinatorics of lattice models: a special issue in honour of Tony Guttmann’s 70th birthday.
Exactly Solved Models and Beyond: a special issue in honour of R J Baxter’s 75th birthday
Professor Aleks L. Owczarek, FAustMS
Redmond Barry Distinguished Professor and Professor of Mathematics and Statistics
Address: School of Mathematics and Statistics,
The University of Melbourne, Vic, 3010, Australia.
Phone: +61 412501370