Success in 2013 Marsden Round

Success in 2013 Marsden Round

Research in the School of Mathematics, Statistics and Operations Research continues to go from strength to strength, with staff being awarded four Marsden grants in the 2013 round and another staff member being an associate investigator on a fifth project.

Associate Professor Noam Greenberg has been awarded Marsden funding for a project on which he is joint Principal Investigator with Professor Andre Nies at the University of Auckland. Dr Greenberg’s project, entitled ‘Randomness, Analysis and Reverse Mathematics’, will relate measures of complexity of mathematical structures and processes. Computationally, one asks what kind of information is required to mechanically implement a process. In terms of proof-theoretic strength, reverse mathematics investigates what basic facts are necessary for understanding a structure or process. The project will investigate the connections between these questions and how they apply to the areas of randomness and real analysis.

Also in the mathematical logic group, Dr Adam Day and Dr Alex Usvyatsov, have each been awarded $300,000 Fast Start grants given to outstanding emerging researchers. Their projects concern questions related to Greenberg's. In Dr Day's research, his point of departure is that two real numbers are computationally equivalent if given one, it is possible to compute the other, and vice versa. He proposes to investigate a longstanding conjecture of leading logician Donald (Tony) Martin, that has many profound consequences. The conjecture proposes that there is a simple classification of the functions that maintain computational equivalence.

Dr Usvyatsov observes that structural dichotomies are an exciting motif in mathematics. In various areas, seemingly unrelated results of a similar flavour are being discovered: objects are either "nice" and "well-understood", or "very complicated" and "unclassifiable". Model theory offers a general approach to such phenomena via investigating the connections between the complexity of theories (collections of axioms) and the mathematical objects that they describe. The goal of his project is to address a mysterious dichotomy-like behavior that (based on all known examples) seems to arise in the world of continuous mathematics. His hope is to uncover the underlying reasons for this poorly understood phenomenon.

The three Marsden grants for members of the mathematical logic group at Victoria confirm the status of Victoria as one of the leading centres for logic in the world.

There has also been considerable acclaim this year for Professor Geoff Whittle who, along with colleagues in Canada and the Netherlands, has solved a 40-year old mathematical problem known as Rota’s Conjecture. It took the team more than 15 years work to formulate the essential ingredients to prove their fundamental result, which is in the area of matroids, a type of finite geometry. Professor Whittle also received a Marsden grant this year to continue his research. He notes that the research group is confident that with the techniques and results they have established, and with the strategies in place, a well-defined program of mathematical research will complete this goal.

Dr John Haywood, in the statistics and operations research group, is working with Professor Phil Lester in the School of Biological Sciences on another Victoria Marsden project. They aim to develop a new approach in biological control and biological invasion theory, to help mediate the impact of exotic species on biodiversity. In particular, they will compare the ecological interaction networks of the invasive wasp Vespula vulgaris in its home range and in invaded regions.