The MSI wishes to congratulate the recipients of the latest ARC grant round which was announced on Friday,10th Nov 17. 

Scheme: ARC Discovery Projects 2018 round 1
Recipient: Professor Alan Welsh; Dr Francis Hui; Associate Professor Samuel Mueller; Professor Yanyuan Ma
Grant amount: $359,083.00
Project: Dimension reduction and model selection for statistically challenging data
 
This project aims to develop a deep theoretical understanding of the relationship between various dimension reduction and model selection methods used in statistical model building, and then use this understanding to develop new, improved methods of model building for statistically challenging data. The research will impact on both the theory and practice of statistics, and on substantive fields which collect and analyse these kinds of data. This will provide a significant improvement in the statistical model building in areas such as epidemiology, chemical and ecological sciences. The project is timely because of the increasing collection of large-dimensional, complex, correlated data sets in these and many other fields.

Scheme: ARC Discovery Projects 2018 round 1
Recipient: Professor Murray Batchelor; Professor Vladimir Bazhanov
Grant amount: $371,950.00
Project: Algebraic and computational approaches for classical and quantum systems

This project aims to investigate regularisation methods for inverse problems which are ill-posed in the sense that their solutions depend discontinuously on the data. When only noisy data is available, regularisation methods define stable approximate solutions by replacing the original inverse problem with a family of well-posed neighbouring problems monitored by a so-called regularisation parameter. The project expects to develop purely data-driven rules to choose the regularisation parameter and show how they work in theory, and in practice. It will also develop convex framework, acceleration strategies as well as preconditioning and splitting ideas to design efficient regularisation solvers.

Scheme: ARC Discovery Projects 2018 round 1
Recipient: Professor Andrew Hassell; Dr Jesse Gell-Redman
Grant amount: $371,950.00
Project: Global wavefront propagation and non-elliptic Fredholm theory

Many significant phenomena in the natural world are described by partial differential equations that involve evolution in time. This project aims to develop new mathematical methods, involving recently discovered global wavefront set analysis and Fredholm theory, to solve such equations. These methods aim to extend the range of equations that can be solved as well as yield more information about solutions, in particular, their long-time asymptotics.

Scheme: ARC Discovery Projects 2018 round 1
Recipient: Dr Peter McNamara; Associate Professor Anthony Licata; Dr Masoud Kamgarpour
Grant amount: $371,950.00
Project: Categorical symmetries in representation theory

This project aims to develop categorical symmetries of central objects in mathematics such as braid groups, the Hilbert scheme of points, and the Virasoro algebra. The concept of symmetry is an important organising principle in science. Representation theory is the field of mathematics concerned with studying symmetries. The problems proposed have connections to many different areas including algebra, geometry, topology, and mathematical physics. This project expects to advance pure mathematics and provide potential benefit in many related fields.

Scheme: Discovery Early Career Researcher Award 2018 round 1
Recipient:Dr Paul Bryan
Grant amount: $343,450.00
Project: Analysis of fully non-linear geometric problems and differential equations

This project aims to investigate non-linear geometric evolution equations that have received considerable attention in the past decades through their use in solving outstanding problems in mathematics, such as the Poincare conjecture. By developing innovative new techniques intertwining geometry and analysis, the project endeavours to make advances in non-linear problems modelling complex phenomena. The project addresses topics as varied as hyperbolic geometry, and a geometric approach to irregularities forming in crystal growth in materials science, focusing on developing cutting-edge mathematical tools and connections to geometry.

Scheme: Discovery Early Career Researcher Award 2018 round 1
Recipient: Dr Anand Deopurkar
Grant amount: $328,075.00
Project: The geometry and cohomology of moduli spaces of curves

This project aims to develop new insights on moduli spaces in algebraic geometry. Algebraic geometry is the field of mathematics that uses geometric methods to analyse algebraic equations, with wide applications ranging from cryptography to genetics. Moduli spaces in algebraic geometry provide powerful methods to geometrically analyse collections of related equations. Using innovative new techniques, the project aims to generate new knowledge about fundamental moduli spaces. Expected outcomes include the establishment of an active community of algebraic geometers in Australia. These outcomes should provide significant benefits to pure mathematics and related scientific fields.