The School of Mathematical Sciences is one of the eight Schools that make up the Faculty of Engineering, Computer and Mathematical Sciences. Pure Mathematics received the top ranking of 5 in Excellence in Research for Australia (ERA) 2018 and ERA 2015, making it one of the premier departments in the country. It hosts the Institute for Geometry and its Applications, which is extremely active at organising workshops, lecture series and instructional schools that benefit Higher Degree Research students, Early Career Researchers and other staff. Interaction with other researchers and students in the school is also encouraged.
There are two fixed term, full time positions available.
The first is a Laureate Postdoctoral Research Fellow position contributing to the ARC funded project 'Advances in Index Theory'. Geometric analysis, especially Index Theory, is a major branch of mathematics, studying geometry and physics via differential equations, often resulting in striking results. The ambitious aims of this research project are to develop novel techniques to investigate Geometric analysis on infinite dimensional bundles, as well as Geometric analysis of pathological spaces with Cantor set as fibre, that arise in models for the fractional quantum Hall effect and topological matter that are areas recognised with the 1998 and 2016 Nobel Prizes. This proposal builds on the applicantŐs expertise in the area, involves postgraduate and postdoctoral training, enhancing AustraliaŐs position at the forefront of international research in Geometric Analysis.
The second position will contribute to the ARC funded project, 'Coarse Geometry: a novel approach to the Callias index & topological matter'. Coarse geometry is the study of the large-scale structure of metric spaces, in terms of operator algebras. This project aims to use coarse geometry to develop novel approaches to Callias index theory and its applications, and to topological phases of matter, where the Nobel Prize in physics in 2016 was awarded. This will yield new techniques in index theory and other areas, and solutions to several important problems. Outcomes include a noncompact generalisation of the famous Guillemin-Sternberg conjecture that quantisation commutes with reduction, and new models of topological phases of matter in terms of K-theory of operator algebras.
For more information and to apply, click here.