Singularities and surgery in geometric evolution equations. The analysis of geometric evolution equations is a very active area of mathematical research internationally. The applications of such systems to physical problems such as crystal growth and flame propagation are also of great interest in the broader scientific community. The proposed research addresses questions central to the understanding of curvature flows. The project will yield internationally significant results in theoretical ....Singularities and surgery in geometric evolution equations. The analysis of geometric evolution equations is a very active area of mathematical research internationally. The applications of such systems to physical problems such as crystal growth and flame propagation are also of great interest in the broader scientific community. The proposed research addresses questions central to the understanding of curvature flows. The project will yield internationally significant results in theoretical mathematics, with applications in physics, engineering and image processing. These results will enhance Australia's reputation for high quality theoretical mathematical research with real world applications.Read moreRead less
Geometric evolution equations and global effects of curvature. This project aims to approach several important problems in global differential geometry, by inventing new processes to deform geometric objects to simpler ones. The deformations are described by carefully constructed geometric evolution equations, designed to exhibit behaviour suited to the given problem. The project proposes methods for building such equations, and new techniques for their analysis. The research is expected to yi ....Geometric evolution equations and global effects of curvature. This project aims to approach several important problems in global differential geometry, by inventing new processes to deform geometric objects to simpler ones. The deformations are described by carefully constructed geometric evolution equations, designed to exhibit behaviour suited to the given problem. The project proposes methods for building such equations, and new techniques for their analysis. The research is expected to yield significant new results, both in differential geometry and in nonlinear heat equations, and should provide substantial progress towards resolving several important long-standing conjectures.
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Global properties of evolution on manifolds. The aim is to analyze global properties of solutions of parabolic equations on manifolds and in particular the equations associated with a family of Hormander fields.
Analysis and applications of geometric evolution equations. This project will keep Australian research in geometric analysis at the leading edge of the field internationally. It will produce fundamental new insights in differential geometry and in the understanding of geometric partial differential equations, and will provide a rich and vigorous training ground for graduate and honours students.