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New directions in geometric evolution equations

Grant


Scheme


  • Discovery Projects

Abstract


  • Geometric evolution equations are modern mathematical tools with diverse applications from modelling crystal growth and flame propagation to digital image cleaning. They also provide a promising approach to many challenging mathematical problems. This project will use these equations to prove significant new results in differential geometry, including geometry of submanifolds and to conformal, inversive and projective geometry. In the process, new techniques will be developed to enable further applications and deepen understanding, particularly in the difficult setting of high order equations. The project will provide excellent research training for Australia's next generation of mathematical analysts at doctoral and post-doctoral level.

Date/time Interval


  • 2012 - 2015

Sponsor Award Id


  • DP120100097

Local Award Id


  • 101436

Scheme


  • Discovery Projects

Abstract


  • Geometric evolution equations are modern mathematical tools with diverse applications from modelling crystal growth and flame propagation to digital image cleaning. They also provide a promising approach to many challenging mathematical problems. This project will use these equations to prove significant new results in differential geometry, including geometry of submanifolds and to conformal, inversive and projective geometry. In the process, new techniques will be developed to enable further applications and deepen understanding, particularly in the difficult setting of high order equations. The project will provide excellent research training for Australia's next generation of mathematical analysts at doctoral and post-doctoral level.

Date/time Interval


  • 2012 - 2015

Sponsor Award Id


  • DP120100097

Local Award Id


  • 101436