Ext. Number:
Research Groups:
  • Differential Geometry
  • Shortest network design
  • Minimal Surfaces
  • Geometric Topology of 3- and 4-manifolds
Recent Publications:
  • The classification of homotopy classes of bounded curvature paths (2016) more
  • Determining the open pit to underground transition: A review of existing methods and a proposed new method (2016) more
  • Bounding Embeddings of VC Classes into Maximum Classes (2015) more
  • Maximizing the net present value of a Steiner tree (2015) more
  • Gradient-constrained discounted Steiner trees I: optimal tree configurations (2015) more

Selected Publications

Extra Information:
I have supervised 15 honours students, 8 masters and 8 PhD students and currently have 3 PhD and 3 Honours students. Research topics in all my areas of interest are possible and my web site has more information.
Current Postgraduate Supervision:
Ana DOW "Cobordism classes of non-positively curved manifolds"
David KIRSZENBLAT "Topics in Optimisation"
Samuel OWEN "Mathematics of Shape Applied to Neuron Morphology"
Tianyu (Tim) YANG "A Combinatorial Ricci Flow for Ideal Triangulations"
Past Postgraduate Supervision:
Jose Manuel AYALA-HOFFMANN "On Spaces of Constrained Paths"
Loretta BARTOLINI "One-sided Heegaard splittings of 3-manifolds"
Julie CAIN "Random graph processes and optimisation"
Alan CHANG "Optimisation in Underground Mining."
James COFFEY "3-manifolds built from injective handlebodies"
Bell FOOZWELL "Haken n-Manifolds"
Christopher GODDARD "Various topics in comparison geometry and discrete mathematics."
Joshua HOWIE "Invariants in low-dimensional topology derived from mathematical physics"
David KIRSZENBLAT "Dubins Network"
Mariam KREYDEM "Analysis and set theory"
Kevin PRENDERGAST "Steiner ratio for gradient constrained networks"
Shanil (Don Buweneka) RAMANAYAKE "Angle structures and triangulations for 3-manifolds"
Tharatorn SUPASITI "Boundary and decomposition in group theory and topology"
Paul WILLIAMS "Unifying fractional calculus with time scales"
Recent Grant History:
Year(s) Source Type Title
2013 - 2015 ARC Discovery Triangulations in dimensions 3 and 4: discrete and geometric structures
2010 - 2012 ARC Discovery Triangulations in dimension three: algorithms and geometric structures
2007 - 2011 ARC Discovery Statistical Topology and its Application to Deriving New Geometric Invariants
2008 - 2010 ARC Linkage Rapid optimisation in underground mining network design
2007 - 2009 AMIRA Contract Planning and Rapid Integrated Mine Optimisation (PRIMO)
2006 - 2008 ARC Discovery Minimal surfaces
2002 - 2006 ARC Discovery Topics on 3- and 4-dimensional manifolds
2004 - 2006 ARC Linkage Decision tools for underground mine development
Year Name Organisation
2004 Hannan Medal Australian Academy of Science
2003 Fellow of the Australian Academic of Science Australian Academy of Science
1987 Medal of the Australian Mathematical Society Australian Mathematical Society
Academic Board member
Strategic Planning Committee