Professor J. Hyam RUBINSTEIN

Professorial Fellow (Associate)

School of Mathematics and Statistics

  • Room: G55
  • Building: Peter Hall Building
  • Campus: Parkville Campus

Research Interests

  • Geometric Topology of 3- and 4-manifolds
  • Minimal Surfaces
  • Shortest network design
  • Differential Geometry

Research Groups

Recent Publications

  • C. Hodgson, J. Rubinstein, H. Segerman. Triangulations of hyperbolic 3-manifolds admitting strict angle structures. Journal of Topology, 5, 887-908, 2012. doi: 10.1112/jtopol/jts022.

  • C. Hodgson, J. Rubinstein, H. Segerman, S. Tillmann, J Hyam Rubinstein. Veering triangulations admit strict angle structures. Geometry and Topology, 15, 2073-2089, 2011. doi: 10.2140/gt.2011.15.2073.

  • P. Norbury, J. Rubinstein. Closed Geodesics on Incomplete Surfaces. Geometriae Dedicata, 116, 1-36, 2005. doi: 10.1007/s10711-005-1892-x.

  • I. Aitchison, J. Rubinstein. Localising Dehn's lemma and the loop theorem in 3-manifolds. Mathematical Proceedings of the Cambridge Philosophical Society, 137, 281-292, 2004. doi: 10.1017/S0305004104007698.

  • J. Hass, P. Norbury, J. Rubinstein. Minimal spheres of arbitrarily high Morse index. Communications in Analysis and Geometry, 11, 425-439, 2003. doi: 10.4310/CAG.2003.v11.n3.a2.

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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

Name Thesis title
Ana DOW "Cobordism classes of non-positively curved manifolds"
David KIRSZENBLAT "Topics in Optimisation"
Samuel OWEN "Mathematics of Shape Applied to Neuron Morphology"

Past Postgraduate Supervision

Name Thesis title
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 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"

Past MSc Students

Name Project title
Oliver LEIGH
Samuel OWEN

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
2008 - 2010 ARC Linkage Rapid optimisation in underground mining network design
2007 - 2011 ARC Discovery Statistical Topology and its Application to Deriving New Geometric Invariants
2007 - 2009 AMIRA Contract Planning and Rapid Integrated Mine Optimisation (PRIMO)


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