Staff profile

Qualifications

• BSc, DipEd(Monash), PhD(La Trobe), FAustMS.

Teaching areas

• Undergraduate mathematics. Recently I have taught MAT1CLA, MAT3AC,MAT3DQ, MAT2VCA, MAT4GM.

Supervision

• Current supervision:
  Paul Martin, MSc. 'The Geometry of Flows'.

• Past supervisions:
  Michael Jerie, PhD, 2005. 'The Geometry of Second Order ODEs'.
  Jon Aldridge, PhD, 2004. 'The Inverse Problem in the Calculus of Variations'.
  Michael Barco, PhD. 2000. 'Symmetry and exterior differential systems'.
  Georgia Stathopoulos, MSc. 1998. 'Geometry of Planar Flows'.
  James Sherring, PhD. 1993. 'Symmetry and Computer Algebra Techniques for Differential Equations'.
  Susan Godfrey, PhD. 1992. 'Reduction of Order Techniques for Classical Orbit Problems'.

Professional involvement

• Board member, Australian Centre of Excellence for Risk Analysis (ACERA) (current).

• Vice President (Annual Conferences), Australian Mathematical Society (AustMS) (2009-2012).

• Director, 2007 Annual Meeting of the Australian Mathematical Society (AustMS) (2007).

• Council member, Australian Mathematical Society (AustMS) (2006-2009).

• ICE-EM Access Grid Project Coordinator at AMSI (2005-2006).

• Executive & Acting Director, Australian Mathematical Sciences Institute (AMSI) (2004-2005).

• Member of the American Mathematical Society (AMS).

Collaborators

• Michael Crampin, Ghent University.
• Alan Head, Division of Materials Science and Technology, CSIRO, Clayton, Victoria.
• Demeter Krupka and Olga Krupkova, Palacky University, Olomouc, Czech Republic.
• Willy Sarlet, Division of Theoretical Mechanics, Rijksuniversiteit Gent, Ghent, Belgium.
• Gerard Thompson, Department of Mathematics, University of Toledo, Toledo, Ohio, USA.

Research interests

• My interests lie in the applications of differential geometry to ordinary and partial differential equations.

• At the moment I am working on the inverse problem in the calculus of variations (“when can a system of second order O.D.E's be rewritten as Euler-Lagrange equations?”), the classification of planar flows according to their perpendicular expansion and tangential rotation, the singularity theory of second order ordinary differential equations, the symmetry of exterior differential systems. Most of this work uses a differential geometric formulation of ordinary differential equations which brings together material from Riemannian and Finsler geometry, tangent and cotangent bundle geometry and the theory of contact manifolds.

Recent publications and presentations

• G.E. Prince and S.P. Dubois, Mathematical Models for Motion of the Rear Ends of Vehicles, in Mathematical and Computer Modelling (to appear).
• G. E. Prince, On the inverse problem for autoparallels pp 395-406 in "Variations, Geometry and Physics" in honour of Demeter Krupkas sixty-fifth birthday, O. Krupková and D.J. Saunders (Editors) Nova Science Publishers (2008).
• O. Krupková and G. Prince, Second Order Ordinary Differential Equations in Jet Bundles and the Inverse Problem of the Calculus of Variations pp 837-904, in Handbook of Global Analysis, edited by D. Krupka and D. Saunders, Elsevier (2007).
• G.E. Prince and D.M. King, The inverse problem in the calculus of variations: nonexistence of Lagrangians pp 131-140, in Differential Geometric Methods on Mechanics and Field theory: Volume in Honour of Willy Sarlet, edited by F.Cantrijn and B. Langerock, Gent, Academia Press (2007).
• O. Krupková and G. Prince, Lepage forms, closed two-forms and second order ordinary differential equations, Izv. Vyssh. Uchebn. Zaved. Mat. (Russian Mathematics) (N.I.Lobachevskii anniversary volume) 51, 1-16 (2007).