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:
  Naghmana Tehseen, PhD, 'Differential Geometric Approaches to PDEs'.

• Past supervisions:
  Paul Martin, MSc. 'The Geometry of Flows'.
  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

• Director, Australian Mathematical Sciences Institute (AMSI) (current).

• Board member, Australian Centre of Excellence for Risk Analysis (ACERA) (2006-2009).

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

• 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, (AMSI) (2004-2005).

• Member of the American Mathematical Society (AMS).

Collaborators

• Michael Crampin, Ghent University.
• 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

• W. Sarlet, G.E. Prince and M. Crampin, Generalized submersiveness of second-order ordinary differential equations. J. Geom. Mech. 1, 209-221 (2009).

• G.E. Prince, Comment: "Period function and normalizers of vector fields in Rn with n−1 first integrals" by D. Peralta-Salas, JDE 244, (2008) 1287-1303. J. Diff. Eqns 246, 3750-3753 (2009).

• G.E. Prince and S.P. Dubois, Mathematical Models for Motion of the Rear Ends of Vehicles, in Mathematical and Computer Modelling 49, 2049-2060 (2009).

• G. E. Prince, On the inverse problem for autoparallels, pp 341-351 in "Variations, Geometry and Physics" in honour of Demeter Krupkas sixty-fifth birthday, O. Krupková and D.J. Saunders (Editors) Nova Science Publishers (2009).
• 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).