Professor Geoff

Professor Geoff Prince

Adjunct Professor

College of Science, Health and Engineering

School of Engineering and Mathematical Sciences

Department of Mathematics and Statistics

Physical Sciences 2, Room 308C, Melbourne (Bundoora)

Research centres

Australian Mathematical Sciences Institute

Qualifications

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

Role

Honorary

Membership of professional associations

Fellow of Aust.Math.Soc., Director of AMSI, member of Amer.Math.Soc.

Area of study

Mathematics and Statistics

Brief profile

I am Director of the Australian Mathematical Sciences Institute www.amsi.org.au.

My research is carried out at La Trobe University in a group with Prof. Philip Broadbridge and a number of early career researchers. My international collaborators are Willy Sarlet & Tom Mestdag (Ghent, Belgium) and Olga Rossi (prev. Krupkova) & David Saunders (Ostrava, Czech Rep.).

Research interests include:

- Applications of differential geometry to ordinary and partial differential equations;

- Inverse problem in the calculus of variations;

-Classical mechanics;

-Riemannian geometry

Recent publications

W. Sarlet, T. Mestdag and G. Prince,  A generalization of Szebehely's inverse problem of dynamics. Rep. Math. Phys. 72, 65-84 (2013).

N.Tehseen and G.E. Prince, Integration of PDEs by Geometric Means. J.Phys.A: Math. Theor. 46, 105201 (20pp)(2013);

W. Sarlet, G.E. Prince, T. Mestdag and O. Krupková, Time-dependent kinetic energymetrics for Lagrangians of electromagnetic type. J.Phys.A: Math.Theor. 45, 085208 (13pp)(2012);

 W. Sarlet and G.E. Prince Alternative kinetic energy metrics for Lagrangian systems. J.Phys.A: Math.Theor. 43, 445204 (13pp)(2010); 

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,  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 Krupka’s 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).  

Resume

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Research projects

"Geometric Mechanics" funded by an EU IRSES grant 2011-2014

"New Geometric & Entropy Techniques for Differential Equations" funded by an ARC Discovery Project 2010-2012

"Harmonic Maps: Geometry, Integrability & Calculus of Variations" 2013

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