Curriculum Vitae

Personal Details
  name:Jonathan Michael Kress
  date of birth:14 January 1968
  citizenship:Australian and British
  address: School of Mathematics and Statistics
The University of New South Wales
Sydney 2052, Australia
  telephone:+61 2 9385 7078
  facsimile:+61 2 9385 7123
  email:j.kress@unsw.edu.au
  web:http://profiles.unsw.edu.au/maths/jkress1
 
 
Education
  The University of Newcastle
 
  degree: Ph. D. (mathematics)
 conferred:June 1998
 supervisors: Drs. I. M. Benn and W. P. Wood
 thesis title: Generalised Killing-Yano Tensors: Applications to Electrodynamics
  The University of Adelaide
 
  degree: B. Sc. (Hons.) Class IIA,
 conferred:May 1991
 supervisor: Prof. P. C. W. Davies
 thesis title: Cosmic Strings
 
 
Referees
 

Prof. W. Miller, Jr.
School of Mathematics
513 Vincent Hall, 206 Church St. SE
University of Minnesota
Minneapolis, MN 55455 USA
tel: +1 612 624 7379
fax: +1 612 626 7370
email: miller@ima.umn.edu

Prof. E. G. Kalnins
Department of Mathematics,
University of Waikato, Private Bag 3105
Hamilton, New Zealand
tel: +64 7 838 4713
fax: +64 7 838 4666
email: e.kalnins@waikato.ac.nz

 
Employment History
  The University of New South Wales
  2009- School of Mathematics -- Senior Lecturer
    Senior Lecturer in the School of Mathematics and Statistics at UNSW.
  • Involved in the design and administration of the School's Blackboard modules.
  • In charge of first year computing in the School.
  • Lectured MATH2111,
  • Tutored MATH1141, MATH1151.
  • Member of the School's computing committee.
  • Member of the School's Teaching and Learning committee.
  • Involved in the implimentation and administration of Maple TA assessment in first year.
  • Supervised a PhD student: Joshua Capel -- degree awarded 2014.
  • Local organiser for PRIMA 2009.
  2005-2009 School of Mathematics -- Lecturer
    Lecturer in the School of Mathematics and Statistics at UNSW.
  2001-2004 School of Mathematics -- Associate Lecturer
    Associate Lecturer in the School of Mathematics at UNSW.
  The University of Waikato
  1999-2001 Department of Mathematics -- Postdoctoral Research Fellow
    Postdoctoral research fellow working with Prof. E. G. Kalnins on `superintegrability and separation of variables' and `black hole perturbations'.
  The University of Sydney
  1998-1999 School of Mathematics and Statistics -- Associate Lecturer (0.5)
    I lectured and helped with the administration of the large first and second year units, MATH 1001 and MATH 2005, which I also taught at the Summer School. I supervised a vacation scholarship student, helped develop the teaching component of the school's web site and was a local organiser of (ACGRG2).
  1998-1999 School of Mathematics and Statistics -- Research Assistant (0.5)
    I held a half-time research assistant position, working with Prof. P. R. Wilson and A. Prof. C. D. Durrant on numerical simulations of solar magnetic fields.
  The University of Newcastle
  1997 School of Science and Technology, Central Coast Campus -- Associate Lecturer (cas.)
    Lectured first year courses at the university's Central Coast Campus and helped with the Central Coast Mathematics Enrichment Group for high school students.
  1997 Centre for the Advancement of Learning and Teaching -- Associate Lecturer (0.2)
    For one day a week, in the `Learning Skills Group', I provided drop-in assistance for mathematical and statistical problems for students throughout the university.
  1993-1997 Department of Mathematics -- Tutor (casual)
    Tutored most of the department's first and second year courses.
  The University of Adelaide
  1990-1992 Departments of Physics & Mathematics -- Tutor (casual)
    Tutored and demonstrated in a range of courses in physics and mathematics. Lab demonstrator for the Malaysian students bridging course.
 
 
Conference Presentations
  2009 Presented at the Australian Mathematical Society Annual Conference 2009.
  2008 Presented at the Superintegrable Systems in Classical and Quantum Mechanics -- Prague 2008.
  2006 Invited to the IMA summer program in Symmetries and Overdetermined Systems of Partial Differential Equations.
  2005 Presented at the Second International Workshop on Superintegrable Systems in Classical and Quantum Mechanics.
  2003 Presented at ICIAM 2003.

Grants and Awards

  2010 UNSW Faculty Research Grant Program, "Polynomial algebras of superintegrable systems" - $8000
  2005 UNSW Faculty Research Grant Program, "Nonlinear algebras in classical and quantum superintegrable systems" - $7000
  2004 UNSW Faculty Research Grant Program, "Closure of Symmetry Algebras in Superintegrable Systems" - $7000
  2003 UNSW Fellowship in Innovative Teaching and Educational Technology
  2003 UNSW Faculty Research Grant Program, "Quadratic Algebras and superintegrable systems" - $5000
  1994-1996 University of Newcastle Postgraduate Research Award - $15000 per annum

Research Interests

  Superintergrable Systems
Many classical Hamiltonian systems possess more constants of the motion than are required for integrability. Such systems are called superintegrable and examples of these can be found amoungst important phyical systems such as the Kepler problem and harmonic oscillator. Finding new examples of and investigating the algebraic properties of such systems, and their quantum counterparts, has been the main focus of my research during the last few of years.
  Differential Geometry and Symmetries of Wave Equations
In a rotating black hole space-time, the massless Dirac and Maxwell equations can be reduced to scalar equations and solved by separation of variables. This remarkable result can be understood in terms of symmetries of the equations resulting from the existence of a Killing-Yano tensor. Solutions to the metric perturbation equations of these space-times can also be found by similar techniques and are of importance to the emerging field of gravity wave astronomy, however, a similar geometrical understanding is lacking. My current research in this area aims to unify and extend these symmetry techniques.

Publications

34. Tools for verifying classical and quantum superintegrability.
E G Kalnins, J M Kress and W Miller Jr.
Preprint (arXiv:1006.0864)
33. Superintegrability and higher order constants for quantum systems.
E G Kalnins, J M Kress and W Miller Jr.
J. Phys. A: Math. Theor. 43 (2010) 265205.
(arXiv:1002.2665 doi:10.1088/1751-8113/43/26/265205)
32. Families of classical subgroup separable superintegrable systems.
E G Kalnins, J M Kress and W Miller Jr.
J. Phys. A: Math. Theor. 43 (2010) 092001.
(arXiv:0912.3158 doi:10.1088/1751-8113/43/9/092001)
31. Laplace-type equations as conformal superintegrable systems.
E G Kalnins, J M Kress, W Miller Jr. and S Post
Adv. Appl. Math. To appear.
(arXiv:0908.4316)
30. Structure Theory for Second Order 2D Superintegrable Systems with 1-Parameter Potentials.
E G Kalnins, J M Kress, W Miller Jr. and S Post
SIGMA. 5 (2009) 008.
(arXiv:0901.3081 doi:10.3842/SIGMA.2009.008)
29. Differential forms relating twistors to Dirac fields.
I M Benn and J M Kress.
In the proceedings of the 10th International Conference on Differential Geometry and its Applications, Palacky University, Olomouc, Czech Republic. August 27 -- 31, 2007 (World Scientific 2008).
28. Nondegenerate 3D Complex Euclidean Superintegrable Systems and Algebraic Varieties.
E G Kalnins, J M Kress and W Miller Jr.
J. Math. Phys. 48 (2007) 113518.
(arXiv:0708.3044 doi:10.1063/1.2817821)
27. Fine structure for second order superintegrable systems.
E G Kalnins, J M Kress and W Miller Jr.
In the IMA Volumes in Mathematics and its Applications, Vol. 144, "Symmetries and Overdetermined Systems of Partial Differential Equations", Springer 2008.
26. Fine structure for 3D second order superintegrable systems: 3-parameter potentials.
E G Kalnins, J M Kress and W Miller Jr.
J. Phys. A: Math. Theor. 40 (2007) 5875-5892.
25. Equivalence of superintegrable systems in two dimensions.
J M Kress.
Phys. Atomic Nuclei 70 (2007) 560-566.
24. Second-order superintegrable quantum systems.
W Miller, E G Kalnins and J M Kress.
Phys. Atomic Nuclei 70 (2007) 576-583.
23. Nondegenerate superintegrable systems in n-dimensional Euclidean spaces.
E G Kalnins, J M Kress, W Miller and G S Pogosyan.
Phys. Atomic Nuclei 70 (2007) 545-553.
22. Nondegenerate 2D complex Euclidean superintegrable systems and algebraic varieties.
E G Kalnins, J M Kress and W Miller Jr.
J. Phys. A: Math. Theor. 40 (2007) 3399-3411.
21. Second order superintegrable systems in conformally flat spaces. V. Two- and three-dimensional quantum systems.
E G Kalnins, J M Kress and W Miller Jr.
J. Math. Phys. 47 (2006) 093501.
20. Second order superintegrable systems in conformally flat spaces. IV. The classical 3D Stackel transform and 3D classification theory.
E G Kalnins, J M Kress and W Miller Jr.
J. Math. Phys. 47 (2006) 043514.
19. Symmetry Operators for the Dirac and Hodge-deRham Equations.
I M Benn and J M Kress.
In 9th International Conference on Differential Geometry and its Applications, Czech Republic. Charles University in Prague, August 30 - September 3, 2004, (2005) 421-430.
18. Infinte-order symmetries for quantum separable systems.
W Miller, E G Kalnins, J M Kress and G Pogosyan
Phys. Atomic Nuclei 68 (2005) 1756-1763.
17. Second order superintegrable systems in conformally flat spaces. III. 3D classical structure theory.
E G Kalnins, J M Kress and W Miller Jr.
J. Math. Phys. 46 (2005) 103507.
16. Second order superintegrable systems in conformally flat spaces. II. The classical two-dimensional Stäckel transform.
E G Kalnins, J M Kress and W Miller Jr.
J. Math. Phys. 46 (2005) 053510.
15. Second-order superintegrable systems in conformally flat spaces. I. Two-dimensional classical structure theory.
E G Kalnins, J M Kress and W Miller Jr.
J. Math. Phys. 46 (2005) 053509.
14. Jacobi, Ellipsoidal Coordinates and Superintegrable Systems.
E G Kalnins, J M Kress and W Miller Jr.
J. Nonlin. Math. Phys. 12 (2005) 209-229.
13. First-Order Dirac Symmetry Operators.
I M Benn and J M Kress.
Class. Quantum Grav. 21 (2004) 427-431.
12. Superintegrable Systems in Darboux Spaces.
E G Kalnins, J M Kress, W Miller Jr. and P Winternitz.
J. Math. Phys. 44(12) (2003) 5811-5848.
(arXiv:math-ph/0307039 or IMA preprint 1929)
11. Multiseparability and Superintegrability in Three Dimensions.
J M Kress and E G Kalnins.
Proceedings of the XXIII International Colloquium on Group Theoretical Methods in Physics, Dubna 2000.
Phys. Atomic Nuclei 65(6) (2002) 1047-1051.
10. Complete sets of invariants for dynamical systems that admit a separation of variables.
E G Kalnins, J M Kress, W Miller, Jr. and G S Pogosyan.
J. Math. Phys. 43(7) (2002) 3592-3609.
(IMA preprint 1846)
9. Superintegrability in a two-dimensional space of non-constant curvature.
E G Kalnins, J M Kress, P Winternitz.
J. Math. Phys. 43(2) (2002) 970-983.
(arXiv:math-ph/0108015)
8. The Evolution of Trailing Plumes from Active Regions.
C J Durrant, J M Kress and P R Wilson.
Sol. Phys. 201(1) (2001) 57-69.
7. Completeness of Multiseparable Superintegrability in Two-Dimensional Constant Curvature Spaces.
E G Kalnins, J M Kress, G S Pogosyan and W Miller Jr.
J. Phys. A: Math. Gen. 34 (2001) 4705-4720
(arXiv:math-ph/0102006 or IMA preprint 1739)
6. Simulations of the Polar Field Reversals during Cycle 22.
H B Snodgrass, J M Kress, P R Wilson.
Sol. Phys. 194 (2000) 1-17.
5. Observations of the Polar Field Reversals during Cycle 22.
H B Snodgrass, J M Kress, P R Wilson.
Sol. Phys. 191(1) (2000) 1-19.
4. Evolution of Isolated Active Regions.
J M Kress and P R Wilson.
Sol. Phys. 189(1) (1999) 147-161.
3. Solutions of Penrose's equation.
E N Glass and Jonathan Kress.
J. Math. Phys. 40(1) (1999) 309-317.
(arXiv:gr-qc/9809074)
2. Debye Potentials for Maxwell and Dirac Fields from a Generalisation of the Killing-Yano Equation.
I M Benn, Philip Charlton and Jonathan Kress.
J. Math. Phys. 38(9) (1997) 4504-4527.
(arXiv:gr-qc/9610037)
1. Force-free fields from Hertz potentials.
I M Benn and Jonathan Kress.
J. Phys. A: Math. Gen. 29 (1996) 6295-6304.