Members
| Name | Marquette Ian |
| Affiliation | |
| Phone (1) | +61 7 334 67952 |
| Areas of research (1) | Superintegrable and exactly solvable systems |
| Area of research (2) | Quadratic algebras, Lie algebras, Casimir and representations |
| Area of research (3) | Painleve transcendents and exceptional orthogonal polynomials |
| Postdoctoral Fellows with dates (current and since last year) (1) | Danilo Latini (2021 – ), The University of Queensland |
| Students with dates (current and since last year) and affiliation (1) | Anthony Parr (2022- ), The University of Queensland |
| Students with dates (current and since last year) and affiliation (2) | Leighton Arnold (2021 – ), The University of Queensland |
| Selected Recent Publications (past 2 years only) (1) | I. Marquette and C. Quesne, Ladder operators and hidden algebras for shape invariant nonseparable and nondiagonalizable models with quadratic complex interaction. II. Three-dimensional model, SIGMA 18 005 (2022) https://doi.org/10.3842/SIGMA.2022.005 |
| Selected Recent Publications (past 2 years only) (2) | I. Marquette and C. Quesne, Ladder operators and hidden algebras for shape invariant nonseparable and nondiagonalizable models with quadratic complex interaction. I. Two-dimensional model, SIGMA 18 004 (2022) https://doi.org/10.3842/SIGMA.2022.004 |
| Selected Recent Publications (past 2 years only) (3) | K.Zelaya, I.Marquette and V.Hussin, Third order shape invariance: Okamoto polynomials and related potentials, J. Phys A Math and Theor. 55 045205 (2022) https://doi.org/10.1088/1751-8121/ac43cc |
| Selected Recent Publications (past 2 years only) (4) | Rutwig Campoamor-Stursberg, Ian Marquette, Quadratic algebras as commutants of algebraic Hamiltonians in the enveloping algebra of Schrödinger algebras, Annals of Physics. 437 168694 (2022) https://doi.org/10.1016/j.aop.2021.168694 |
| Selected Recent Publications (past 2 years only) (5) | D.Latini, I. Marquette and Y.Z. Zhang, Racah algebra R(n) from coalgebraic structures and chains of R(3), J. Phys. A: Math. Theor. 54 395202 (2021), https://doi.org/10.1088/1751-8121/ac1ee8 |
| Selected Recent Publications (past 2 years only) (6) | F. Correa, F.Hoque, I. Marquette and Y.Z Zhang, N-dimensional Smorodinsky-Winternitz model and related higher rank quadratic algebra SW(N), J. Phys. A: Math. Theor. 54 395201 (2021) https://doi.org/10.1088/1751-8121/ac1dc1 |
| Selected Recent Publications (past 2 years only) (7) | R Campoamor-Stursberg, I Marquette, Hidden symmetry algebra and construction of quadratic algebras of superintegrable systems, Annals of Physics 424 168378 (2021), https://doi.org/10.1016/j.aop.2020.168378 |
| Selected Recent Publications (past 2 years only) (8) | F Correa, MA del Olmo, I Marquette, J Negro, Polynomial algebras from su(3) and a quadratically superintegrable model on the two sphere, J.PhysA. Math. and Theor 54 015205 (2021), https://doi.org/10.1088/1751-8121/abc909 |
| Selected Recent Publications (past 2 years only) (9) | D.Latini, I. Marquette and Y.Z. Zhang, Embedding of Racah algebras R(n) and superintegrability, Annals of Physics, 168397 (2021), https://doi.org/10.1016/j.aop.2021.168397 |
| Selected Recent Publications (past 2 years only) (10) | J.Moran, V. Hussin and I.Marquette, Non-linear ladder operators and coherent states for the 2:1 oscillator, J.Phys A:Math and Theor. 54 275301 (2021), https://doi.org/10.1088/1751-8121/ac0200 |
| Selected Recent Publications (past 2 years only) (11) | K. Zelaya, I. Marquette, and V. Hussin, Fourth Painleve and Ermakov equations: quantum invariants and new exactly-solvable time-dependent Hamiltonians, J.Phys.A Math. and Theor 54 015206 (2021), https://doi.org/10.1088/1751-8121/abcab8 |
| Selected Recent Publications (past 2 years only) (12) | BK Berntson, I Marquette, W Miller Jr, A new way to classify 2D higher order quantum superintegrable systems, J.Phys.A Math. and Theor. 53 494003 (2020), https://doi.org/10.1088/1751-8121/abc04a |
| Selected Recent Publications (past 2 years only) (13) | I Marquette, S Post and L Ritter, A fourth-order superintegrable system with a rational potential related to Painleve VI, J.Phys.A Math. and Theor. 53 50LT01 (2020), https://doi.org/10.1088/1751-8121/abbf06 |
| Selected Recent Publications (past 2 years only) (14) | S Kuru, I Marquette, J Negro, The general Racah algebra as the symmetry algebra of generic systems on pseudo-spheres, J.Phys.A: Math. and Theor. 53 405203 (2020), https://doi.org/10.1088/1751-8121/abadb7 |
| Selected Recent Publications (past 2 years only) (15) | BK Berntson, I Marquette, W Miller Jr, A new approach to analysis of 2D higher order quantum superintegrable systems, Quantum theory and symmetries (QTS) XI, CRM Series on Mathematical Physics (2020), https://doi.org/10.1007/978-3-030-55777-5_10 |
| Recent Invited Talks and Lectures (past year only) (1) | Painleve VI, rational potentials and cubic algebras , Online AUSTMS 9 December 2021 |
| Recent Invited Talks and Lectures (past year only) (2) | Higher order superintegrability, Painlevé transcendents and representations of polynomial algebras, colloquium, The University of Hawaii, USA, 19 November 2021 |
| Recent Invited Talks and Lectures (past year only) (3) | Hidden algebras for shape invariant nonseparable and nondiagonalizable models, .Algebraic and analytical methods in physics, 2 September 2021, Prague (online) |
| Recent Invited Talks and Lectures (past year only) (4) | Embedding of Racah algebra and superintegrable systems, CRM Mathematical physics seminar, 3 November 2020 (online) |
| Recent Invited Talks and Lectures (past year only) (5) | Construction of polynomials algebras related to superintegrable systems, APIOS The Asia Pacific integrable online seminars, 4th August 2020 (online) |