Dr Ian Marquette

Lecturer in Mathematics

School of Mathematics and Physics
Faculty of Science
i.marquette@uq.edu.au
+61 7 334 67952

Overview

I obtained a Ph.D in physics in 2009 from the Université de Montréal. I also obtained a FQRNT fellowship and spend two years in England. More recently, I obtained in 2013 a Discovery early career award from the ARC and in 2018 a Future Fellowship.

My research lie in the field of mathematical physics. I am interested by integrable exactly solvable systems, their related algebraic structures and special functions.

1.Integrable, superintegrable and exactly solvable models, related differential equations and algebraic structures

2.Lie, quadratic and polynomial Lie algebras, realizations, indecomposable representations

3.Casimir invariants, construction and applications, non-semi simple Lie algebras

4.Algebraic Bethe Ansatz, quantum inverse scattering method and phase transitions

5.Painlevé transcendents, exceptional orthogonal polynomials and relation to quantum mechanics

Qualifications

  • Doctor of Philosophy, Université de Montréal
  • Bachelor of Sciences, Université de Montréal

Publications

View all Publications

Grants

View all Grants

Supervision

  • (2018) Doctor Philosophy

  • Doctor Philosophy

  • Master Philosophy

View all Supervision

Available Projects

  • This project will intend to make new discoveries in regard of quadratic algegbras which naturally occur in context of integrable systems and to develop method to develop to obtain their Casimir operators. These results will allow to make further progress in their representation theory and obtain the spectrum of new superintegrable systems.

  • This project will intend to develop differential operator realizations connected to indecomposable representations and apply to the construction of exactly solvable systems.

View all Available Projects

Publications

Journal Article

Conference Publication

  • Hoque, Md Fazlul, Marquette, Ian and Zhang, Yao-Zhong (2018). On superintegrable monopole systems. In: Journal of Physics: Conference Series. 25th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2017, Prague, Czech Republic, (1-8). June 6-10, 2017. doi:10.1088/1742-6596/965/1/012018

  • Hoque, Md Fazlul, Marquette, Ian and Zhang, Yao-Zhong (2016). Family of N-dimensional superintegrable systems and quadratic algebra structures. In: C. Burdik, O. Navratil and S. Posta, XXIII International Conference on Integrable Systems and Quantum Symmetries (ISQS-23). 23rd International Conference on Integrable Systems and Quantum Symmetries, ISQS 2015, Prague, Czech Republic, (). 23 - 27 June 2015. doi:10.1088/1742-6596/670/1/012024

  • Marquette, Ian (2015). New families of superintegrable systems from k-step rational extensions, polynomial algebras and degeneracies. In: Journal of Physics: Conference Series. 30th International Colloquium on Group Theoretical Methods in Physics (Group30), Ghent, Belgium, (012057.1-012057.10). 14-18 July 2014. doi:10.1088/1742-6596/597/1/012057

  • Marquette, Ian (2011). An infinite family of superintegrable systems from higher order ladder operators and supersymmetry. In: GROUP 28: Physical and mathematical aspects of symmetry: Proceedings of the 28th International Colloquium on Group-Theoretical Methods in Physics. GROUP 28 Conference: XXVIIIth International Colloquium on Group-Theoretical Methods in Physics (ICGTMP), Newcastle upon Tyne, United Kingdom, (012047-1-012047-8). 26–30 July 2010. doi:10.1088/1742-6596/284/1/012047

  • Hussin, Veronique and Marquette, Ian (2011). Generalized Heisenberg algebras, SUSYQM and degeneracies: Infinite well and Morse potential. In: Alexander Andrianov, Veronique Hussin, Javier Negro, Luismi Nieto and Andrei Smilga, Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design”. Workshop on Supersymmetric Quantum Mechanics and Spectral Design, Benasque, Spain, (024.1-024.16). 18-30 July 2010. doi:10.3842/SIGMA.2011.024

  • Marquette, Ian (2008). Polynomial associative algebras for quantum superintegrable systems with a third order integral of motion. In: Michael Eastwood and Willard Miller, Symmetries and Overdetermined Systems of Partial Differential Equations. Proceedings. Institute for Mathematics and its Applications: Summer Program 2006, Minneapolis, MN, U.S.A., (461-469). 17 July-4 August, 2006. doi:10.1007/978-0-387-73831-4_24

Grants (Administered at UQ)

PhD and MPhil Supervision

Current Supervision

Completed Supervision

Possible Research Projects

Note for students: The possible research projects listed on this page may not be comprehensive or up to date. Always feel free to contact the staff for more information, and also with your own research ideas.

  • This project will intend to make new discoveries in regard of quadratic algegbras which naturally occur in context of integrable systems and to develop method to develop to obtain their Casimir operators. These results will allow to make further progress in their representation theory and obtain the spectrum of new superintegrable systems.

  • This project will intend to develop differential operator realizations connected to indecomposable representations and apply to the construction of exactly solvable systems.