Dr Ian Marquette

ARC Future Fellowship

Mathematics
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

Research Interests

  • Integrable, superintegrable and exactly solvable models, related differential equations and algebraic structures
  • Lie, quadratic and polynomial Lie algebras, realizations, indecomposable representations
  • Casimir invariants, construction and applications, non-semi simple Lie algebras
  • Algebraic Bethe Ansatz, quantum inverse scattering method and phase transitions
  • Painlevé transcendents, exceptional orthogonal polynomials and relation to quantum mechanics

Qualifications

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

Publications

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Supervision

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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

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.