Dr Ian Marquette

School of Mathematics and Physics

School of Mathematics and Physics

Phone: +61 7 3346 7952

Office: Room 807, Priestly Building, UQ St Lucia campus

2013- : ARC DECRA Postdoctoral Fellow, The University of Queensland, Australia

2011-2013 : Postdoctoral Researcher, The University of Queensland, Australia

2009-2011 : FQRNT Postdoctoral Fellow, The University of York, England

March 2009 : PhD in Physics ( Mathematical Physics ), Universite de Montreal, Canada

I received my PhD in physics from The Universite de Montreal in 2009. My PhD thesis was titled "Superintegrability with third order integrals of motion, polynomial algebras and supersymmetric quantum mechanics". My PhD supervisor was Prof. Pavel Winternitz. I also obtained a Bachelor bidisciplinary in Mathematics and Physics from the Universite de Montreal, Canada.

Before moving to Brisbane, I spent two years as a postdoctoral research fellow under a FQRNT fellowship at The University of York. I worked in the group of mathematical physics and collaborated with Dr Niall Mackay on superintegrable systems involving a monopole interaction. I also introduced new superintegrable systems with higher order supercharges involving Painleve transcendents. I also studied very interesting and new relations between superintegrability and supersymmetric quantum mechanics.

I'm now a post-doctoral research fellow in the School of Mathematics and Physics at The University of Queensland, Brisbane, Australia and a member of the Centre of Mathematical Physics. I work on Topological properties of exactly-solvable, two-dimensional quantum systems with Dr. Jon Links. More precisely, I study classes of exactly solvable Bardeen-Cooper-Schrieffer type pairing models of superconductivity and demonstrated their quantum phases using various new mathematical approaches. More recently, I extended the study of phase transition to BEC models using combination of analytical and numerical methods.

In June 2013, I also began a three years DECRA ( Discovery Early Career Researcher Award ) project with title "New constructions of superintegrable systems and the connection with Painleve transcendents". I introduced new methods to construct and study algebraically superintegrable systems and obtained new families related to exceptionnal othogonal polynomials.In 2014 I also become associated supervisor of two PhD students Fazlul Hoque with project "Aspects of superintegrability, special functions and orthogonal polynomials" and Fahad Alshammari with project "Symmetry algebras of differential equations and related aspects of representation theory".

My interests of research lie in the domain of mathematical physics. I am interested by :

-Superintegrable systems in classical and quantum mechanics

-Integrable and exactly solvable systems in condensed matter (BSC and BEC models), algebraic Bethe ansatz, BA/ODE correspondence, singular integrals equations

-Lie algebras, quadratic and polynomial algebras, Casimir operators their representations and applications

-Special functions, exceptionnal orthogonal polynomials and Painlev\'e transcendents in quantum mechanics

-Exactly and quasi exactly solvable quantum systems and supersymmetric quantum mechanics

-Symmetries of nonlinear ordinary and partial differential equations, non semisimple Lie algebras

This is a link to my Google Scholar page and my ArXiv page.

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