Project DE : New constructions of superintegrable systems and the connection with Painlevé transcendents.

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1 Ian Marquette School of Mathematics and Physics The University of Queensland Brisbane, QLD 4072 Australia B i.marquette@uq.edu.au people/ianmarquette/ Research interests My research interests lie in the field of Mathematical Physics in particular: 1.Superintegrable Hamiltonians in classical and quantum mechanics. 2.Quadratic associative and polynomial algebras, their representations and applications. 3.Exceptionnal orthogonal polynomials and Painlevé transcendents in quantum mechanics. 4.Exactly solvable models in condensed matter and their phase transitions. 5.Quasi exactly solvable quantum systems and supersymmetric quantum mechanics Title Employment History Discovery Early Career Researcher Award (DECRA) Postdoctoral Fellowship, Australia Research Council (ARC)., School of Mathematics and Physics., The University of Queensland, Australia. Home: Project DE : New constructions of superintegrable systems and the connection with Painlevé transcendents Postdoctoral Researcher, School of Mathematics and Physics, The University of Queensland, Australia. Home: Title Project: Topological properties of exactly-solvable, two-dimensional quantum systems. Supervisor Assoc. Prof. Jon Links Postdoctoral Fellowship, The Fonds de recherche du Québec-Nature et technologies (FRQNT), Department of Mathematics, The University of York, England. Home: Title Project B3 : Integrability, superintegrability, algebraic structures and applications. Education 2009 Ph.D. in Physics. ( in area of mathematical physics), Department of Physics, Université de Montréal, Home: title Supervisor Superintegrability with third order integrals, polynomial algebras and supersymmetric quantum mechanics. Prof. Pavel Winternitz Accelerated passage to PhD. The thesis was rated in the top 2% within the university BSc in Mathematics and Physics, Department of Physics, Université de Montréal,. Member of the Provost s honour roll, Faculty of Arts and Sciences, Université de Montréal. 1/8

2 Scholarships, Fellowship, Grants, Funding Discovery Early Career Researcher Award (DECRA), Project DE , Australian Research Council, Australia, AUD Raybould Fellowship, The University of Queensland, Australia, 3000 AUD Fond de la Recherche Scientifique (FNRS) Fellowship, for stay at L Université Libre de Bruxelles, Belgium, 1300 EUR ResTeach Fellowship, The University of Queensland, Australia, AUD Travel Funding, Centre de Recherches Mathématiques (CRM), Canada, 3000 CAD Fond de la Recherche Scientifique (FNRS) Fellowship, for stay at L Université Libre de Bruxelles, Belgium, 1300 EUR ResTeach Fellowship, The University of Queensland, Australia, AUD Fond de la Recherche Scientifique (FNRS), Fellowship for stay at L Université Libre de Bruxelles, Belgium, 1300 EUR Postdoctoral Fellowship, Project B3, The Fonds de recherche du Québec-Nature et technologies (FRQNT), Canada, CAD Doctoral Fesearch Scholarships, Project B2, The Fonds de recherche du Québec- Nature et technologies (FRQNT), Canada, CAD PBCSE Travel Awards, Ministère de l Éducation du Québec. Short stay at the Universita di Roma Tre, Italia, 1 September December 2007, 3000 CAD Support from The Doppler Institute in Prague and Prof. Pavel Winternitz for The 3rd International Conference on Superintegrable systems 4000 CAD Scholarship for Accelerated Passage to Ph.D., Faculty of Arts and Science, Université de Montréal, Canada CAD Master Research Scholarships, Project B1, The Fonds de recherche du Québec- Nature et technologies (FRQNT), Canada CAD Excellence Scholarships, Physics Department, Université de Montréal, Canada CAD Industrial Research Scholarships for undergraduate students, National Sciences and Engineering Research Council of Canada (NSERC),Lockheed Martin, Canada 5000 CAD University research scholarships for undergraduate students, National Sciences and Engineering Research Council of Canada (NSERC). PICASSO experiment, Canada 5000 CAD. Publications Journal Papers: Refereed 1. Md Fazlul Hoque, Ian Marquette and Yao-Zhong Zhang, A new family of N dimensional superintegrable double singular oscillators and quadratic algebra Q(3) so(n) so(n n), Submitted J. Phys.A : Math. Theor. (To appear). 2. J.Links, I. Marquette and A. Moghaddam, Exact solution of the p+ip Hamiltonian revisited: duality relations and hole-pair picture, J. Phys. A: Math. Theor (2015). 3. I. Marquette and C. Quesne, Deformed oscillator algebra approach of some of the quantum superintegrable Lissajous systems on the sphere and of their rational extensions, J. Math. Phys. 56, (2015). 4. B. Bagchi and I. Marquette, New 1-step extension of the Swanson oscillator and superintegrability of its two-dimensional generalization, Phys. Lett. A (2015). 5. F. Hoque, I. Marquette and Y.-Z. Zhang, Quadratic algebra structure and spectrum of a new superintegrable system in N-dimension J. Phys. A: Math. Theor (2015). 6. J. Links and I. Marquette, Ground-state Bethe root densities and quantum phase transitions, J.Phys. A: Math. Theor (2015). 7. I. Marquette and C. Quesne, Combined state-adding and state-deleting approaches to type III multi-step rationally-extended potentials: applications to ladder operators and superintegrability, J. Math. Phys (2014). 2/8

3 Conference Papers: Refereed 8. P. S. Isaac and I. Marquette, On realizations of polynomial algebras with three generators via deformed oscillator algebras, J.Phys.A: Math. Theor (2014). 9. D. Agboola, J. Links, I. Marquette and Y.-Z. Zhang, New quasi-exactly solvable class of generalized isotonic oscillators, J.Phys.A: Math. Theor (2014). 10. I.Marquette and C. Quesne, New ladder operators for a rational extension of the harmonic oscillator and superintegrability of some two-dimensional systems, J. Math. Phys (2013). 11. I. Marquette, Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras, J. Math. Phys (2013). 12. I.Marquette and C. Quesne, Two-step rational extensions of the harmonic oscillator: exceptional orthogonal polynomials and ladder operators, J. Phys. A: Math. Theor (2013). 13. I.Marquette and C. Quesne, New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials, J. Math. Phys (2013). 14. J. Links and I.Marquette, Integrability of an extended d+id-wave pairing Hamiltonian, Nucl. Phys. B (2013). 15. I. Marquette, Singular isotonic oscillator, supersymmetry and superintegrability, SIGMA 8 063, 14 pages (2012). 16. J. Links and I. Marquette, Generalised Heine-Stieltjes and Van Vleck polynomials associated with degenerate, integrable BCS models, J. Stat. Mech. P08019 (2012). 17. I. Marquette, Generalized 5D-Kepler system, Yang-coulomb monopoles and Hurwitz transformation, J. Math. Phys (2012). 18. I. Marquette, Classical ladder operators, polynomial Poisson algebras and classification of superintegrable systems, J. Math. Phys (2012). 19. I. Marquette, Generalized Kaluza-Klein monopole, quadratic algebras and ladder operators,j.phys.a: Math. Theor. 44, (2011). 20. I. Marquette, Quadratic algebras approach to relativistic quantum Smorodinsky- Winternitz systems, J.Math.Phys (2011). 21. I. Marquette, Generalized MICZ-Kepler system, duality, polynomial and deformed oscillator algebras, J.Math.Phys (2010). 22. I. Marquette, Construction of classical superintegrable systems with higher order integrals of motion from ladder operators, J.Math.Phys (2010). 23. I. Marquette, Superintegrability and higher order polynomial algebras, J.Phys. A: Math. Theor. 43, (2010). 24. I. Marquette, Supersymmetry as a method of obtaining new superintegrable systems with higher order integrals of motion, J.Math.Phys. 50, (2009). 25. I. Marquette, Superintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics II: Painlevé transcendent potentials, J. Math. Phys. 50, (2009). 26. I. Marquette, Superintegrability with third order integrals of motion, cubic algebras and supersymmetric quantum mechanics I:Rational function potentials, J. Math. Phys. 50, (2009). 27. I. Marquette and P. Winternitz, Superintegrable systems with a third order integral, J. Phys. A: Math. Theor. 41, (2008). 28. I. Marquette and P. Winternitz, Polynomial Poisson algebras for superintegrable systems with a third order integral of motion, J. Math. Phys. 48, (2007). 29. I. Marquette, New families of superintegrable systems from k-step rational extensions, polynomial algebras and degeneracies, Proceeding of the GROUP28: The XXVIII International Colloquium on Group-Theoretical Methods in Physics, J. Phys.: Conf. Ser (2015) 3/8

4 Papers in preparation 30. I. Marquette, An infinite family of superintegrable systems from higher order ladder operators and supersymmetry, Proceeding of the GROUP30: The 30 International Colloquium on Group-Theoretical Methods in Physics, J.Phys.:Conf. Series (2011). 31. V. Hussin and I. Marquette, Generalized Heisenberg algebras, SUSYQM and degeneracies: Infinite well and Morse potential,sigma 7, 024, 16 pages (2011),A. Andrianov, V. Hussin, J. Negro, L. Nieto and A. Smilga, Proceedings of the Workshop Supersymmetric Quantum Mechanics and Spectral Design. Benasque, Spain, July (2010). 32. I. Marquette, Cubic associative algebras for quantum superintegrable systems with a third order integral of motion, Proceeding for IMA Volume 144 (2008). 33. P.S. Isaac and I. Marquette, Families of 2D superintegrable anisotropic Dunkl oscillators and algebraic derivation of their spectrum (Submitted J.Phys.A. :Math. and Theor. 34. I. Marquette, M. Sajedi, and P.Winternitz. On structure and classification of 2D fourth order superintegrable systems separable in Cartesian coordinates. 35. I. Marquette, M. Sajedi, and P.Winternitz. Fourth order superintegrable systems separating in Cartsian coordinates 36. I.Marquette and C. Quesne, On connection betwen quantum systems involving fourth Painlevé transcendent and k-step extension related to EOP 37. F. Hoque, I. Marquette and Y.-Z. Zhang, Recurrence approach to N-dimensional system 38. F. Hoque, I. Marquette and Y.-Z. Zhang, Family of N-dimensional superintegrable systems and quadratic algebra structures (submitted J.Phys.A : Conf. Series) PhD Thesis 39. I. Marquette, Superintegrability with third order integrals, polynomial algebras and supersymmetric quantum mechanics, Universite de Montreal (2009) 2015 Talks 1. Deformed oscillator algebra approach of superintegrable systems on the sphere, QTS9, The 9th Symposium on Quantum Theory and Symmetries, Yerevan, Armenia, 16 July k-step rational extension, EOP and polynomial Heisenberg algebras,department of Mathematics and Statistics, Montréal, Canada, 23 June Ladder Operators for Rationally-Extended Potentials Connected with Exceptional Orthogonal Polynomials and Superintegrability, International Symposium on Orthogonal Polynomials, Special functions and Applications, Gaithersburgh, USA, 4 June Phase transition in exactly solvable BEC models from Bethe Ansatz equations, Université Libre de Bruxelles, Physique Nucleaire Theorique et Physique Mathematique, Bruxelles, Belgium, 18 May Deformed oscillator algebra approach of superintegrable systems on the sphere, Mathematical Physics Semiar, University of Queensland, Brisbane, Australia, 24 April Superintegrable systems from k-step extensions and degeneracies, 8th Australia-New Zealand Mathematics Convention, ANZAMP session, Melbourne, Australia, 11 December Phase transition in exactly solvable BEC models from Bethe Ansatz equations, Quantum Science Seminar, University of Queensland, Brisbane,Australia, 20 November New families of superintegrable systems from k-step rational extensions, polynomial algebras and degeneracies, The 30th International Colloquium on Group Theoretical Methods in Physics, Ghent, Belgium, 14 July k-step rational extensions of harmonic and radial oscillator, superintegrability and degeneracies, The XXIInd International Conference on Integrable Systems and Quantum symmetries, Prague, Czech Republic, 24 June /8

5 10. Quadratic algebras of superintegrable systems with monopole interaction and noncentral potential, Group Analysis of Differential Equations and Integrable Systems, Larnaca, Cyprus, 16 June Construction of new ladder operators, exceptionnal orthogonal polynomials and superintegrability, CRM, Montréal, Canada, 14 January Quantum system with the fourth Painleve transcendent, rational solutions and new ladder operators, ANZAMP meeting, Mooloolaba, Australia, 27 November Construction of new ladder operators and applications to superintegrability, Austms meeting, Australia Sydney, Australia, 4 October New ladder operators and polynomial algebras of superintegrable systems associated with Hermite exceptionnal orthogonal polynomials, QTS8, The 8th Symposium on Quantum Theory and Symmetries, El Colegio Nacional, Mexico City, 6 August Realizations of polynomial algebras as deformed oscillator algebras and superintegrability, QGQIS ( Quantum Groups and Quantum Integrable Systems), BITP, Kiev, Ukraine, 21 June Realizations of polynomial algebras as deformed oscillator algebras and superintegrability, Université Libre de Bruxelles, Physique Nucléaire Théorique et Physique Mathématique PNTPM, Bruxelles, Belgium, 22 May Realizations of polynomial algebras as deformed oscillator algebras and superintegrability, University of Queensland, Centre for Mathematical Physics, Seminar, Brisbane, Australia, 10 May Generalised Heine-Stieltjes and Van Vleck polynomials associated with integrable BCS models, Inaugural meeting of the ANZAMP, Lorne, Australia, 5 December Generalised Heine-Stieltjes and Van Vleck polynomials associated with degenerate, integrable BCS models, XVIIth International Congress on Mathematical Physics (ICMP12), Alborg, Denmark, 3 August Generalised Heine-Stieltjes and Van Vleck polynomials associated with degenerate, integrable BCS models, Mathematical Physics seminar, University of Queensland, Brisbane, Australia, 6 June Polynomial algebras and superintegrability,55th Annual Meeting of the Australian Mathematical Society, University of Wollongong, Australia, 26 September Polynomial algebras and superintegrability, The University of Queensland, Centre for mathematical physics, Seminar, Brisbane, Australia, 21 September Quadratic algebras and generalization of the MICZ-Kepler system, British Mathematical Colloquium 2011, University of Leicester, England, 18 April Quantum mechanics and Painlevé transcendents, Young Researchers in Mathematics 2011, University of Warwick, England, 16 April An infinite family of superintegrable systems with the fifth Painlevé transcendent from higher order ladder operators and supersymmetry, 28th International Colloquium on Group-Theoretical Methods in Physics Northumbria University, Newcastle, England, 26 July Superintegrability, supersymmetric quantum mechanics and ladder operators, Maths HEP Lunchtime Seminars, Department of Mathematics, Durham University, Durham, England, 7 May Lecture on Superintegrability 3: Superintegrability, supersymmetric quantum mechanics and ladder operators, University of York, England, 17 November Lecture on Superintegrability 2: Quadratic symmetry algebras and beyond the quadratic superintegrability, University of York, England, 10 November Lecture on Superintegrability 1: Origin of the search for superintegrable systems, classification and general properties of quadratically superintegrable systems, University of York, England, 3th November Superintegrability with higher order integrals of motion, North British Mathematical Physics Seminar, University of Edinburgh, Edinburgh, Scotland, 30 September /8

6 31. Superintegrability with second and third order integrals of motion, cubic algebras and supersymmetry, Seminar of the Laboratory of Mathematical Physics, Centre de recherches mathématiques, Montreal, Canada, February Supersymmetry and quantum mechanics, seminar ISM of graduate students in mathematics, Concordia University, Montreal, Canada, 7 October Superintegrable systems with a third order integral of motion, Cubic algebras and SUSYQM, The 3rd International Conference on Superintegrable Systems in Classical and Quantum Mechanics, Prague 2008, Prague, Czech Republic, 4-10 May Ising model in 2D. Department of Mathematics and Statistics, Université de Montréal,Montréal, Canada, March Superintegrable systems with a third order integral of motion, Università di Roma Tre, Rome, Italy, 26 November Applications of polynomial and parafermionic algebras in quantum superintegrable systems, McGill University. The 3rd (Canada-America-Mexico) physics graduate student conference), McGill University, Montréal, Canada, Cubic algebras, parafermionic algebras and application in quantum mechanics, Colloque panquébecois ISM, Concordia University, Montréal, Canada, May Dynamical symmetry of the hydrogen atom and connection with so(4), e(3) and so(3, 1) Lie algebras, Department of Mathematics and Statistics, Université de Montréal, Montréal, Canada, Mars A little introduction to renormalisation in quantum field theory, Graduate students in mathematical and theoretical physics, Université de Montréal, Montréal, Canada, 26 February Superintegrability and polynomial algebras, Department of Mathematics and Statistics, Université de Montréal, Montréal, Canada, 3 February Superintegrability and nonlinear symmetries, Graduate students in mathematical and theoretical physics seminar, Université de Montréal, Montréal, Canada, January Algebraic methods for the solution of ODE, Department of Mathematics and Statistics, Université de Montréal, Montréal, Canada, October Symmetries of the nonlinear Schrodinger algebra with cubic and quintic terms, Department of Mathematics and Statistics, Université de Montréal, Montréal, Canada, November Renormalization in quantum field theory, Colloquium ISM of graduate students in mathematics, UQAM, Montréal, Canada, May Supervision of graduate students Associate PhD advisor of Fazlul Hoque. Thesis title : Aspects of superintegrability, special functions and orthogonal polynomials, The University of Queensland confirmation obtained 9 April Associate PhD advisor of Fahad Alshammari, Thesis title : Casimir Operators of Conformal Galilei Algebras and Related Structures, The University of Queensland confirmation obtained 16 April 2015 Referee for thesis 2014 Member of the confirmation panel of the MPhil of Christopher Raymond. Title: W-algebra Conformal Field Theory and Holography. The University of Queensland, 12 September Referee for the Master thesis of Fahad Alshammari. Title : Symmetry Methods for Differential Equations. The University of Queensland, 13 October /8

7 Semester Semester Semester Spring 2011 Teaching experiences Lecturer: PHYS2100, Dynamics, Chaos and Special Relativity. The University of Queensland, Australia. Lecturer: PHYS2100, Dynamics, Chaos and Special Relativity. The University of Queensland, Australia. Lecturer: PHYS2100, Dynamics, Chaos and Special Relativity. The University of Queensland, Australia. Seminar leader: MAT00012I, Vector Calculus II. University of York, England. Autumn 2010 Seminar leader: MAT00004C, Introduction to Probability and Statistics. University of York, England. Summer 2010 Seminar leader: MAT00005C, Analysis II. University of York, England. Winter 2009 Lecturer: PHY1902, Electricity and optics. Université de Montréal, Autumn 2008 Lecturer: PHY1901, Classical mechanics and modern physics. Université de Montréal, Autumn 2008 Teaching assistant: PHY1955, Acoustics. Université de Montréal, Winter 2008 Teaching assistant: PHY2810, Quantum Mechanics. Université de Montréal, Autumn 2006 Teaching assistant: PHY2810, Quantum Mechanics. Université de Montréal, Winter 2006 Teaching assistant: PHY3070, Relativity 2 (General Relativity). Université de Montréal, Winter 2005 Teaching assistant: PHY3070, Relativity 2 (General relativity). Université de Montréal, Autumn 2005 Teaching assistant: PHY3080, Application of Groups in Physics. Université de Montréal, Autumn 2004 Teaching assistant: PHY1652, Relativity 1 (Special Relativity). Université de Montréal, Journal Reviewer Constructive Approximation European Physical Journal A Few-Body Systems Journal SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) Journal of Mathematical Physics Journal of Physics A: Mathematical and Theoretical Physical Review B Modern Physics Letters A Physics Letters A Annals of Physics Conference organization 2013 Organizer in the local comittee for ANZAMP meeting, Mooloolaba, Australia Co-chair for CAM 2007 the 3rd (Canada-America-Mexico) physics graduate student conference, Montreal, Canada 7/8

8 References These persons are familiar with my professional qualifications: Professor Pavel Winternitz PhD thesis supervisor Phone: Dept. of Mathematics and Statistics Fax: Université de Montréal H3C 3J7, Montréal, Canada Professor Jon Links Dept. of Mathematics Phone:(07) School of Mathematics and Physics Fax: (07) The University of Queensland QLD 4072, Brisbane, Queesnland, Australia Professor Willard Miller School of Mathematics Phone: University of Minnesota Fax: Vincent Hall, 206 Church St. SE United States Professor Véronique Hussin Dept. of Mathematics and Statistics Phone: Université de Montréal Fax: H3C 3J7, Montréal, Canada Professor Christiane Quesne Dept. of Theoretical Nuclear Physics and Phone: Mathematical Physics Université Libre de Bruxelles Fax: CP229, 1050 Bruxelles, Belgium 8/8

Laureate Postdoctoral Research Associate at The University of Sydney. Research Fellow of the Japan Society for the Promotion of Science (DC1)

Laureate Postdoctoral Research Associate at The University of Sydney. Research Fellow of the Japan Society for the Promotion of Science (DC1) NAME: Nobutaka Nakazono Curriculum Vitae 1 CONTACT DETAILS: Address: School of Mathematics and Statistics, Carslaw Building F07, The University of Sydney, Sydney NSW 2006, Australia Tel: +61 2 9351 3879