Journal Article: A Nekrasov–Okounkov formula for Macdonald polynomials
Rains, Eric M. and Warnaar, S. Ole (2017) A Nekrasov–Okounkov formula for Macdonald polynomials. Journal of Algebraic Combinatorics, 48 1: 1-30. doi:10.1007/s10801-017-0790-2
Journal Article: Discrete analogues of Macdonald-Mehta integrals
Brent, Richard P., Krattenthaler, Christian and Warnaar, Ole (2016) Discrete analogues of Macdonald-Mehta integrals. Journal of Combinatorial Theory. Series A, 144 80-138. doi:10.1016/j.jcta.2016.06.005
Journal Article: Fifty years of The Journal of Combinatorial Theory
Barcelo, Helene, Rothschild, Bruce L. and Warnaar, S. Ole (2016) Fifty years of The Journal of Combinatorial Theory. Journal of Combinatorial Theory. Series A, 144 3: 1-6. doi:10.1016/j.jcta.2016.06.003
Symmetric functions and Hodge polynomials
(2017–2019) ARC Discovery Projects
(2016–2019) UQ Fellowships
(2014–2016) ARC Discovery Projects
Stabilisers of eigenvectors in complex reflection groups
(2019) Master Philosophy
Algebraic combinatorics and q-series
Master Philosophy
Nahm's conjecture in the Cartan case
(2015) Master Philosophy
Logarithmic and complex constant term identities
Chappell, Tom, Lascoux, Alain, Warnaar, S. Ole and Zudilin, Wadim (2013). Logarithmic and complex constant term identities. In David H. Bailey, Heinz H. Bauschke, Peter Borwein, Frank Garvan, Michel Théra, Jon D. Vanderwerff and Henry Wolkowicz (Ed.), Computational and analytical mathematics (pp. 219-250) New York, United States: Springer. doi:10.1007/978-1-4614-7621-4_11
A Nekrasov–Okounkov formula for Macdonald polynomials
Rains, Eric M. and Warnaar, S. Ole (2017) A Nekrasov–Okounkov formula for Macdonald polynomials. Journal of Algebraic Combinatorics, 48 1: 1-30. doi:10.1007/s10801-017-0790-2
Discrete analogues of Macdonald-Mehta integrals
Brent, Richard P., Krattenthaler, Christian and Warnaar, Ole (2016) Discrete analogues of Macdonald-Mehta integrals. Journal of Combinatorial Theory. Series A, 144 80-138. doi:10.1016/j.jcta.2016.06.005
Fifty years of The Journal of Combinatorial Theory
Barcelo, Helene, Rothschild, Bruce L. and Warnaar, S. Ole (2016) Fifty years of The Journal of Combinatorial Theory. Journal of Combinatorial Theory. Series A, 144 3: 1-6. doi:10.1016/j.jcta.2016.06.003
A framework of Rogers-Ramanujan identities and their arithmetic properties
Griffin, Michael J., Ono, Ken and Warnaar, S. Ole (2016) A framework of Rogers-Ramanujan identities and their arithmetic properties. Duke Mathematical Journal, 165 8: 1475-1527. doi:10.1215/00127094-3449994
Hall-Littlewood polynomials and characters of affine Lie algebras
Bartlett, Nick and Warnaar, S. Ole (2015) Hall-Littlewood polynomials and characters of affine Lie algebras. Advances in Mathematics, 285 1066-1105. doi:10.1016/j.aim.2015.08.011
Constant term identities and Poincaré polynomials
Károlyi, Gyula, Lascoux, Alain and Ole Warnaar, S. (2015) Constant term identities and Poincaré polynomials. Transactions of the American Mathematical Society, 367 10: 6809-6836. doi:10.1090/tran/6119
Koornwinder, Tom, Van Assche, Walter and Warnaar, Ole (2015) A tribute to Dick Askey. Journal of Approximation Theory, 193 1-3. doi:10.1016/j.jat.2015.03.001
Remarks on the paper "Skew Pieri rules for Hall-Littlewood functions" by Konvalinka and Lauve
Warnaar, S. Ole (2013) Remarks on the paper "Skew Pieri rules for Hall-Littlewood functions" by Konvalinka and Lauve. Journal of Algebraic Combinatorics, 38 3: 519-526. doi:10.1007/s10801-013-0423-3
Dedekind's eta-function and Rogers-Ramanujan identities
Warnaar, S. Ole and Zudilin, Wadim (2012) Dedekind's eta-function and Rogers-Ramanujan identities. Bulletin of the London Mathematical Society, 44 1: 1-11. doi:10.1112/blms/bdr019
Warnaar, Ole and Zudilin, Wadim (2011, December 07). The Riemann Hypothesis. , .
New multiple 6ψ6 summation formulas and related conjectures
Spiridonov, Vyacheslav P. and Warnaar, S. Ole (2011) New multiple 6ψ6 summation formulas and related conjectures. The Ramanujan Journal, 25 3: 319-342. doi:10.1007/s11139-011-9310-5
Warnaar, S. Ole and Zudilin, W. (2011) A q-rious positivity. Aequationes Mathematicae, 81 1-2: 177-183. doi:10.1007/s00010-010-0055-9
Branching rules for symmetric Macdonald polynomials and sl_n basic hypergeometric series
Lascoux, Alain and Warnaar, S. Ole (2011) Branching rules for symmetric Macdonald polynomials and sl_n basic hypergeometric series. Advances in Applied Mathematics, 46 1-4: 424-456. doi:10.1016/j.aam.2010.01.012
Warnaar, S. Ole (2010) The sl(3) Selberg integral. Advances in Mathematics, 224 2: 499-524. doi:10.1016/j.aim.2009.11.011
A Selberg integral for the Lie algebra An
Warnaar, S. Ole (2009) A Selberg integral for the Lie algebra An. Acta Mathematica, 203 2: 269-304. doi:10.1007/s11511-009-0043-x
Nonsymmetric interpolation Macdonald polynomials and gln basic hypergeometric series
Lascoux, Alain, Rains, Eric. M. and Warnaar, S. Ole (2009) Nonsymmetric interpolation Macdonald polynomials and gln basic hypergeometric series. Transformation Groups, 14 3: 613-647. doi:10.1007/s00031-009-9061-1
The importance of the Selberg integral
Forrester, P. J. and Warnaar, S. O. (2008) The importance of the Selberg integral. Bulletin (New Series) of the American Mathematical Society, 45 4: 489-534. doi:10.1090/S0273-0979-08-01221-4
Bisymmetric functions, Macdonald polynomials and sl3 basic hypergeometric series
Warnaar, S. O. (2008) Bisymmetric functions, Macdonald polynomials and sl3 basic hypergeometric series. Compositio Mathematica, 144 02: 271-303. doi:10.1112/S0010437X07003211
On the generalised Selberg integral of Richards and Zheng
Warnaar, S. O. (2008) On the generalised Selberg integral of Richards and Zheng. Advances in Applied Mathematics, 40 2: 212-218. doi:10.1016/j.aam.2006.12.002
Characters of graded parafermion conformal field theory
Fortin, J. F., Mathieu, P. and Warnaar, S. O. (2007) Characters of graded parafermion conformal field theory. Advances in Theoretical and Mathematical Physics, 11 6: 945-989.
Proof of the Flohr-Grabow-Koehn conjectures for characters of logarithmic conformal field theory
Warnaar, S. O. (2007) Proof of the Flohr-Grabow-Koehn conjectures for characters of logarithmic conformal field theory. Journal Of Physics A-Mathematical And Theoretical, 40 40: 12243-12254. doi:10.1088/1751-8113/40/40/015
The Bailey transform and false theta functions
Andrews, G. E. and Warnaar, S. O. (2007) The Bailey transform and false theta functions. Ramanujan Journal, 14 1: 173-188. doi:10.1007/s11139-006-9006-4
The product of partial theta functions
Andrews, G. E. and Warnaar, S. O. (2007) The product of partial theta functions. Advances in Applied Mathematics, 39 1: 116-120. doi:10.1016/j.aam.2005.12.003
Inversions of integral operators and elliptic beta integrals on root systems
Vyacheslav P., Spiridonov, S. and Warnaar, S. O. (2006) Inversions of integral operators and elliptic beta integrals on root systems. Advances in Mathematics, 207 1: 91-132. doi:10.1016/j.aim.2005.11.007
Rogers-Szego polynomials and Hall-Littlewood symmetric functions
Warnaar, S. Ole (2006) Rogers-Szego polynomials and Hall-Littlewood symmetric functions. Journal of Algebra, 303 2: 810-830. doi:10.1016/j.jalgebra.2006.04.026
Hall–Littlewood functions and the A2 Rogers–Ramanujan identities
Warnaar, S. O. (2006) Hall–Littlewood functions and the A2 Rogers–Ramanujan identities. Advances in Mathematics, 200 2: 403-434. doi:10.1016/j.aim.2004.12.001
A generalization of the Farkas and Kra partition theorem for modulus 7
Warnaar, S. O. (2005) A generalization of the Farkas and Kra partition theorem for modulus 7. Journal of Combinatorial Theory Series A, 110 1: 43-52. doi:10.1016/j.jcta.2004.08.008
Positivity preserving transformations for q-binomial coefficients
Berkovich, A. and Warnaar, S. O. (2005) Positivity preserving transformations for q-binomial coefficients. Transactions of the American Mathematical Society, 357 6: 2291-2351. doi:10.1090/S0002-9947-04-03680-3
Summation formulae for elliptic hypergeometric series
Warnaar, S. O. (2005) Summation formulae for elliptic hypergeometric series. Proceedings of the American Mathematical Society, 133 2: 519-527. doi:10.1090/S0002-9939-04-07558-6
Warnaar, S. O. (2005) q-Hypergeometric proofs of polynomial analogues of the triple product identity, Lebesgue's identity and Euler's pentagonal number theorem. Ramanujan Journal, 8 4: 467-474. doi:10.1007/s11139-005-0275-0
The Bailey Lemma and Kostka Polynomials
Warnaar, S. O. (2004) The Bailey Lemma and Kostka Polynomials. Journal of Algebraic Combinatorics, 20 2: 131-171. doi:10.1023/B:JACO.0000047280.16877.1f
On the q-analogue of the sum of cubes
Warnaar, S. Ole (2004) On the q-analogue of the sum of cubes. The Electronic Journal of Combinatorics, 11 1: N13-1-N13-2.
Extensions of the well-poised and elliptic well-poised Bailey lemma
Warnaar, S. O. (2003) Extensions of the well-poised and elliptic well-poised Bailey lemma. Indagationes Mathematicae, 14 3-4: 571-588. doi:10.1016/S0019-3577(03)90060-7
The generalized borwein conjecture. II. Refined q-trinomial coefficients
Warnaar, S. O. (2003) The generalized borwein conjecture. II. Refined q-trinomial coefficients. Discrete Mathematics, 272 2-3: 215-258. doi:10.1016/S0012-365X(03)00047-5
Partial Theta Functions. I. Beyond the Lost Notebook
Warnaar, S. O. (2003) Partial Theta Functions. I. Beyond the Lost Notebook. Proceedings of the London Mathematical Society, 87 2: 363-395. doi:10.1112/S002461150201403X
Partial-sum analogues of the Rogers-Ramanujan identities
Warnaar, S. O. (2002) Partial-sum analogues of the Rogers-Ramanujan identities. Journal of Combinatorial Theory, Series A, 99 1: 143-161. doi:10.1006/jcta.2002.3266
Warnaar, S. O. (2002) Hyp. Australian Mathematical Society Gazette, 29 5: 277-279.
Summation and transformation formulas for elliptic hypergeometric series
Warnaar, S. O. (2002) Summation and transformation formulas for elliptic hypergeometric series. Constructive Approximation, 18 4: 479-502. doi:10.1007/s00365-002-0501-6
Theta functions, elliptic hypergeometric series, and Kawanaka's Macdonald polynomial conjecture
Langer, Robin, Schlosser, Michael J. and Warnaar, S. Ole (2009). Theta functions, elliptic hypergeometric series, and Kawanaka's Macdonald polynomial conjecture. In: Masatoshi Noumi, Eric M. Rains, Hjalmar Rosengren and Vyacheslav P. Spiridonov, Proceedings of the Workshop: Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions. Workshop on Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions, Bonn, Germany, (055.1-055.20). 21-25 Jul 2008. doi:10.3842/SIGMA.2009.055
The Mukhin-Varchenko conjecture for type A
Warnaar, S. Ole (2008). The Mukhin-Varchenko conjecture for type A. In: 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2008). Proceedings. FPSAC 2008: 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics, Viña del Mar, Chile, (83-92). 23-27 June, 2008.
q-Selberg Integrals and Macdonald Polynomials
Warnaar, S. O. (2005). q-Selberg Integrals and Macdonald Polynomials. In: The Ramanujan Journal. Conference on Number Theory and Combinatorics in Physics, Gainesville, Florida, (237-268). 21-23 Mar 2003. doi:10.1007/s11139-005-4849-7
Schilling , A. and Warnaar, S. O. (2002). Conjugate Bailey pairs. From configuration sums and fractional-level string functions to Bailey's lemma. In: S. Berman, P. Fendley, Y-Z. Huang, K. Misra and B. Parshall, Contemporary Mathematics: International Conference on Infinite-Dimensional Lie Theory and Conformal Field Theory. Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory, Charlottesville, Virginia, USA, (227-255). 23 - 27 may 2000.
Counting Complexity: An International Workshop on Statistical Mechanics and Combinatorics
Counting Complexity: An International Workshop on Statistical Mechanics and Combinatorics (2006) . Edited by Jan de Gier and Ole Warnaar. Counting Complexity: An International Workshop on Statistical Mechanics and Combinatorics, 10–15 July 2005, Dunk Island, Queensland, Australia.
Symmetric functions and Hodge polynomials
(2017–2019) ARC Discovery Projects
(2016–2019) UQ Fellowships
(2014–2016) ARC Discovery Projects
The Mukhin-Varchenko and Rogers-Ramanujan conjectures
(2011–2016) ARC Discovery Projects
(2009–2011) University of Melbourne
Macdonald Polynomials: Combinatorics and representations
(2008–2010) ARC Discovery Projects
Algebraic combinatorics and q-series
Master Philosophy — Principal Advisor
Other advisors:
Stabilisers of eigenvectors in complex reflection groups
(2019) Master Philosophy — Principal Advisor
Other advisors:
Nahm's conjecture in the Cartan case
(2015) Master Philosophy — Principal Advisor
Modified Hall--Littlewood polynomials and characters of affine Lie algebras
(2014) Doctor Philosophy — Principal Advisor
Ideal Theory of Cones and Right Mori Orders
(2013) Doctor Philosophy — Principal Advisor
Jordan Decomposition for Differential Operators
(2017) Master Philosophy — Associate Advisor
Other advisors:
Regularity Results for Nonlinear Elliptic Systems
(2016) Doctor Philosophy — Associate Advisor
Other advisors: