Professor Ole Warnaar
Chair and Professor of Pure Maths
Mathematics
+61 7 336 53487
Priestley Building (67), Room 756
Personal page
Professor Ole Warnaar's personal page
Teaching and learning
Professor Warnaar teaches 3rd year algebra and number theory.
Book Chapter
Chappell, Tom, Lascoux, Alain, Warnaar, S. Ole and Zudilin, Wadim (2013). Logarithmic and complex constant term identities. Computational and analytical mathematics. (pp. 219-250) edited by David H. Bailey, Heinz H. Bauschke, Peter Borwein, Frank Garvan, Michel Théra, Jon D. Vanderwerff and Henry Wolkowicz. New York, United States: Springer. doi: 10.1007/978-1-4614-7621-4_11
Journal Articles
Albion, Seamus P., Rains, Eric M. and Warnaar, S. Ole (2021). AFLT-type Selberg integrals. Communications in Mathematical Physics, 388 (2), 735-791. doi: 10.1007/s00220-021-04157-0
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
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
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
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
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
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
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
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, 12 07). The Riemann Hypothesis
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
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
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
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
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
Warnaar, S. O. (2008). Bisymmetric functions, Macdonald polynomials and sl3 basic hypergeometric series. Compositio Mathematica, 144 (02), 271-303. doi: 10.1112/S0010437X07003211
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
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.
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
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
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
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
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
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
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
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
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
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
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
Warnaar, S. Ole (2004). On the q-analogue of the sum of cubes. The Electronic Journal of Combinatorics, 11 (1), N13-1-N13-2.
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
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
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
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.
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
Conference Papers
Langer, Robin, Schlosser, Michael J. and Warnaar, S. Ole (2009). Theta functions, elliptic hypergeometric series, and Kawanaka's Macdonald polynomial conjecture. Workshop on Elliptic Integrable Systems, Isomonodromy Problems, and Hypergeometric Functions, Bonn, Germany, 21-25 Jul 2008. Kyiv, Ukraine: Natsional'na Akademiya Nauk Ukrainy. doi: 10.3842/SIGMA.2009.055
Warnaar, S. Ole (2008). The Mukhin-Varchenko conjecture for type A. FPSAC 2008: 20th Annual International Conference on Formal Power Series and Algebraic Combinatorics, Viña del Mar, Chile, 23-27 June, 2008. Nancy, France: INRIA.
Warnaar, S. O. (2005). q-Selberg Integrals and Macdonald Polynomials. Conference on Number Theory and Combinatorics in Physics, Gainesville, Florida, 21-23 Mar 2003. Dordrecht, The Netherlands: Springer. 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. Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory, Charlottesville, Virginia, USA, 23 - 27 may 2000. American Mathematical Society.