Journal Article: AFLT-type Selberg integrals
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
Journal Article: Bounded Littlewood identities
Rains, Eric M. and Warnaar, S. Ole (2021). Bounded Littlewood identities. Memoirs of the American Mathematical Society, 270 (1317), 1-115. doi: 10.1090/memo/1317
Book Chapter: Elliptic hypergeometric functions associated with root systems
Rosengren, H. and Warnaar, S. O. (2020). Elliptic hypergeometric functions associated with root systems. Encyclopedia of special functions: the Askey-Bateman Project. (pp. 159-186) Cambridge, United Kingdom: Cambridge University Press. doi: 10.1017/9780511777165.007
Towards logarithmic representation theory of W-algebras
(2021–2024) ARC Discovery Projects
Symmetric functions and Hodge polynomials
(2017–2022) ARC Discovery Projects
(2016–2019) UQ Fellowships
Selberg integrals of Alba-Fateev-Litvinov-Tarnopolsky type
(2020) Master Philosophy
Stabilisers of eigenvectors in complex reflection groups
(2019) Master Philosophy
Nahm's conjecture in the Cartan case
(2015) Master Philosophy
Elliptic hypergeometric functions associated with root systems
Rosengren, H. and Warnaar, S. O. (2020). Elliptic hypergeometric functions associated with root systems. Encyclopedia of special functions: the Askey-Bateman Project. (pp. 159-186) Cambridge, United Kingdom: Cambridge University Press. doi: 10.1017/9780511777165.007
Logarithmic and complex constant term identities
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
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 (2021). Bounded Littlewood identities. Memoirs of the American Mathematical Society, 270 (1317), 1-115. doi: 10.1090/memo/1317
An elliptic hypergeometric function approach to branching rules
Lee, Chul-Hee, Rains, Eric M. and Warnaar, S. Ole (2020). An elliptic hypergeometric function approach to branching rules. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 16 142, 1-52. doi: 10.3842/SIGMA.2020.142
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
Srinivasa Ramanujan: Going Strong at 125, Part II
Alladi, Krishnaswami, Ono, Ken, Soundararajan, K., Vaughan, R. C. and Warnaar, S. Ole (2013). Srinivasa Ramanujan: Going Strong at 125, Part II. Notices of the American Mathematical Society, 60 (01), 10-22. doi: 10.1090/noti926
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, 12 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
Refined q-trinomial coefficients and character identities
Warnaar, SO (2001). Refined q-trinomial coefficients and character identities. Journal of Statistical Physics, 102 (3-4), 1065-1081. doi: 10.1023/A:1004827709169
An A(2) Bailey lemma and Rogers-Ramanujan-type identities
Andrews, GE, Schilling, A and Warnaar, SO (1999). An A(2) Bailey lemma and Rogers-Ramanujan-type identities. Journal of the American Mathematical Society, 12 (3), 677-702. doi: 10.1090/S0894-0347-99-00297-0
Warnaar, SO (1999). q-trinomial identities. Journal of Mathematical Physics, 40 (5), 2514-2530. doi: 10.1063/1.532880
Inhomogeneous lattice paths, generalized Kostka polynomials and A(n-1) supernomials
Schilling, A and Warnaar, SO (1999). Inhomogeneous lattice paths, generalized Kostka polynomials and A(n-1) supernomials. Communications in Mathematical Physics, 202 (2), 359-401. doi: 10.1007/s002200050586
A higher level Bailey lemma: Proof and application
Schilling, A and Warnaar, SO (1998). A higher level Bailey lemma: Proof and application. Ramanujan Journal, 2 (3), 327-349. doi: 10.1023/A:1009746932284
A note on the trinomial analogue of Bailey's lemma
Warnaar, SO (1998). A note on the trinomial analogue of Bailey's lemma. Journal of Combinatorial Theory Series a, 81 (1), 114-118. doi: 10.1006/jcta.1997.2830
Supernomial coefficients, polynomial identities and q-series
Schilling, A and Warnaar, SO (1998). Supernomial coefficients, polynomial identities and q-series. Ramanujan Journal, 2 (4), 459-494. doi: 10.1023/A:1009780810189
OBrien, DL, Pearce, PA and Warnaar, SO (1997). Analytic calculation of conformal partition functions: Tricritical hard squares with fixed boundaries. Nuclear Physics B, 501 (3), 773-799. doi: 10.1016/S0550-3213(97)00424-0
Berkovich, A, McCoy, BM, Schilling, A and Warnaar, SO (1997). Bailey flows and Bose-Fermi identities for the conformal coset models (A(1)((1)))(N) x (A(1)((1)))(N')/(A(1)((1)))(N+N'). Nuclear Physics B, 499 (3), 621-649. doi: 10.1016/S0550-3213(97)82955-0
The Andrews-Gordon identities and q-multinomial coefficients
Warnaar, SO (1997). The Andrews-Gordon identities and q-multinomial coefficients. Communications in Mathematical Physics, 184 (1), 203-232. doi: 10.1007/s002200050058
Fermionic solution of the Andrews-Baxter-Forrester model .2. Proof of Melzer's polynomial identities
Warnaar, SO (1996). Fermionic solution of the Andrews-Baxter-Forrester model .2. Proof of Melzer's polynomial identities. Journal of Statistical Physics, 84 (1-2), 49-83. doi: 10.1007/BF02179577
Finitized conformal spectrum of the Ising model on the cylinder and torus
OBrien, DL, Pearce, PA and Warnaar, SO (1996). Finitized conformal spectrum of the Ising model on the cylinder and torus. Physica a, 228 (1-4), 63-77. doi: 10.1016/S0378-4371(96)00055-6
A bijection which implies Melzer's polynomial identities: The chi(1,1)((p,p+1)) case
Foda, O and Warnaar, SO (1996). A bijection which implies Melzer's polynomial identities: The chi(1,1)((p,p+1)) case. Letters in Mathematical Physics, 36 (2), 145-155. doi: 10.1007/BF00714377
Foda, O, Okado, M and Warnaar, SO (1996). A proof of polynomial identities of type s(l(n))over-cap(1)circle times s(l(n))over-cap(1)/s(l(n))over-cap(2). Journal of Mathematical Physics, 37 (2), 965-986. doi: 10.1063/1.531698
Yang-Baxter algebras based on the two-colour BWM algebra
Grimm, U and Warnaar, SO (1995). Yang-Baxter algebras based on the two-colour BWM algebra. Journal of Physics A-Mathematical and General, 28 (24), 7197-7207. doi: 10.1088/0305-4470/28/24/017
ALGEBRAIC CONSTRUCTION OF HIGHER-RANK DILUTE A-MODELS
WARNAAR, SO (1995). ALGEBRAIC CONSTRUCTION OF HIGHER-RANK DILUTE A-MODELS. Nuclear Physics B, 435 (3), 463-481. doi: 10.1016/0550-3213(94)00424-D
SOLVABLE RSOS MODELS BASED ON THE DILUTE BWM ALGEBRA
GRIMM, U and WARNAAR, SO (1995). SOLVABLE RSOS MODELS BASED ON THE DILUTE BWM ALGEBRA. Nuclear Physics B, 435 (3), 482-504. doi: 10.1016/0550-3213(94)00405-4
EXCEPTIONAL STRUCTURE OF THE DILUTE A(3) MODEL - E(8) AND E(7) ROGERS-RAMANUJAN IDENTITIES
WARNAAR, SO and PEARCE, PA (1994). EXCEPTIONAL STRUCTURE OF THE DILUTE A(3) MODEL - E(8) AND E(7) ROGERS-RAMANUJAN IDENTITIES. Journal of Physics A-Mathematical and General, 27 (23), L891-L897. doi: 10.1088/0305-4470/27/23/005
LATTICE ISING-MODEL IN A FIELD - E8 SCATTERING-THEORY
BAZHANOV, VV, NIENHUIS, B and WARNAAR, SO (1994). LATTICE ISING-MODEL IN A FIELD - E8 SCATTERING-THEORY. Physics Letters B, 322 (3), 198-206. doi: 10.1016/0370-2693(94)91107-X
ORDER PARAMETERS OF THE DILUTE A-MODELS
WARNAAR, SO, PEARCE, PA, SEATON, KA and NIENHUIS, B (1994). ORDER PARAMETERS OF THE DILUTE A-MODELS. Journal of Statistical Physics, 74 (3-4), 469-531. doi: 10.1007/BF02188569
SOLVABLE LATTICE MODELS LABELED BY DYNKIN DIAGRAMS
WARNAAR, SO and NIENHUIS, B (1993). SOLVABLE LATTICE MODELS LABELED BY DYNKIN DIAGRAMS. Journal of Physics A-Mathematical and General, 26 (10), 2301-2316. doi: 10.1088/0305-4470/26/10/005
EXACT MULTICRITICAL BEHAVIOR OF THE POTTS-MODEL
NIENHUIS, B, WARNAAR, SO and BLOTE, HWJ (1993). EXACT MULTICRITICAL BEHAVIOR OF THE POTTS-MODEL. Journal of Physics A-Mathematical and General, 26 (3), 477-493. doi: 10.1088/0305-4470/26/3/013
NEW CONSTRUCTION OF SOLVABLE LATTICE MODELS INCLUDING AN ISING-MODEL IN A FIELD
WARNAAR, SO, NIENHUIS, B and SEATON, KA (1992). NEW CONSTRUCTION OF SOLVABLE LATTICE MODELS INCLUDING AN ISING-MODEL IN A FIELD. Physical Review Letters, 69 (5), 710-712. doi: 10.1103/PhysRevLett.69.710
WARNAAR, SO, BATCHELOR, MT and NIENHUIS, B (1992). CRITICAL PROPERTIES OF THE IZERGIN-KOREPIN AND SOLVABLE O(N) MODELS AND THEIR RELATED QUANTUM SPIN CHAINS. Journal of Physics A-Mathematical and General, 25 (11), 3077-3095. doi: 10.1088/0305-4470/25/11/016
BETHE-ANSATZ RESULTS FOR A SOLVABLE O(N) MODEL ON THE SQUARE LATTICE
BATCHELOR, MT, NIENHUIS, B and WARNAAR, SO (1989). BETHE-ANSATZ RESULTS FOR A SOLVABLE O(N) MODEL ON THE SQUARE LATTICE. Physical Review Letters, 62 (21), 2425-2428. doi: 10.1103/PhysRevLett.62.2425
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. 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
The Mukhin-Varchenko conjecture for type A
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.
q-Selberg Integrals and Macdonald Polynomials
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.
Warnaar, SO (2001). 50 years of Bailey's lemma. Euroconference on Algebraic Combinatorics and Applications (Alcoma99), Grossweinstein Germany, Sep 12-19, 1999. BERLIN: SPRINGER-VERLAG BERLIN.
A generalization of the q-Saalschutz sum and the Burge transform
Schilling, A and Warnaar, SO (2000). A generalization of the q-Saalschutz sum and the Burge transform. Workshop on Physical Combinatorics, Kyoto Japan, Feb 01-02, 1999. CAMBRIDGE: BIRKHAUSER BOSTON.
Schilling, A and Warnaar, SO (1997). A higher-level Bailey lemma. Proceedings of the Conference on Exactly Soluble Models in Statistical Mechanics - Current Status and Historical Perspectives, Boston Ma, Mar, 1996. SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD. doi: 10.1142/S0217979297000253
A CRITICAL ISING-MODEL IN A MAGNETIC-FIELD
WARNAAR, SO, NIENHUIS, B and SEATON, KA (1993). A CRITICAL ISING-MODEL IN A MAGNETIC-FIELD. Conf On Yang-Baxter Equations in Paris, Paris France, Jul 24-30, 1992. SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD. doi: 10.1142/S0217979293003474
Counting Complexity: An International Workshop on Statistical Mechanics and Combinatorics
Jan de Gier and Ole Warnaar eds. (2006). Counting Complexity: An International Workshop on Statistical Mechanics and Combinatorics. Counting Complexity: An International Workshop on Statistical Mechanics and Combinatorics, Dunk Island, Queensland, Australia, 10–15 July 2005.
Towards logarithmic representation theory of W-algebras
(2021–2024) ARC Discovery Projects
Symmetric functions and Hodge polynomials
(2017–2022) 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
Arithmetic Geometry of Moduli of Representations
Master Philosophy — Associate Advisor
Other advisors:
Selberg integrals of Alba-Fateev-Litvinov-Tarnopolsky type
(2020) 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: