Professor Christian Korff
- Professor of Mathematical Physics (Mathematics)
telephone:
01413306198
email:
Christian.Korff@glasgow.ac.uk
R441 - Level 4, Mathematics, The Mathematics & Statistics Building, Glasgow, G12 8SQ
https://orcid.org/0000-0002-9818-6135Biography
Before coming to Glasgow in October 2006, I held positions at City University London (2005-6), the University of Edinburgh (2002-2005) and the C.N. Yang Institute for Theoretical Physics at Stony Brook, New York (2000-2002). I completed my PhD (theoretical physics) at the Freie Universität Berlin, Germany in 2000.
Research interests
I am interested in areas where algebra and representation theory meet problems arising in physical systems. My research focusses on quantum integrable models connected with solutions of the Yang-Baxter equation. The latter include exactly solvable lattice models in statistical mechanics, quantum many body systems and low dimensional quantum field theories.
For further information please consult my personal website.
https://sites.google.com/view/christiankorff/home
Research groups
Publications
2025
Korff, C. (Ed.) (2025) Encyclopedia of Mathematical Physics, 2nd edition, Volume 3: Integrable Systems. Elsevier. ISBN 9780323957069
2021
2020
Gorbounov, V.G., Korff, C. and Stroppel, C. (2020) Yang-Baxter algebras, convolution algebras, and Grassmannians. Russian Mathematical Surveys, 75(5), 791. (doi: 10.1070/RM9959)
Korff, C. and Palazzo, D. (2020) Cylindric symmetric functions and positivity. Algebraic Combinatorics, 3(1), pp. 191-247. (doi: 10.5802/alco.90)
2018
2017
Gorbounov, V. and Korff, C. (2017) Quantum integrability and generalised quantum Schubert calculus. Advances in Mathematics, 313, pp. 282-356. (doi: 10.1016/j.aim.2017.03.030)
Korff, C. (2017) Dimers, crystals and quantum Kostka numbers. Seminaire Lotharingien de Combinatoire, 78B.40, 12pp.
2014
Korff, C. (2014) Quantum cohomology via vicious and osculating walkers. Letters in Mathematical Physics, 104(7), pp. 771-810. (doi: 10.1007/s11005-014-0685-2)
2013
2011
2010
Korff, C. (2010) Noncommutative Schur polynomials and the crystal limit of the Uq sl(2)-vertex model. Journal of Physics A: Mathematical and Theoretical, 43(43), p. 434021. (doi: 10.1088/1751-8113/43/43/434021)
Korff, C. and Stroppel, C. (2010) The sl(n)k-WZNW fusion ring: a combinatorial construction and a realisation as quotient of quantum cohomology. Advances in Mathematics, 225(1), pp. 200-268. (doi: 10.1016/j.aim.2010.02.021)
2009
Feigin, M., Korff, C. and Strachan, I. (2009) Workshop island 3: algebraic aspects of integrability. Introduction to an additional volume of selected papers arising from the conference on algebraic aspects of integrable systems, Island 3, Islay 2007. Glasgow Mathematical Journal, 51(A), pp. 1-3. (doi: 10.1017/S0017089508004734)
Korff, C. and Stroppel, C. (2009) A combinatorial description of the sl(n) fusion ring. Oberwolfach Reports, 6(1), pp. 846-850. (doi: 10.4171/OWR/2009/15)
2008
Korff, C. (2008) PT symmetry of the non-Hermitian XX spin-chain: non-local bulk interaction from complex boundary fields. Journal of Physics A: Mathematical and Theoretical, 41(29), p. 295206. (doi: 10.1088/1751-8113/41/29/295206)
Korff, C. (2008) Turning the quantum group invariant XXZ spin-chain Hermitian: a conjecture on the invariant product. Journal of Physics A: Mathematical and Theoretical, 41(19), p. 194013. (doi: 10.1088/1751-8113/41/19/194013)
2007
Korff, C. and Weston, R. (2007) PT symmetry on the lattice: the quantum group invariant XXZ spin chain. Journal of Physics A: Mathematical and Theoretical, 40(30), pp. 8845-8872. (doi: 10.1088/1751-8113/40/30/016)
Korff, C. (2007) A Q-operator for the quantum transfer matrix. Journal of Physics A: Mathematical and Theoretical, 40(14), pp. 3749-3774. (doi: 10.1088/1751-8113/40/14/002)
Korff, C. (2007) PT-invariance and representations of the Temperley-Lieb algebra on the unit circle. Recent Advances in Quantum Integrable Systems, Annecy-le-Vieux, France, 11-14 Sept 2007.
2006
Korff, C. (2006) A Q-operator for the twisted XXX model. Journal of Physics A: Mathematical and General, 39(13), pp. 3203-3219. (doi: 10.1088/0305-4470/39/13/002)
Fring, A. and Korff, C. (2006) Non-crystallographic reduction of generalized Calogero–Moser models. Journal of Physics A: Mathematical and General, 39(5), pp. 1115-1131. (doi: 10.1088/0305-4470/39/5/007)
Korff, C. (2006) Representation theory and Baxter's TQ equation for the six-vertex model. A pedagogical overview. In: Solvable Lattice Models 2004 - Recent Progress on Solvable Lattice Models, Kyoto, Japan, 20-23 July 2004, pp. 79-93.
2005
Fring, A. and Korff, C. (2005) Affine Toda field theories related to Coxeter groups of noncrystallographic type. Nuclear Physics B, 729(3), pp. 361-386. (doi: 10.1016/j.nuclphysb.2005.08.044)
Korff, C. (2005) A Q-operator identity for the correlation functions of the infinite XXZ spin-chain. Journal of Physics A: Mathematical and General, 38(30), pp. 6641-6657. (doi: 10.1088/0305-4470/38/30/002)
Korff, C. (2005) Auxiliary matrices on both sides of the equator. Journal of Physics A: Mathematical and General, 38(1), pp. 47-67. (doi: 10.1088/0305-4470/38/1/003)
Korff, C. (2005) Solving Baxter's TQ equation via representation theory. In: Fuchs, J. (ed.) Noncommutative Geometry and Representation Theory in Mathematical Physics: Satellite Conference to the Fourth European Congress of Non-commutative Geometry and Representation Theory in Mathematical Physics, Karlstad, Sweden, July 5-10, 2004. Series: Contemporary Mathematics (391). American Mathematical Society: Providence, USA, pp. 199-211. ISBN 9780821837184
2004
Fring, A. and Korff, C. (2004) Exactly solvable potentials of Calogero type for q-deformed Coxeter groups. Journal of Physics A: Mathematical and General, 37(45), pp. 10931-10949. (doi: 10.1088/0305-4470/37/45/012)
Korff, C. (2004) Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz. Journal of Physics A: Mathematical and General, 37(29), pp. 7227-7253. (doi: 10.1088/0305-4470/37/29/005)
Korff, C. (2004) The twisted XXZ chain at roots of unity revisited. Journal of Physics A: Mathematical and General, 37(5), pp. 1681-1689. (doi: 10.1088/0305-4470/37/5/014)
Korff, C. (2004) Auxiliary matrices for the six-vertex model at qN = 1: II. Bethe roots, complete strings and the Drinfeld polynomial. Journal of Physics A: Mathematical and General, 37(2), pp. 385-406. (doi: 10.1088/0305-4470/37/2/009)
2002
Korff, C. and Seaton, K.A. (2002) Universal amplitude ratios and Coxeter geometry in the dilute AL model. Nuclear Physics B, 636(3), pp. 435-464. (doi: 10.1016/S0550-3213(02)00438-8)
Korff, C. and Roditi, I. (2002) Quantum superalgebras at roots of unity and non-Abelian symmetries of integrable models. Journal of Physics A: Mathematical and General, 35(24), pp. 5115-5137. (doi: 10.1088/0305-4470/35/24/310)
2001
Korff, C. and McCoy, B.M. (2001) Loop symmetry of integrable vertex models at roots of unity. Nuclear Physics B, 618(3), pp. 551-569. (doi: 10.1016/S0550-3213(01)00417-5)
Korff, C. (2001) Colours associated to nonsimply-laced Lie algebras and exact S-matrices. Physics Letters B, 501(3-4), pp. 289-296. (doi: 10.1016/S0370-2693(01)00164-2)
2000
Castro-Alveredo, O., Fring, A. and Korff, C. (2000) Form factors of the homogeneous Sine-Gordon models. Physics Letters B, 484, pp. 167-176. (doi: 10.1016/S0370-2693(00)00565-7)
Korff, C. , Castro-Alveredo, O., Fring, A. and Miramontes, J. (2000) Thermodynamic Bethe Ansatz of the homogeneous sine-gordon models. Nuclear Physics B, 575(3), pp. 535-560. (doi: 10.1016/S0550-3213(00)00162-0)
Fring, A., Korff, C. and Schulz, B. (2000) On the universal representation of the scattering matrix of affine Toda field theory. Nuclear Physics B, 567(3), pp. 409-453. (doi: 10.1016/S0550-3213(99)00578-7)
Fring, A. and Korff, C. (2000) Colour valued scattering matrices. Physics Letters B, 477, pp. 380-386. (doi: 10.1016/S0370-2693(00)00226-4)
Fring, A. and Korff, C. (2000) Large and small density approximations to the thermodynamic Bethe Ansatz. Nuclear Physics B, 579, pp. 617-631. (doi: 10.1016/S0550-3213(00)00250-9)
1999
Fring, A., Korff, C. and Schulz, B. (1999) The ultraviolet behaviour of integrable quantum field theories, affine Toda field theory. Nuclear Physics B, 549(3), pp. 579-612. (doi: 10.1016/S0550-3213(99)00216-3)
Korff, C. , Lang, G. and Schrader, R. (1999) Two-particle scattering theory for anyons. Journal of Mathematical Physics, 40, pp. 1831-1869.
Articles
Korff, C. (2021) Cylindric Hecke characters and Gromov-Witten invariants via the asymmetric six-vertex model. Communications in Mathematical Physics, 381(2), pp. 591-640. (doi: 10.1007/s00220-020-03906-x)
Gorbounov, V.G., Korff, C. and Stroppel, C. (2020) Yang-Baxter algebras, convolution algebras, and Grassmannians. Russian Mathematical Surveys, 75(5), 791. (doi: 10.1070/RM9959)
Korff, C. and Palazzo, D. (2020) Cylindric symmetric functions and positivity. Algebraic Combinatorics, 3(1), pp. 191-247. (doi: 10.5802/alco.90)
Korff, C. and Palazzo, D. (2018) Cylindric reverse plane partitions and 2D TQFT. Séminaire Lotharingien de Combinatoire, 80B, 30.
Gorbounov, V. and Korff, C. (2017) Quantum integrability and generalised quantum Schubert calculus. Advances in Mathematics, 313, pp. 282-356. (doi: 10.1016/j.aim.2017.03.030)
Korff, C. (2017) Dimers, crystals and quantum Kostka numbers. Seminaire Lotharingien de Combinatoire, 78B.40, 12pp.
Korff, C. (2016) From quantum Bäcklund transforms to topological quantum field theory. Journal of Physics A: Mathematical and Theoretical, 49(10), 104001. (doi: 10.1088/1751-8113/49/10/104001)
Korff, C. (2014) Quantum cohomology via vicious and osculating walkers. Letters in Mathematical Physics, 104(7), pp. 771-810. (doi: 10.1007/s11005-014-0685-2)
Korff, C. (2013) Cylindric versions of specialised Macdonald functions and a deformed Verlinde algebra. Communications in Mathematical Physics, 318(1), pp. 173-246. (doi: 10.1007/s00220-012-1630-9)
Korff, C. (2011) The su(n) WZNW fusion ring as integrable model: a new algorithm to compute fusion coefficients. RIMS Kokyuroku Bessatsu, B28, pp. 121-153.
Korff, C. (2010) Noncommutative Schur polynomials and the crystal limit of the Uq sl(2)-vertex model. Journal of Physics A: Mathematical and Theoretical, 43(43), p. 434021. (doi: 10.1088/1751-8113/43/43/434021)
Korff, C. and Stroppel, C. (2010) The sl(n)k-WZNW fusion ring: a combinatorial construction and a realisation as quotient of quantum cohomology. Advances in Mathematics, 225(1), pp. 200-268. (doi: 10.1016/j.aim.2010.02.021)
Feigin, M., Korff, C. and Strachan, I. (2009) Workshop island 3: algebraic aspects of integrability. Introduction to an additional volume of selected papers arising from the conference on algebraic aspects of integrable systems, Island 3, Islay 2007. Glasgow Mathematical Journal, 51(A), pp. 1-3. (doi: 10.1017/S0017089508004734)
Korff, C. and Stroppel, C. (2009) A combinatorial description of the sl(n) fusion ring. Oberwolfach Reports, 6(1), pp. 846-850. (doi: 10.4171/OWR/2009/15)
Korff, C. (2008) PT symmetry of the non-Hermitian XX spin-chain: non-local bulk interaction from complex boundary fields. Journal of Physics A: Mathematical and Theoretical, 41(29), p. 295206. (doi: 10.1088/1751-8113/41/29/295206)
Korff, C. (2008) Turning the quantum group invariant XXZ spin-chain Hermitian: a conjecture on the invariant product. Journal of Physics A: Mathematical and Theoretical, 41(19), p. 194013. (doi: 10.1088/1751-8113/41/19/194013)
Korff, C. and Weston, R. (2007) PT symmetry on the lattice: the quantum group invariant XXZ spin chain. Journal of Physics A: Mathematical and Theoretical, 40(30), pp. 8845-8872. (doi: 10.1088/1751-8113/40/30/016)
Korff, C. (2007) A Q-operator for the quantum transfer matrix. Journal of Physics A: Mathematical and Theoretical, 40(14), pp. 3749-3774. (doi: 10.1088/1751-8113/40/14/002)
Korff, C. (2006) A Q-operator for the twisted XXX model. Journal of Physics A: Mathematical and General, 39(13), pp. 3203-3219. (doi: 10.1088/0305-4470/39/13/002)
Fring, A. and Korff, C. (2006) Non-crystallographic reduction of generalized Calogero–Moser models. Journal of Physics A: Mathematical and General, 39(5), pp. 1115-1131. (doi: 10.1088/0305-4470/39/5/007)
Fring, A. and Korff, C. (2005) Affine Toda field theories related to Coxeter groups of noncrystallographic type. Nuclear Physics B, 729(3), pp. 361-386. (doi: 10.1016/j.nuclphysb.2005.08.044)
Korff, C. (2005) A Q-operator identity for the correlation functions of the infinite XXZ spin-chain. Journal of Physics A: Mathematical and General, 38(30), pp. 6641-6657. (doi: 10.1088/0305-4470/38/30/002)
Korff, C. (2005) Auxiliary matrices on both sides of the equator. Journal of Physics A: Mathematical and General, 38(1), pp. 47-67. (doi: 10.1088/0305-4470/38/1/003)
Fring, A. and Korff, C. (2004) Exactly solvable potentials of Calogero type for q-deformed Coxeter groups. Journal of Physics A: Mathematical and General, 37(45), pp. 10931-10949. (doi: 10.1088/0305-4470/37/45/012)
Korff, C. (2004) Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz. Journal of Physics A: Mathematical and General, 37(29), pp. 7227-7253. (doi: 10.1088/0305-4470/37/29/005)
Korff, C. (2004) The twisted XXZ chain at roots of unity revisited. Journal of Physics A: Mathematical and General, 37(5), pp. 1681-1689. (doi: 10.1088/0305-4470/37/5/014)
Korff, C. (2004) Auxiliary matrices for the six-vertex model at qN = 1: II. Bethe roots, complete strings and the Drinfeld polynomial. Journal of Physics A: Mathematical and General, 37(2), pp. 385-406. (doi: 10.1088/0305-4470/37/2/009)
Korff, C. (2003) Auxiliary matrices for the six-vertex model at qN = 1 and a geometric interpretation of its symmetries. Journal of Physics A: Mathematical and General, 36(19), pp. 5229-5266. (doi: 10.1088/0305-4470/36/19/305)
Korff, C. and Seaton, K.A. (2002) Universal amplitude ratios and Coxeter geometry in the dilute AL model. Nuclear Physics B, 636(3), pp. 435-464. (doi: 10.1016/S0550-3213(02)00438-8)
Korff, C. and Roditi, I. (2002) Quantum superalgebras at roots of unity and non-Abelian symmetries of integrable models. Journal of Physics A: Mathematical and General, 35(24), pp. 5115-5137. (doi: 10.1088/0305-4470/35/24/310)
Korff, C. and McCoy, B.M. (2001) Loop symmetry of integrable vertex models at roots of unity. Nuclear Physics B, 618(3), pp. 551-569. (doi: 10.1016/S0550-3213(01)00417-5)
Korff, C. (2001) Colours associated to nonsimply-laced Lie algebras and exact S-matrices. Physics Letters B, 501(3-4), pp. 289-296. (doi: 10.1016/S0370-2693(01)00164-2)
Castro-Alveredo, O., Fring, A. and Korff, C. (2000) Form factors of the homogeneous Sine-Gordon models. Physics Letters B, 484, pp. 167-176. (doi: 10.1016/S0370-2693(00)00565-7)
Korff, C. , Castro-Alveredo, O., Fring, A. and Miramontes, J. (2000) Thermodynamic Bethe Ansatz of the homogeneous sine-gordon models. Nuclear Physics B, 575(3), pp. 535-560. (doi: 10.1016/S0550-3213(00)00162-0)
Fring, A., Korff, C. and Schulz, B. (2000) On the universal representation of the scattering matrix of affine Toda field theory. Nuclear Physics B, 567(3), pp. 409-453. (doi: 10.1016/S0550-3213(99)00578-7)
Fring, A. and Korff, C. (2000) Colour valued scattering matrices. Physics Letters B, 477, pp. 380-386. (doi: 10.1016/S0370-2693(00)00226-4)
Fring, A. and Korff, C. (2000) Large and small density approximations to the thermodynamic Bethe Ansatz. Nuclear Physics B, 579, pp. 617-631. (doi: 10.1016/S0550-3213(00)00250-9)
Fring, A., Korff, C. and Schulz, B. (1999) The ultraviolet behaviour of integrable quantum field theories, affine Toda field theory. Nuclear Physics B, 549(3), pp. 579-612. (doi: 10.1016/S0550-3213(99)00216-3)
Korff, C. , Lang, G. and Schrader, R. (1999) Two-particle scattering theory for anyons. Journal of Mathematical Physics, 40, pp. 1831-1869.
Book Sections
Korff, C. (2005) Solving Baxter's TQ equation via representation theory. In: Fuchs, J. (ed.) Noncommutative Geometry and Representation Theory in Mathematical Physics: Satellite Conference to the Fourth European Congress of Non-commutative Geometry and Representation Theory in Mathematical Physics, Karlstad, Sweden, July 5-10, 2004. Series: Contemporary Mathematics (391). American Mathematical Society: Providence, USA, pp. 199-211. ISBN 9780821837184
Edited Books
Korff, C. (Ed.) (2025) Encyclopedia of Mathematical Physics, 2nd edition, Volume 3: Integrable Systems. Elsevier. ISBN 9780323957069
Conference or Workshop Item
Korff, C. (2007) PT-invariance and representations of the Temperley-Lieb algebra on the unit circle. Recent Advances in Quantum Integrable Systems, Annecy-le-Vieux, France, 11-14 Sept 2007.
Conference Proceedings
Korff, C. (2006) Representation theory and Baxter's TQ equation for the six-vertex model. A pedagogical overview. In: Solvable Lattice Models 2004 - Recent Progress on Solvable Lattice Models, Kyoto, Japan, 20-23 July 2004, pp. 79-93.
Grants
-
Integrable models and deformations of vertex algebras via symmetric functions (PI); EPSRC standard research grant (May 2022- April 2026) GBP 278,228
-
ICMS conference grant and research support grants from the Glasgow Mathematical Journal Trust and the Edinburgh Mathematical Society (2018) Integrability, Special Functions and Combinatorics, funding for an international conference to be held on the Isle of Skye, June 2019 (joint with Misha Feigin, Glasgow) GBP 25,000
-
Royal Society Theo-Murphy Meeting (2018) competitive international scientific meeting scheme funded by the Royal Society of London and held at the Society’s International Research Centre (joint with V. Gorbounov, Aberdeen).
- Quantum integrable systems and infinite dimensional algebras (PI); Royal Society University Research Fellowship (extension 2009-2012) GBP 338,708
- Tropical geometry and integrable systems (PI); EPSRC Mathematical Sciences Small Grant with Chris Athorne (Glasgow, 2011) GBP 22,910
- Discrete integrable systems and the crystal limit of quantum integrable models (Co-I); British Council Cooperation Research Award with the U of Tokyo joint with the ISMP group (Glasgow 2008-11) GBP 37,346
- Geometric Aspects of Discrete and Ultra-discrete Integrable Systems (Co-I); London Mathematical Society grant joint with Jon Nimmo and Claire Gilson (Glasgow, 2009) GBP 4,800
- q-deformed algebras symmetric functions and quantum integrable systems (PI); The Nuffield Foundation, funding for summer project with R Fornear (Glasgow 2008) GBP 1,400
- INSTANS Short Visit Grant (PI); European Science Foundation travel grant to visit J.-S. Caux at U of Amsterdam (Amsterdam, 2008) EUR 706
- Integrable Systems: Linear and Nonlinear Dynamics III (Co-I); EPSRC Mathematical Sciences Small Grant with Ian Strachan (Glasgow, 2007) GBP 10,623
- Lectures on the chiral Potts model by Prof Rinat Kedem (PI); Edinburgh Mathematical Society research grant joint with Robert Weston, Heriot-Watt (Glasgow, 2007) GBP 633
- New developments in correlation functions of integrable lattice models (PI); EPSRC Mathematical Sciences Small Grant (City U, 2005) GBP 5,233
- Quantum integrable systems and infinite dimensional algebras (PI); Royal Society University Research Fellowship (2004-2009) GBP 250,000 (non FEC)
- Affine algebras in integrable models of statistical mechanics and QFT (PI); EPSRC Postdoctoral Fellowship in Mathematics (Edinburgh U, 2002-4) GBP 75,462 (non FEC)
Supervision
Please contact me if you are interested in doing a PhD in mathematical physics, representation theory and related combinatorics.
Applications should be made by mid December each year with funding decisions being made in February. Late applications will be considered if funds are still available: Online application form for prostgraduate students
Once you have submitted your application form send me an e-mail and we can discuss possible projects based on your qualifications and interests.
Potential PhD projects can be found on my personal website.
https://sites.google.com/view/christiankorff/home
Current research students
- Seago, Willoughby
Algebraic and combinatorial structures of integrable models - Vasilev, Mikhail
Quantum-Classical Duality in Integrable Systems - Vrabec, Martin
Relativistic integrable systems and related structures
Past PhD students
- David Palazzo (2014-2019)
- Bart Vlaar (2007-2011)
- Damian Wierzbicki (2020-23; joint supervision with Sira Gratz)
Master students
- Anna Clancy (MSc (R) 2021-24)
- Jamie Payton (MSc 2021-22)
- Jamie Mason (MSc 2019-20)
- Mary Clark (2012-2015)
Teaching
Project supervision
4H projects
I offer projects on algebraic combinatorics. The mathematics involved is similar to what you might have seen in courses such as 2T Discrete Mathematics in second year and Algebra in 3rd year. More specifically,
- the representations of the symmetric group
- symmetric functions and their applications
- the Robinson-Schensted-Knuth correspondence and plane partitions
5H projects
I offer projects at the intersection of algebra (representation theory), enumerative combinatorics and mathematical physics. Examples include:
- the representations of the Hecke and Temperley-Lieb algebras
- the Boson-Fermion correspondence
- two-dimensional quantum field theory
Additional information
- REF2021 Co-Coordinator for the School of Mathematics and Statistics joint with Prof. Marian Scott OBE (Statistics).
- Chair of the Theoretical and Mathematical Physics Goup, Institute of Physics (2010-13)
- Grant reviewer for EPSRC, British Council, Dutch Research Council (NWO), German Research Foundation (DFG)
