Dr Christian Korff

  • Reader (Mathematics)

telephone: 01413306198
email: Christian.Korff@glasgow.ac.uk

R441 - Level 4
Mathematics
The Mathematics and Statistics Building
Glasgow G12 8SQ

Research interests

Personal website

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 lower dimensional quantum field theories.

Research Groups


Publications

All publications | View selected publications

List all by: Type | Date

Jump to: 2017 | 2016 | 2014 | 2013 | 2011 | 2010 | 2009 | 2008 | 2007 | 2006 | 2005 | 2004 | 2003 | 2002 | 2001 | 2000 | 1999
Number of items: 39.

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. 29th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2017), London, UK, 9-13 July 2017. (Accepted for Publication)

2016

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)

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

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)

2011

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.

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)

Korff, C., Okado, M., Schief, W.K. and Tokihiro, T. (Eds.) (2010) Proceedings of the Workshop "Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems" (March 30 − April 3, 2009, University of Glasgow, UK). Series: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). Institute of Mathematics of National Academy of Sciences of Ukraine.

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)

2003

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)

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.

This list was generated on Sun Aug 20 15:09:41 2017 BST.
Number of items: 39.

Articles

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. (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., Okado, M., Schief, W.K. and Tokihiro, T. (Eds.) (2010) Proceedings of the Workshop "Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems" (March 30 − April 3, 2009, University of Glasgow, UK). Series: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA). Institute of Mathematics of National Academy of Sciences of Ukraine.

Conference or Workshop Item

Korff, C. (2017) Dimers, Crystals and Quantum Kostka Numbers. 29th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2017), London, UK, 9-13 July 2017. (Accepted for Publication)

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.

This list was generated on Sun Aug 20 15:09:41 2017 BST.

Grants

 


Supervision

Current PhD students

David Palazzo (Quantum integrable systems)
Lucia Rotheray

Postgraduate opportunities

Integrable quantum field theory and Y-systems
Quantum spin-chains, exactly solvable lattice models and representation theory

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. The online application form for prostgraduate students can be found here.

Once you have submitted your application form send me an e-mail and we can discuss possible projects based on your qualifications and interests.

Past PhD students

Bart Vlaar (2007-2011)

 


Teaching

Possible 4H projects

  • "The Robinson-Schensted-Knuth correspondence"
  • "Ice and Alternating Sign Matrices"
  • "Representations of the symmetric group"

Possible 5H projects

  • "The Boson-Fermion correspondence"
  • "Knutson-Tao puzzles"
  • "Crystal Graphs"

Additional information

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.