School of Mathematics, Statistics and Physics

Staff Profile

Dr Andrew Duncan

Reader in Algebra


Roles and Responsibilities

2 Postgraduate Students

Exams and Admissions databases

Staff Student Committee

EPSRC peer review college and mathematics prioritisation panel.


Research Interests

Google Scholar

Geometric and Combinatorial Group Theory

Low Dimensional Topology

Quantum Computation


Algebraic Geometry of Partially Commutative Groups: visit of Remeslennikov and Kazachkov - 6 weeks of June and July 2006

Quantum Computation and group theory. 2002-2005, c. 100K.

Visit of Myasnikov, May 2005, 350.

Algebraic geometry and algorithms in Artin groups. 2004, 10K.

LMS Northern Regional Meeting (PI Prof S Rees, Ncl) 2004, 10K.

Visit of Dr Vdovina, April 2004, 600.


  • Duncan AJ. Exponential Genus Problems in One-Relator Products of Groups. Memoirs of the American Mathematical Society 2007, 140.
  • Duncan AJ, Kazachkov IV, Remeslennikov VN. Centraliser dimension of partially commutative groups. Geometriae Dedicata 2006, 120(1), 73-97.
  • Batty M, Duncan A, Braunstein SL. Extending the Promise of the Deutsch-Jozsa-Høyer Algorithm for Finite Groups. London Mathematical Society: Journal of Computation and Mathematics 2006, 9, 40-63.
  • Duncan A, Gilman RH. Word hyperbolic semigroups. Mathematical Proceedings of the Cambridge Philosophical Society 2004, 136(3), 513-524.
  • A.J. Duncan, E. Robertson and N. Ruskuc. Automatic Monoids and Change of generators. Math. Proc. Camb. Phil. Soc 1999, 127(2), 403-409.
  • Batty M, Braunstein SL, Duncan AJ, Rees SE. Quantum Algorithms in Group Theory. Contemporary Mathematics 2004, 349, 1-62.
  • A.J. Duncan, N.D. Gilbert and G. Ellis. A Mayer-Vietoris sequence in group homology and the decomposition of relation modules. Glasgow Math. J 1995, 37(2), 159-171.
  • A J Duncan, J. Howie. Spelling Theorems and a Cohen-Lyndon Theorem for one-relator products of groups. J. Pure Appl. Algebra, 92 (1994) no. 2, 123-136. ISSN 0022-4049 1994.
  • Duncan,A.J.,Gilbert,N.G.,Howie J. Combinatorial and Geometric Group Theory. Papers from the Workshop on Geometric and Combinatorial Methods in Group Theory held at Heriot-Watt University, Edinburgh. Edited by A J Duncan, N D Gilbert and James Howie. 1993, Heriot-Watt University, Edinburgh: Cambridge University Press.
  • A J Duncan, J. Howie. The 3-Torus is Kervaire. In: Proceedings of the AMS Workshop on Geometric Topology, Technion, Haifa, Contemp. Math. 164 AMS 1994 1992.
  • A J Duncan, J. Howie. Weinbaum's conjecture on unique subwords of nonperiodic words. Proc. Amer. Math. Soc 1992, 115(4), 947-954.
  • P J Duncan, J. Howie. One-relator products with high powered relators. in Geometric Group Theory, Sussex, Volume 1 Proceedings of the Symposium held in Sussex, 1991, G.A.Niblo and M.A.Roller (Eds.), LMS Lecture Note Series,Cambridge University Press, 1993 1991, 181.
  • A J Duncan, J. Howie. The Genus Problem for one-relator products of locally indicable groups. Math. Z 1991, 208, 225-237.
  • A J Duncan, J. Howie. The non-orientable genus problem for one-relator products. Comm. in Alg 1991, 19, 2547-2556.
  • A J Duncan. Infinite coverings of ideals by cosets with applications to regular sequences and balanced big Cohen-Macaulay modules. Math. Proc. Camb. Phil. Soc 1990, 107, 443-460.
  • A J Duncan, L. O'Carroll. On Zariski-regularity, the vanishing of Tor and a uniform Artin-Rees theorem. In Topics in Algebra, Banach Centre Publications. (PWN Polish Scientific Publishers, Warsaw, 1990) 1990, 26(2), 49-55.
  • A J Duncan, L.O'Carroll. A full Uniform Artin-Rees Theorem. J. reine angew. Math 1989, 394, 203-207.
  • Barker N, Duncan AJ, Robertson DM. The power conjugacy problem in Higman-Thompson groups. International Journal of Algebra and Computation 2016, 26(2), 309-374.
  • Casals-Ruiz M, Duncan A, Kazachkov I. Embeddings between partially commutative groups: two counterexamples. Journal of Algebra 2013, 390, 87-99.
  • Duncan AJ, Remeslennikov VN. Automorphism of partially commutative groups II: Combinatorial subgroups. International Journal of Algebra and Computation 2012, 22(7), 1250074.
  • Diekert V, Duncan A, Myasnikov AG. Cyclic rewriting and conjugacy problems. Groups Complexity Cryptology 2012, 4(2), 321-355.
  • Duncan AJ, Remeslennikov VN. Automorphisms of Partially Commutative Groups II: Combinatorial Subgroups. 2011, 44. Submitted.
  • Batty M, Braunstein S, Duncan A. Extending The Promise of the Deutsch-Jozsa-Hoyer Algorithm for Finite Groups. Ithaca, New York, USA: Cornell University Library, 2004. Available at:
  • Batty M, Braunstein SL, Duncan AJ, Rees S. Quantum algorithms in group theory. In: Computational and Experimental Group Theory. 2004, Baltimore, Maryland, USA: American Mathematical Society.
  • Batty M, Braunstein SL, Duncan A, Rees S. Quantum algorithms in group theory. In: Interactions between Logic, Group Theory and Computer Science. 2003, Maryland, USA: American Mathematical Society.
  • Duncan AJ, Robertson EF, Ruskuc N. Automatic monoids and change of generators. Mathematical Proceedings of the Cambridge Philosophical Society 1999, 127(3), 403-409.