Professor Derek Holt
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Derek HoltEmeritus Professor of Mathematics Office: B1.25 |
Teaching Responsibilities 2023/24:
Term 2: MA442: Group Theory
Research Interests:
Group theory, computational algebra
Selected recent publications:
Derek Holt, with B.Eick and E.A. O'Brien. Handbook of Computational Group Theory, CRC Press 2005.
D. Holt and S. Rees. Artin groups of large type are shortlex automatic with regular geodesics, Proc. London Math. Soc. 104 (2012), 486--12.
D. Holt and C. Roney-Dougal. Minimal and random generation of permutation and matrix groups. J. Algebra 387 (2013), 195-214.
J. Cannon and D. Holt. Computing projective indecomposable modules and higher cohomology groups, Experiment. Math. 22 (2013), 51-59.
H. Bäärnhielm, D. Holt, C. Leedham-Green and E. O'Brien. A practical model for computation with matrix groups, J. Symbolic Computation 68 (2015), 27-60.
D. Holt and S. Rees. Shortlex automaticity and geodesic regularity in Artin groups, Groups Complex. Cryptol. 05 (2013), 1--3.
L. Ciobanu, D. Holt and S. Rees. Sofic groups: graph products and graphs of groups, Pacific J. Math. 271, no 1 (2014), 53-64
M. Brittenham, S. Hermiller and D. Holt. Algorithms and topology of Cayley graphs for groups, J. Algebra 415, no 1 (2014), 112-136.
John Bray, Derek Holt and Colva Roney-Dougal. The Maximal Subgroups of the Low-Dimensional Classical Groups, London Mathematical Society Lecture Notes 407, CUP, 2013.
D. Holt and S. Rees. Conjugacy in Artin groups of extra-large type, J. Algebra 434 (2015), 12-26.
L. Ciobanu, D. Holt and S. Rees. Rapid decay and Baum-Connes for large type Artin groups, Trans. Amer. Math. Soc. 368 (2016), 6103-6129
L. Ciobanu, S. Hermiller, D. Holt and S. Rees. Conjugacy languages in groups, Israel J. Math. 211 (2016), 311-348.
Derek Holt, Sarah Rees and Claas R\"over. Groups, Languages and Automata, London Mathematical Society Student Texts 88, CUP, 2017.
P. Dehornoy, D. Holt and S. Rees. Multifraction reduction IV: padding and Artin–Tits monoids of sufficiently large type, J. Pure Appl. Algebra 222 (2018), 4082-4098.
L. Ciobanu, D. Holt and S. Rees. The generalised word problem in hyperbolic and relatively hyperbolic groups, J. Algebra 516 (2018) 149-171.
J. Cannon, D. Holt and W. Unger. The use of permutation representations in structural computations in large finite matrix groups, J. Symbolic Computation 95 (2019), 26-38.
L. Ciobanu, D. Holt and S. Rees. Equations in groups that are virtually direct products, J. Algebra 545 (2020), 88-99.
D. Holt, C. Leedham-Green and E. O'Brien. Constructing composition factors for a linear group in polynomial time, J. Algebra 561, (2020), 215-236.
D. Holt, S.n Linton, M. Neunh\"offer, R. Parker, M. Pfeiffer and C. Roney-Dougal. Polynomial-time proofs that groups are hyperbolic, J. Symbolic Computation 104 (2021), 419-475.
S. Hermiller, D. Holt, S. Rees and T. Susse. Automaticity for graphs of groups, Groups, Geometry, and Dynamics} 15, No. 2 (2021), 503-551.
D. Holt and S. Rees. Biautomatic structures in systolic Artin groups, Internat. J. Algebra Comput. 31, No. 3 (2021), 365-391.
D. Holt, G. Royle and G. Tracey. The transitive groups of degree 48 and some applications, J. Algebra 607, Part A (2022), 372-386.
D. Holt and S. Rees. The compressed word problem in relatively hyperbolic groups, J. Algebra 607, Part B (2022), 305-343.
Research grants:
LMS, Visit of Prof S Hermiller (May 2006)
LMS, Visit of Prof E A O'Brien (July 2007)
LMS, Visit of Prof E A O'Brien (September 2011)
For more information and further publications see Derek Holt's homepage