Sarah Rees

Professor Emerita,
School of Mathematics, Statistics and Physics,
University of Newcastle
Newcastle NE1 7RU
UK

Email: Sarah(DOT)Rees@newcastle(DOT)ac(DOT)uk

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My retirement from the University of Newcastle

I have retired from the University of Newcastle, and continue as an professor emerita.

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Research Interests

I work mainly on geometrical, combinatorial and computational aspects of group theory. In particular I am currently interested in
• decision problems,
• links between group theory and formal language theory,
• the theory of automatic groups and group combings,
• the language theoretical complexity of the word problem,
• the theoretical and practical development of algorithms in group theory.

My book

My book, Groups Languages and Automata, authors Derek F. Holt, Sarah Rees, Claas E. Röver, was published by CUP in February 2017, as volume 88 of the London Mathematical Society student texts series. We three authors are maintaining a list of errors and misprints in our book as we discover them; so please let one of us know (e.g. by e-mail) if you find any problems that are not in that list.

Electronic copies of articles from 1998 onwards

• Rachael Boyd, Ruth Charney, Sarah Rees and Rose Morris-Wright, The Artin monoid Cayley graph, to appear in Journal of Combinatorial Algebra.
• Derek Holt and Sarah Rees, The compressed conjugacy problem in relatively hyperbolic groups, submitted for publication.
• Andrew Duncan, Alex Evetts, Derek F. Holt and Sarah Rees, Using EDT0L systems to solve some equations in the solvable Baumslag-Solitar groups, to appear in J. Algebra.
• Sarah Rees, The development of the theory of automatic groups, in `In the tradition of Thurston II', K. Oshika and A. Papadopoulos (editors), 449--473, Springer 2022.
• Barbara Baumeister, Derek Holt, George Neaime and Sarah Rees, Proving isomomorphism and non-isomomorphism for interval groups of type Dn, to appear in J. Alg.
• Barbara Baumeister, Derek Holt, George Neaime and Sarah Rees, Interval groups related to finite Coxeter groups, part II, to appear in Transactions of the LMS.
• Barbara Baumeister, George Neaime and Sarah Rees, Interval groups related to finite Coxeter groups I, Algebraic Combinatorics 6 (2023) 471--506
• Derek Holt and Sarah Rees, The compressed word problem in relatively hyperbolic groups, Journal of Algebra 607 (2022), Part B,305--343.
• Susan Hermiller, Derek Holt, Sarah Rees and Tim Susse, Automaticity for graphs of groups, Geometry, Groups and Dynamics 15 (2021) 503--551.
• Derek Holt, and Sarah Rees, Biautomatic structures in systolic Artin groups, Int. J. Algebra and Computation Int. J. Algebra and Computation 31 (2021) 365--391
• Laura Ciobanu, Derek Holt, and Sarah Rees, Equations in groups that are virtually direct products, J. Algebra 516 (2018) 149--171.
• Patrick Dehornoy, Derek F. Holt and Sarah Rees, Multifraction reduction IV: Padding and Artin-Tits monoids of sufficiently large type , J. Pure and Applied Algebra 222 (2018) 4082--4098.
• Laura Ciobanu, Derek Holt, and Sarah Rees, The generalised word problem in hyperbolic and relatively hyperbolic groups, J. Algebra 516 (2018) 149--171.
• Gabriele Nebe, Richard Parker and Sarah Rees, A method for building permutation representations of finitely presented groups, in Proceedings of Finite Simple Groups: Thirty Years of the Atlas and Beyond, Princeton 2015.
• Derek F. Holt and Sarah Rees, Some closure results for C-approximable groups, Pac. J. Math. 287-2 (2017) 393--409.
• Eddy Godelle and Sarah Rees, Rewriting systems in sufficiently large Artin-Tits groups, J. Alg. 466 (2016) 284--307.
• Laura Ciobanu, Derek Holt and Sarah Rees, Rapid decay and Baum-Connes for large type Artin groups, TAMS 368 (2016) 6103--6129.
• My review of the film The Imitation Game, which appeared in the Newsletter of the Association for Women in Mathematics (AWM), March-April 2015, 17--19.
• Laura Ciobanu, Susan Hermiller, Derek Holt, and Sarah Rees, Conjugacy languages in groups, Israel J. Math. 211 (2015) 311--347.
• Derek F. Holt and Sarah Rees, Conjugacy in Artin groups of extra-large type, J. Alg. 434 (2015) 12--26.
• Laura Ciobanu, Derek Holt and Sarah Rees, Sofic groups: graph products and graphs of groups, Pac. J. Math. 271 (2014) 53--64.
• Mark Lawson, Liam O'Carroll and Sarah Rees, David Rees 1918-2013, Semigroup Forum 88 (2014) 513-522.
• Derek F. Holt and Sarah Rees, Shortlex automaticity and geodesic regularity in Artin groups, Groups, Complexity and Cryptology 5 (2013) 1--23.
• Laura Ciobanu, Derek F. Holt and Sarah Rees, Rapid Decay is Preserved by Graph Products, Journal of Topology and Analysis 5 (2013) 225--237.
• Derek F. Holt and Sarah Rees, Generalising some results about right-angled Artin groups to graph products of groups, Journal of Algebra 371 (2012) 94--104.
• Derek F. Holt and Sarah Rees, Artin groups of large type are shortlex automatic with regular geodesics, Proc. London Math. Soc 104 (2012) 486--512.
• Derek F. Holt, Sarah Rees, Claas E. Röver, Groups with Context-Free Conjugacy Problems, Int. J. Alg. Comput. 21 (2011) 193-216.
• Derek F. Holt, Sarah Rees and Michael Shapiro, Groups that do and do not have growing context-sensitive word problem, Int. J. Alg. Comput. 18 (2008) 1179-1191.
• Susan Hermiller, Derek Holt and Sarah Rees, Groups whose geodesics are locally testable, Int. J. Alg. Comput. 18 (2008) 911-923.
• Robert H. Gilman, Susan Hermiller, Derek F. Holt and Sarah Rees, A characterisation of virtually free groups, Archiv der Math. 89 (2007) 289--295
• Sarah Rees, The automata that define representations of monomial algebras, Algebras and Representation Theory 11 (2008) 207--214.
• Oliver Payne and Sarah Rees, Computing subgroup presentations using the coherence arguments of McCammond and Wise, J. Alg. 300 (2006) 109--133 (Leedham-Green birthday volume).
• Susan Hermiller, Derek Holt and Sarah Rees, Star-free geodesic languages for groups, Int. J. Alg. Comp. 17 (2007) 329--345.
• Michael Batty, Sam Braunstein, Andrew Duncan and Sarah Rees, Quantum algorithms in group theory, Computational and experimental group theory, 1--62, Contemp. Math., 349, Amer. Math. Soc., Providence, RI, 2004
• Derek F. Holt, Sarah E. Rees, Claas E Röver, and Richard M. Thomas, Groups with context-free co-word problem, Journal of the London Mathematical Society 71 (2005) 643-- 657.
• Sarah Rees, How hard is the word problem?, in Proceedings of Conference for European Women in Mathematics, Varna, Bulgaria, September 2002.
• Derek F. Holt and Sarah Rees, Regularity of quasigeodesics in a hyperbolic group,, Internat. J. Alg. Comp. 13 (2003) 585--596.
• Derek F. Holt and Sarah Rees, Solving the word problem in real time, J. London Math. Soc. 63 (2001), 623--639.
• George Havas, Derek F. Holt, P.E.Kenne and Sarah Rees, Some challenging group presentations, J. Austral. Math. Soc. 67 (1999) 137--163.
• Sarah Rees and Leonard H. Soicher, An algorithmic approach to fundamental groups and covers of combinatorial cell complexes, Symb. J. Comput. 29 (2000) 59--77.
• Robert H. Gilman, Derek F. Holt and Sarah Rees, Combing nilpotent and polycyclic groups, Inter. J. Alg. Comput. 9 (1999) 135--155.
• Derek F. Holt and Sarah Rees, Computing with abelian sections of finitely presented groups, J. Algebra 214 (1999) 714--728.
• Sarah Rees, Hairdressing in groups: a survey of combings and formal languages, Geometry and Topology Monographs 1 (1998), The Epstein Birthday Schrift, paper no. 24, pages 493-509.
• Sarah Rees, A language theoretic analysis of combings, Contemp. Math. 250, 117--136
• Sarah Rees, Automatic groups associated with word orders other than shortlex, Inter. J. Alg. Comput. 8 (1998), 575--598.

Computer packages

• quotpic, an interactive graphics package to compute and display quotients of a finitely present group, and testisom, which attempts to test for isomorphism between two finitely presented groups, both developed jointly with Derek Holt, and available from the Warwick mathematics ftp-archive. as a joint package isom_quotpic.
• automata, a suite of programs, developed with David Epstein and Derek Holt, to constructively verify that a finitely presented group is shortlex automatic. Now superceded by Derek Holt's kbmag package, which is available from the Warwick mathematics ftp-archive. and contains my own code to test for automaticity with respect to other word orders than shortlex.
• matrix group algorithms developed jointly with Derek Holt, Charles Leedham-Green and Eamonn O'Brien, and now part of the matrix package within the GAP system
• I have contributed to the magnus system, developed by the New York Group Theory Cooperative, led by Gilbert Baumslag.

Useful links

(these are generally for my personal use)

within Newcastle:-

• Authenticated password access to Newcastle University facilities.
• My link to Newcastle University library. The search facility in on this page, and from that I have password access to MathSciNet, JCR, and journals to which Newcastle has electronic access.
• Newcastle's page about videoconferencing
• School wiki, which also has access only by password.
• Secure entry to the the outlook e-mail service in Newcastle.
• List of upcoming Geometry and Algebra Seminars at Newcastle

and outside Newcastle:-

• the North British Geometric Group Theory Seminar .
• the archive on Mactutor of the British Mathematical colloquium
• the EPSRC's useful list of its grants on the web
• the arXiv