Alan James Cain  ·  Curriculum Vitæ (Short) [ Download as PDF ]
Address Centro de Matemática
Universidade do Porto
Rua do Campo Alegre, 687
4169–007 Porto
Portugal
Email addressajcain AT fc DOT up DOT pt
Replace ‘AT’ with ‘@’ and ‘DOT’ with ‘.’
Web pagewww.fc.up.pt/pessoas/ajcain
 
Date of birth9th March 1981
NationalityBritish citizen
LanguagesEnglish (Native)
French (Intermediate)
Japanese (Basic: JLPT N4)
Portuguese (Basic)

Positions held

Jul. 2009
–Present		Research Fellow
Centro de Matemática da Universidade do Porto
Rua do Campo Alegre 687, 4169–007 Porto, Portugal
  • This position is an FCT-funded five-year personal research fellowship, making me responsible for directing my own research in areas such as hyperbolic semigroups and automatic presentations for relational structures.
  • Lectured the master’s-level course in semigroup theory, writing the course from scratch and producing high-quality printed lecture notes.
Sep. 2008
–Jun. 2009		Research Fellow
Centro de Álgebra da Universidade de Lisboa
Av. Prof. Gama Pinto 2, 1649–003 Lisboa, Portugal
  • Research within the project ‘Semigroups and Languages’, funded by FCT and PIDDAC (PTDC/MAT/69514/2006).
Teaching:
Postgraduate-level short course on automatic groups and semigroups.
Sep. 2005
–Aug. 2008		Research Fellow
School of Mathematics & Statistics, University of St Andrews
St Andrews, Fife KY16 9AJ, United Kingdom
  • Worked as part of a large research team on the EPSRC-funded project ‘Critical Mass in Computational Algebra’ (EP/C523229/1).
  • Lectured the honours-level class ‘Fundamentals of Pure Mathematics’; student feedback was enthusiastically supportive, with 85% overall approval.
Sep. 2002
–May 2005		Tutor & Computer laboratory demonstrator
School of Mathematics & Statistics, University of St Andrews
St Andrews, Fife KY16 9AJ, United Kingdom
  • Tutored first-year undergraduates in using MAPLE to solve various problems related to pre-honours lecture courses.

Education

Sep. 2002
–Jul. 2005		Ph.D. in Mathematics
University of St Andrews
St Andrews, Fife KY16 9AJ, United Kingdom

Thesis: Presentations for Subsemigroups of Groups
Supervisors: Prof. E.F. Robertson, Prof. Nik Ruškuc.
Examiners: Dr M. Quick (Internal), Prof. D.F. Holt (External, Univ. of Warwick).

  • My thesis was accepted without corrections.
Sep. 1998
–Jul. 2002		M.Sci. in Mathematics with First-class Honours
University of Glasgow
Glasgow G12 8QQ, United Kingdom
  • Cunninghame Prize in Mathematics; Class prizes in Mathematics in first and second year; Class prize in Computer Science in second year.
  • President of the Maclaurin Society, the University of Glasgow student society for mathematics and statistics.

Membership of Professional Societies

Research funding

Oct. 2002
–Sep. 2005		Carnegie Doctoral Scholarship
  • Prestigious scheme funded by the Carnegie Trust for the Universities of Scotland.
Jul. 2009
–Present		FCT Ciência fellowship
  • Five-year individual advanced fellowship.
2009
–Present		EPSRC Project ‘Automata, Languages, Decidability in Algebra’, EP/H011978/1
  • Joint application with Nik Ruškuc & Martyn Quick. Value £350,974.

Selected Publications

[ Full List of Publications ]

‘Subsemigroups of virtually free groups: finite Malcev presentations and testing for freeness’
[with E. F. Robertson & N. Ruškuc] Math. Proc. Cambridge Philos. Soc., 141.1 (2006), 57–66.
‘Subsemigroups of groups: presentations, Malcev presentations, and automatic structures’
[with E. F. Robertson & N. Ruškuc] J. Group Theory, 9.3 (2006), 397–426.
‘A group-embeddable non-automatic semigroup whose universal group is automatic’
Glasg. Math. J., 48.2 (2006), 337–342.
‘Cancellativity is undecidable for automatic semigroups’
Q. J. Math., 57.3 (2006), 285–295.
‘Malcev presentations for subsemigroups of groups — a survey’
In C. M. Campbell et al., eds, Groups St Andrews 2005 (Vol. 1), no. 339 in LMS Lecture Notes, 256–268 (Cambridge University Press, 2007).
‘Cancellative and Malcev presentations for finite Rees index subsemigroups and extensions’
[with E. F. Robertson & N. Ruškuc] J. Aust. Math. Soc., 84.1 (2008), 39–61.
‘Automatic presentations for cancellative semigroups’
[with G. Oliver, N. Ruškuc & R. M. Thomas] In C. Martín-Vide et al., eds, LATA 2008, no. 5196 in Lecture Notes in Comp. Sci., 149–159 (Springer, 2008).
‘Malcev presentations for subsemigroups of direct products of coherent groups’
J. Pure Appl. Algebra, 213.6 (2009), 977–990.
‘Automaton semigroups’
Theoret. Comput. Sci., 410.47–49 (2009), 5022–5038.
‘Automatic presentations for semigroups’
[with G. Oliver, N. Ruškuc & R. M. Thomas] Inform. and Comput., 207.11 (2009), 1156–1168.
‘Decision problems for finitely presented and one-relation semigroups and monoids’
[with V. Maltcev] Internat. J. Algebra Comput., 19.6 (2009), 747–770.
‘Monoids presented by rewriting systems and automatic structures for their submonoids’
Internat. J. Algebra Comput., 19.6 (2009), 771–790.
‘Automatic semigroups and Bruck–Reilly extensions’
Acta Math. Hungar., 126.1–2 (2010), 1–15.
‘Automatic presentations and semigroup constructions’
[with G. Oliver, N. Ruškuc & R. M. Thomas] Theory Comput. Syst., 47.2 (2010), 568–592.
‘Deus ex machina and the aesthetics of proof’
Math. Intelligencer, 32.3 (2010), 7–11.
‘Unary FA-presentable semigroups’
[with N. Ruškuc & R. M. Thomas] Internat. J. Algebra Comput., 22.4 (2012).
‘Green index in semigroup theory: generators, presentations, and automatic structures’
[with R. Gray & N. Ruškuc] Semigroup Forum, 85.3 (2012), 448–476.
‘Context-free rewriting systems and word-hyperbolic structures with uniqueness’
[with V. Maltcev] Internat. J. Algebra Comput., 22.7 (2012).
‘Hyperbolicity of monoids presented by confluent monadic rewriting systems’
Beitr. Algebra Geom., 2013. Forthcoming.
‘Automatic structures for subsemigroups of Baumslag–Solitar semigroups’
Semigroup Forum, 2013. Forthcoming.
‘Finite Gröbner–Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids’
[with R. Gray & A. Malheiro] Submitted.
‘Markov semigroups, monoids, and groups’
[with V. Maltcev] Submitted.
‘Finitely presented monoids with linear Dehn function need not have regular cross-sections’
[with V. Maltcev] Submitted.
‘Subalgebras of FA-presentable algebras’
[with N. Ruškuc] Submitted.
‘Unary FA-presentable binary relations: transitivity and classification results’
[with N. Ruškuc] Submitted.
‘Decision problems for word-hyperbolic semigroups’
Submitted.
‘For a few elements more: A survey of finite Rees index’
[with V. Maltcev] In preparation.

Selected Seminars & Conference talks

[ Full List of Talks ]

‘Malcev presentations for subsemigroups of groups’
Invited seminar: Univ. of Glasgow, 2004/10/13.
‘Decidability and undecidability for automatic semigroups’
Invited seminar: Edinburgh & Heriot–Watt Univ. (Joint), 2005/11/15.
‘Cancellative and Malcev presentations for subsemigroups and extensions’
Conference talk: Semigroup Day ’06, Heriot–Watt Univ., 2006/07/05.
‘Automatic presentations for cancellative semigroups’
Conference talk: LATA 2008, Universitat Rovira i Virgili, 2008/03/18.
‘Automatic presentations for semigroups’
Conference talk: BMC 2008, Univ. of York, 2008/03/27.
‘Automaton semigroups’
Seminar: Pure Mathematics Colloquium, Univ. of St Andrews, 2008/05/29.
‘Malcev presentations for subsemigroups of groups’
Seminar: Centro de Álgebra da Universidade de Lisboa, 2008/10/31.
‘Automaton semigroups’
Invited conference talk: NBSAN, Univ. of St Andrews, 2009/04/16.
‘Automatic presentations and semigroups’
Invited seminar: Centro de Álgebra da Universidade de Lisboa, 2010/09/10.
‘Hyperbolic and word-hyperbolic semigroups’
Invited conference talk: NBSAN, Univ. of St Andrews, 2010/05/19.
‘Unary FA-presentable algebraic and relational structures’
Seminar: Centro de Matemática da Universidade do Porto, 2012/02/15.
‘Hyperbolicity for semigroups’
Invited seminar: Centro de Álgebra da Universidade de Lisboa, 2012/05/11.
‘Automatic presentations for algebraic and combinatorial structures’
Invited seminar: Centro de Matemática da Universidade de Coimbra, 2013/03/20.
Colophon © 1998–2013 A. J. Cain