Alan James Cain  ·  Curriculum Vitæ (Short) Download as PDF ]
AddressCentro de Matemática e Aplicações
Faculdade de Ciência e Tecnologia
Universidade Nova de Lisboa
2829–516 Caparica
Portugal
Email addressDOT cain AT fct DOT unl DOT pt
Replace ‘AT’ with ‘@’ and ‘DOT’ with ‘.’
Web pagehttp://www-groups.st-and.ac.uk/~alanc
LanguagesEnglish (Native)
Japanese (Intermediate)
Portuguese (Basic)
French (Basic)
ORCiD0000-0002-0706-1354
ResearcherIDG-7986-2014
Scopus ID13608823100

Positions held

2014/01–
Present
‘Investigador FCT’ Senior Research Fellow
Centro de Matemática e Aplicações, Universidade Nova de Lisboa
2829–516 Caparica, Portugal
  • FCT-funded five-year personal research fellowship.
  • Awarded an associated grant of € 50000.
  • Taught courses ‘Semigroups, Automata, and Languages’, ‘Algebraic Theory of Automata’, ‘Rewriting Systems’, ‘Combinatorial Group Theory’.
  • Supervised two Ph.D. students (one unofficially, one officially) and one master’s student.
2009/07–
2014/01
‘Ciência 2008’ Research Fellow
Centro de Matemática da Universidade do Porto
Rua do Campo Alegre 687, 4169–007 Porto, Portugal
  • FCT-funded five-year personal research fellowship.
  • Developed and taught a master’s course ‘Semigroups’.
2008/09–
2009/06
Postdoctoral researcher
Centro de Álgebra da Universidade de Lisboa
Av. Prof. Gama Pinto 2, 1649–003 Lisboa, Portugal
  • Research within the project on ‘Semigroups and Languages’, funded by FCT and PIDDAC.
2005/09–
2008/08
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).
2002/09–
2005/05
Tutor & Computer laboratory demonstrator
School of Mathematics & Statistics, University of St Andrews
St Andrews, Fife KY16 9AJ, United Kingdom
  • Tutored students in using MAPLE to solve practical exercises and marked their work.

Education

2002/09–
2005/07
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 (Univ. of Warwick)

  • Thesis accepted without corrections.
1998/09–
2002/07
M.Sci. in Mathematics with First-class Honours
University of Glasgow
Glasgow G12 8QQ, United Kingdom
  • President of the Maclaurin Society, the University of Glasgow student society for mathematics and statistics.

Research funding

2002/10–
2005/09
Carnegie Doctoral Scholarship
Carnegie Trust for the Universities of Scotland
  • Tuition fees; living and travel expenses.
2009/07–
2014/01
‘Ciência 2008’ fellowship
Fundação para a Ciência e a Tecnologia (FCT) [National science agency]
  • Five-year personal fellowship.
2010/06–
2014/05
Project ‘Automata, Languages, Decidability in Algebra’
EP/H011978/1
Engineering and Physical Sciences Research Council (EPSRC)
  • Joint application with Nik Ruškuc & Martyn Quick. Value £ 348646.
2014/01–
Present
‘Investigador FCT’ fellowship
Fundação para a Ciência e a Tecnologia (FCT) [National science agency]
  • Five-year individual advanced fellowship.
2014/07–
Present
Exploratory Project (Principal investigator)
IF/01622/2013/CP1161/CT0001
Fundação para a Ciência e a Tecnologia (FCT) [National science agency]
  • Value € 50000; administrative costs waived.
2015/04‘Research in Pairs’ grant
London Mathematical Society
  • Small grant (value £ 1000) to visit the University of St Andrews to work with Dr Markus Pfeiffer and speak at a conference.
2016/06–
Present
Project ‘Hilbert’s 24th Problem’ (Subproject leader)
PTDC/MHC-FIL/2583/2014
Fundação para a Ciência e a Tecnologia (FCT) [National science agency]
  • Value € 199902.

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., 54.2 (2013), 593–608.
Markov semigroups, monoids, and groups
[with V. Maltcev] Internat. J. Algebra Comput., 24.5 (2014).
Subalgebras of FA-presentable algebras
[with N. Ruškuc] Algebra Universalis, 72.2 (2014), 101–123.
Hopfian and co-hopfian subsemigroups and extensions
[with V. Maltcev] Demonstratio Math., 47.4 (2014), 791–804.
Finite Gröbner–Shirshov bases for Plactic algebras and biautomatic structures for Plactic monoids
[with R. D. Gray & A. Malheiro] J. Algebra, 423 (2015), 37–53.
Rewriting systems and biautomatic structures for Chinese, hypoplactic, and sylvester monoids
[with R. D. Gray & A. Malheiro] Internat. J. Algebra Comput., 25.1-2 (2015).
Growths of endomorphisms of finitely generated semigroups
[with V. Maltcev] J. Aust. Math. Soc., Forthcoming.
Decision problems for word-hyperbolic semigroups
[with M. Pfeiffer] J. Algebra, 465 (2016), 287–321.
Crystallizing the hypoplactic monoid: from quasi-Kashiwara operators to the Robinson–Schensted–Knuth-type correspondence for quasi-ribbon tableaux
[with A. Malheiro] Journal of Algebraic Combinatorics, Forthcoming.
Crystal monoids & crystal bases: rewriting systems and biautomatic structures for plactic monoids of types ${A}_n$, ${B}_n$, ${C}_n$, ${D}_n$, and ${G}_2$
[with R. D. Gray & A. Malheiro] Submitted.

Selected invited 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.
‘Automaton semigroups’
Invited conference talk: NBSAN, Univ. of St Andrews, 2009/04/16.
‘Hyperbolic and word-hyperbolic semigroups’
Invited conference talk: NBSAN, Univ. of St Andrews, 2010/05/19.
‘Automatic presentations for algebraic and combinatorial structures’
Invited seminar: Centro de Matemática da Universidade de Coimbra, 2013/03/20.
‘Unary FA-presentable algebraic and combinatorial structures’
Invited conference talk: Workshop on Algebraic Structures and Semigroups, Centro de Álgebra da Universidade de Lisboa, 2013/07/05.
‘Endomorphisms of semigroups: growth and interactions with subsemigroups’
Invited conference talk: NBSAN, Univ. of York, 2013/11/20.
‘Combinatorial and computational properties of the sylvester monoid’
Invited conference talk: 6th IMM, University of Santiago de Compostela, 2016/10/06.