| Address |
Centro de Matemática
Universidade do Porto
Rua do Campo Alegre 687
4169–007 Porto
Portugal |
| Email address |
ajcain AT fc DOT up DOT pt
Replace ‘AT’ with ‘@’ and ‘DOT’ with ‘.’
|
| Web page |
www.fc.up.pt/pessoas/ajcain |
| |
|
| Date of birth |
9th March 1981 |
| Nationality |
British citizen |
| Languages |
English (Native), French (Intermediate),
Portuguese (Basic), Japanese (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.
|
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 PTDC/MAT/69514/2006
‘Semigroups and Languages’, funded by FCT
and PIDDAC.
- Gave a 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 9SS, United Kingdom |
- Worked as part of a large research team on
the epsrc-funded Critical Mass in Computational Algebra
project (EP/C523229/1).
- Lectured the honours-level course ‘Fundamentals of Pure Mathematics’; student feedback was enthusiastically supportive, with 85% overall approval.
|
Education
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
- London Mathematical Society
- Elected: 17th Nov. 2006
- Edinburgh Mathematical Society
- Elected: 14th Jan. 2003
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., 2012.
Forthcoming.
‘Green index in semigroup theory: generators, presentations, and automatic structures’
[with R. Gray & N. Ruškuc]
Semigroup Forum,
Forthcoming.
‘Automatic structures for subsemigroups of Baumslag–Solitar semigroups’
Submitted.
‘Hyperbolicity of monoids presented by confluent monadic rewriting systems’
Submitted.
‘Markov semigroups, monoids, and groups’
[with V. Maltcev]
Submitted.
‘Context-free rewriting systems and word-hyperbolic structures with uniqueness’
[with V. Maltcev]
Submitted.
‘Finitely presented monoids with linear Dehn function need not have regular cross-sections’
[with V. Maltcev]
Submitted.
‘For a few elements more: A survey of finite Rees index’
[with V. Maltcev]
In preparation.
‘Unary FA-presentable algebraic and relational structures’
[with N. Ruškuc]
In preparation.
‘Decision problems for word-hyperbolic monoids’
In preparation.
‘Notions of hyperbolicity in monoids’
In preparation.
‘On weak automatic presentations’
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.
‘Decidability for automatic semigroups’
Conference talk: Workshop on Computational Semigroup Theory, Univ. of St Andrews, 2006/09/06.
‘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.
