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 a five year FCT Ciência 2008 research fellowship.

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.

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. 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. N. Ruškuc Examiners: Dr M. Quick (Internal) & Prof. D.F. Holt (External) My thesis was accepted with no corrections being required. I won a Carnegie Doctoral Scholarship to fund my Ph.D. studies.

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]
Mathematical Proceedings of the Cambridge Philosophical Society 141 (2006), no. 1, pp. 57–66.

‘Subsemigroups of groups: presentations, Malcev presentations, and automatic structures’

[with E. F. Robertson & N. Ruškuc]
Journal of Group Theory 9 (2006), no. 3, pp. 397–426.

‘A group-embeddable non-automatic semigroup whose universal group is automatic’

Glasgow Mathematical Journal 48 (2006), no. 2, pp. 337–342.

‘Cancellativity is undecidable for automatic semigroups’

Quarterly Journal of Mathematics 57 (2006), no. 3, pp. 285–295.

‘Malcev presentations for subsemigroups of groups — a survey’

in C. M. Campbell, M. Quick, E. F. Robertson & G. C. Smith, editors, Groups St Andrews 2005 (Vol. 1), no. 339 in London Mathematical Society Lecture Note Series, Cambridge University Press, 2007, pp. 256–268.

‘Cancellative and Malcev presentations for finite Rees index subsemigroups and extensions’

[with E. F. Robertson & N. Ruškuc]
Journal of the Australian Mathematical Society 84 (2008), no. 1, pp. 39–61.

‘Automatic presentations for cancellative semigroups’

[with G. Oliver, N. Ruškuc & R. M. Thomas]
in C. Martín-Vide, H. Fernau & F. Otto, editors, Language and Automata Theory and Applications: Second International Conference, Tarragona, Spain, March 13–19, 2008, no. 5196 in Lecture Notes in Computer Science, Springer, 2008, pp. 149–159.

‘Malcev presentations for subsemigroups of direct products of coherent groups’

Journal of Pure and Applied Algebra 213 (2009), no. 6, pp. 977–990.

‘Automaton semigroups’

Theoretical Computer Science 410 (2009), no. 47–49, pp. 5022–5038.

‘Automatic presentations for semigroups’

[with G. Oliver, N. Ruškuc & R. M. Thomas]
Information and Computation 207 (2009), no. 11, pp. 1156–1168.

‘Decision problems for finitely presented and one-relation semigroups and monoids’

[with V. Maltcev]
International Journal of Algebra and Computation 19 (2009), no. 6, pp. 747–770.

‘Monoids presented by rewriting systems and automatic structures for their submonoids’

International Journal of Algebra and Computation 19 (2009), no. 6, pp. 771–790.

‘Automatic semigroups and Bruck–Reilly extensions’

Acta Mathematica Hungarica 126 (2010), no. 1–2, pp. 1–15.

‘Automatic presentations and semigroup constructions’

[with G. Oliver, N. Ruškuc & R. M. Thomas]
Theory of Computing Systems 47 (2010), no. 2, pp. 568–592.

‘Deus ex machina and the aesthetics of proof’

Mathematical Intelligencer 32 (2010), no. 3, pp. 7–11.

‘Unary FA-presentable semigroups’

[with N. Ruškuc & R. M. Thomas]
International Journal of Algebra and Computation, 2012. Forthcoming.

‘Automatic structures for subsemigroups of Baumslag–Solitar semigroups’

Submitted.

‘Green index in semigroup theory: generators, presentations, and automatic structures’

[with R. Gray & N. Ruškuc]
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.

‘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’

[with V. Maltcev]
In preparation.

‘On weak automatic presentations’

In preparation.

Selected Seminars & Conference talks

[ Full List of Talks ]

‘Malcev presentations for subsemigroups of groups’

Invited seminar: University of Glasgow, 13th October 2004.

‘Decidability and undecidability for automatic semigroups’

Invited seminar: University of Edinburgh & Heriot–Watt University (Joint), 15th November 2005.

‘Decidability for automatic semigroups’

Conference talk: International Workshop on Computational and Algorithmic Aspects of Semigroup Theory, University of St Andrews, 6th September 2006.

‘Automatic presentations for cancellative semigroups’

Conference talk: 2nd International Conference on Language and Automata Theory and Applications, Universitat Rovira i Virgili, Tarragona, Spain, 18th March 2008.

‘Automatic presentations for semigroups’

Conference talk: 2008 British Mathematical Colloquium, University of York, 27th March 2008.

‘Automaton semigroups’

Seminar: Pure Mathematics Colloquium, University of St Andrews, 29th May 2008.

‘Malcev presentations for subsemigroups of groups’

Seminar: Centro de Álgebra da Universidade de Lisboa, 31st October 2008.

‘Automaton semigroups’

Invited conference talk: North Britain Semigroups and Applications Network, University of St Andrews, 16th April 2009.

‘Computing with automatic semigroups’

Conference talk: Centro de Matemática da Universidade do Porto, 15th June 2010.

‘Automatic presentations and semigroups’

Invited seminar: Centro de Álgebra da Universidade de Lisboa, 10th September 2010.

‘Hyperbolic and word-hyperbolic semigroups’

Invited conference talk: North Britain Semigroups and Applications Network, University of St Andrews, 19th May 2011.