Alan J. Cain

Institutional Address:

Centro de Álgebra da Universidade de Lisboa
Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal

Tel: || Fax: || E-mail: -
Web: www-groups.mcs.st-and.ac.uk/~alanc/

Qualifications:

• M.Sci Mathematics (1st class honours), University of Glasgow, 2002.
• Ph.D. Mathematics, University of St Andrews, U.K., 2005.

Current Position, starting date:

Principal Area:

Automata & semigroups, combinatorial semigroup theory, decidability

Other Areas of Interest:

Publications

1. Cain, Alan J.
   Presentations for Subsemigroups of Groups
   University of St Andrews, 2005
   (Thesis)
   
   
2. Cain, Alan J.; Robertson, Edmund F.; Ruškuc, Nik
   Subsemigroups of virtually free groups: finite Malcev presentations and testing for freeness
   Mathematical Proceedings of the Cambridge Philosophical Society, 141 (2006), 57-66
   (Paper in International Scientific Journal with refereeing)
   
   
3. Cain, Alan J.; Roberston, Edmund F.; Ruškuc, Nik
   Subsemigroups of groups: presentations, Malcev presentations, and automatic structures
   Journal of Group Theory, 9 (2006), 397-426
   (Paper in International Scientific Journal with refereeing)
   
   
4. Cain, Alan J.
   A group-embeddable non-automatic semigroup whose universal group is automatic
   Glasgow Mathematical Journal, 48 (2006), 337-342
   (Paper in International Scientific Journal with refereeing)
   
   
5. Cain, Alan J.
   Cancellativity is undecidable for automatic semigroups
   Quarterly Journal of Mathematics, 57 (2006), 285-295
   (Paper in International Scientific Journal with refereeing)
   
   
6. Cain, Alan J.
   Malcev presentations for subsemigroups of groups — a survey
   Groups St Andrews 2005, 1 (2006), 256-268
   (Communication in Conference Proceedings with refereeing)
   
   
7. Cain, Alan J.
   Cancellative and Malcev presentations for finite Rees index subsemigroups and extensions
   Journal of the Australian Mathematical Society, 84 (2008), 39-61
   (Paper in International Scientific Journal with refereeing)
   
   
8. Cain, Alan J.; Oliver, Graham P.; Ruškuc, Nik; Thomas, Richard M.
   Automatic presentations for cancellative semigroups
   Language and Automata Theory and Applications: Second International Conference, Tarragona, Spain, March 13–19, 2008, (2008), 149-159
   (Communication in Conference Proceedings with refereeing)
   
   
9. Cain, Alan J.
   Malcev presentations for subsemigroups of direct products of coherent groups
   To appear in Journal of Pure and Applied Algebra
   (Paper in International Scientific Journal with refereeing)
   
   
10. Cain, Alan J.
    On monoids presented by rewriting systems and automatic structures for their submonoids
    Submitted
    (Paper in International Scientific Journal with refereeing)
    
    
11. Cain, Alan J.
    Automatic structures and Malcev presentations for subsemigroups of Baumslag–Solitar semigroups
    Submitted
    (Paper in International Scientific Journal with refereeing)
    
    
12. Cain, Alan J.; Maltcev, Victor
    Decision problems for finitely presented and one-relation semigroups and monoids
    Submitted
    (Paper in International Scientific Journal with refereeing)
    
    
13. Cain, Alan J.
    Automatic semigroups and Bruck–Reilly extensions
    Submitted
    (Paper in International Scientific Journal with refereeing)
    
    
14. Cain, Alan J.; Oliver, Graham P.; Ruškuc, Nik; Thomas, Richard M.
    Automatic presentations for semigroups
    Submitted
    (Paper in International Scientific Journal with refereeing)
    
    
15. Cain, Alan J.
    Automaton semigroups
    Submitted
    (Paper in International Scientific Journal with refereeing)
    
    
16. Cain, Alan J.; Oliver, Graham P.; Ruškuc, Nik; Thomas, Richard M.
    Automatic presentations and semigroup constructions
    Submitted
    (Paper in International Scientific Journal with refereeing)
    
    

Talks given

1. Certain properties of subsemigroups of free groups
   University of St Andrews, U.K., 13/08/2003
   
   
2. Automatic semigroups & Malcev presentations
   Friday Group, University of St Andrews, U.K., 26/03/2004
   
   
3. Malcev presentations
   University of St Andrews, U.K., 17/06/2004
   
   
4. Malcev presentations
   Postgraduate Pure Mathematics in the North East 2004, University of Newcastle, U.K., 28/06/2004
   
   
5. A survey of Malcev presentations for subsemigroups of groups
   Groups St Andrews 2005, University of St Andrews, U.K., 31/07/2005
   
   
6. Decidability and undecidability for automatic semigroups
   University of Edinburgh & Heriot–Watt University (Joint seminar), U.K., 15/11/2005
   
   
7. An introduction to decidability for automatic semigroups
   University of St Andrews, U.K., 28/11/2005
   
   
8. Cancellative and Malcev presentations for subsemigroups and extensions
   Semigroup Day ’06, Heriot–Watt University, U.K., 05/07/2006
   
   
9. Automatic presentations for cancellative semigroups
   2nd International Conference on Language and Automata Theory and Applications, Universitat Rovira i Virgili, Tarragona, Spain, 18/03/2008
   
   
10. Automatic presentations for semigroups
    British Mathematical Colloquium, University of York, 27/03/2008
    
    
11. Automaton semigroups
    University of St Andrews, U.K., 29/05/2008
    
    
12. Decidability for automatic semigroups
    International Workshop on Computational and Algorithmic Aspects of Semigroup Theory, University of St Andrews, U.K., 06/09/2008
    
    
13. Automatic Semigroups
    Courses, CAUL, 10/2008
    
    
14. Malcev presentations for subsemigroups of groups
    Algebra and Combinatorics Seminars, CAUL, 31/10/2008
    
    

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CAUL database last updated: 6-12-2009