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The University of Southampton
Mathematical Sciences
(023) 8059 3673

Dr Jim H Renshaw BSc, PhD

Associate Professor of Pure Mathematics, Faculty Admissions Controller

Dr Jim H Renshaw's photo

Dr Jim H Renshaw is an Associate Professor within Mathematical Sciences at the University of Southampton. He is also the Faculty Admissions Controller for the Faculty of Social Sciences.


2014 - present Associate Professor in Mathematics, University of Southampton

2005 - 2014 Senior Lecturer Mathematics, University of Southampton

1987 - 2005 Lecturer Mathematics and Computing, University of Southampton

1985 -1987 Temporary Lecturer Mathematics, Heriot-Watt University, Edinburgh

1985 PhD Pure Mathematics, University of St Andrews

1982 BSc Pure Mathematics, University of St Andrews

Research interests

My research interests are in algebraic semigroup theory with a particular interest in actions of semigroups and monoids on sets. My early work focused on applications of monoid actions to the theory of semigroup amalgams and on the so-called homological classification theory of monoids. Recently, together with Mojgan Mahmoudi, I have initiated the study of flat covers of monoid acts and in particular described strongly flat and condition-(P) covers of cyclic acts.

More recently I have started to consider actions of inverse semigroups and in particular their actions on graphs and trees. The theory of group actions on graphs and trees has proved to be an especially powerful tool and as inverse semigroups are seen more and more to be important in a number of areas of mathematics it is hoped we can develop similar tools related to inverse semigroup actions.

I have also been studying, with my former research student Jehan Al-Bar, transversals of abundant semigroups and in particular of quasi-adequate semigroups. We have developed some new structure theorems based on “Rees matrix” type constructions as well as some related to spined products. A number of applications to inverse transversals have been discovered as a consequence.

Research group

Pure Mathematics

Affiliate research group

Semigroup Theory

Faculty Admissions Controller
Mathematics intranet & Cipher Challenge website

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  • Renshaw, J. (2004). Inverse semigroups acting on graphs. In I. M. Araújo, M. J. J. Branco, V. H. Fernandes, & G. M. S. Gomes (Eds.), Semigroups and Languages (pp. 212-239). World Scientific.
  • Golchin, A., & Renshaw, J. (1998). A flatness property of acts over monoids. In J. M. Howie, & N. Ruškuc (Eds.), Semigroups and Applications: Proceedings of the Conference (pp. 72-77). Singapore, SG: World Scientific.
  • Renshaw, J. (1996). Testmaker. 85-85. Paper presented at International Conference on Technology in Mathematics Teaching, .
  • Beevers, C. E., Foster, M. G., McGuire, G. R., & Renshaw, J. H. (1992). Some Problems of Mathematical CAL. In M. R. Kibby, & J. R. Hartley (Eds.), Computer Assisted Learning: Selected Contributions from the Cal91 Symposium (pp. 119-125). Oxford, UK: Pergamon Press.
  • Beevers, C. E., Agnew, A. R., Cherry, B. S. G., Clark, D. E. R., Foster, M. G., McGuire, G. R., & Renshaw, J. H. (1989). The CALM Project. 145-151. Paper presented at Proceedings of the International Conference on Mathematical Software, .
  • Beevers, C. E., Foster, M. G., McGuire, G. R., & Renshaw, J. H. (1988). Software tools for Mathematical CAL. Paper presented at 5th International Conference For Technology in Education, .
  • Beevers, C. E., Agnew, A. R., Cherry, B. S. G., Clark, D. E. R., Foster, M. G., McGuire, G. R., & Renshaw, J. H. (1988). The CALM project - Evaluation and development. 285-298. Paper presented at Conference on Mathematics and Statistics Curriculum in Higher Education for the 1990's, .
  • Beevers, C. E., Cherry, B. S. G., Clark, D. E. R., Foster, M. G., McGuire, G. R., & Renshaw, J. H. (1987). TUTTI FRUTTI - Tutorials To Improve First Year Results Using Technological Teaching Initiatives. 24-27. Paper presented at Mathematics Teaching 1987, .

Working Papers

MATH1001 Number Theory & Cryptography

MATH6095 Introduction to Semigroup Theory

Dr Jim H Renshaw
Mathematical Sciences,
University of Southampton
Highfield Campus,
Southampton, SO17 1BJ

Room Number: 54/8005

Facsimile: (023) 8059 5147

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