Mike Grannell       Other Information

Career summary

I graduated in 1967 from Imperial College with a B.Sc. (Hons class I) in Mathematics, and subsequently obtained my Ph.D., also from Imperial College, in 1970. For two years I worked as an investment analyst and for a further two years as a school teacher before moving in 1974 to Preston Polytechnic (now the University of Central Lancashire) as a lecturer in Mathematics. While at Preston I worked in a variety of roles, in particular as Programme Coordinator and as Examinations Officer for Combined Studies, as a designer of the credit accumulation scheme, and as acting Head of the Department of Mathematics and Statistics. I was awarded a University Professorship in 1993. During my time at Preston, I undertook research work in combinatorics in partnership with my colleague Terry Griggs, as well as educational projects both in Combined Studies and within Mathematics. I also undertook consultancy work for a local engineering company. My main teaching activities were in mathematical methods, analysis and combinatorics.

Terry Griggs and I took early retirement from Central Lancashire in 1997 and subsequently joined the Open University in 1999 as Research Fellows. Here we joined the active Combinatorics Research Group. I have published around 90 papers in refereed journals since 1999, many being joint with Terry and several being joint with other OU colleagues. In addition, Terry and I produced the 30-point M.Sc. course M836 (Coding Theory) which has run very successfully since 2002.

In March 2008 I retired from my full-time post and I am now a Visiting Research Professor and an Emeritus Professor of the University.

Combinatorics Research Group (CRG)

Combinatorics is a rich source of mathematical questions which are easily described but difficult to solve. The CRG's current investigations focus on topological representations of designs, configurations and trades in designs, and graph colourings. Our interest is primarily and unashamedly in the theoretical aspects. However, many of the questions connect with practical issues in areas such as experimental design, data transmission, and data security. A specific example is the application of graph colourings to mobile telephone transmission systems. The questions which we seek to address are recognised as significant both for their theoretical importance and for their practical implications.

My research

Most of my research over the past 30 years has been done jointly with my colleague Terry Griggs. Our interests are focused on Steiner triple systems, their properties and those of related combinatorial designs. We have several papers on configurations in Steiner triple systems and other designs.  Since the mid-1990s we have developed an interest in topological representations of designs and from 2002 - 2006 we held a Leverhulme Trust grant to pursue this topic with colleagues at the Slovak University of Technology.

For anyone wishing to study combinatorial designs, a good general introduction may be found in

        I. Anderson. A first course in combinatorial mathematics (second edition), Oxford University Press, 1989.

Research aspects are dealt with more fully in

        C. J. Colbourn and A. Rosa, Triple systems, Oxford University Press, 1999.

A survey of work in topological design theory is given in

        Designs and topology. (M. J. Grannell and T. S. Griggs.) Invited paper for the 2007 British Combinatorial Conference,

        in "Surveys in Combinatorics 2007", Cambridge University Press, London Mathematical Society Lecture Note Series

        346 (ISBN13: 9780521698238), 2007, 121-174.

For a full list of my publications, follow this link

Recent talks that I have given    

• A flaw in the use of minimal defining sets for secret sharing schemes. (Contributed talk.) British Combinatorial Conference, Durham, July 2005

• Topological aspects of combinatorial designs. (Invited plenary talk.) Australasian conference on combinatorial mathematics and combinatorial computing, University of Queensland, December 2005

• Configurations in combinatorial designs. (Invited plenary talk.) Postgraduate Students' Combinatorial Conference, Glamorgan, July 2006.

• Consecutively row Hamiltonian Latin squares and surface embeddings of K_n and K_{n,n,n}. (Invited plenary talk.)   Combinatorial Design and Graph Theory Workshop, University of Queensland, April 2007.

• Designs and topology (Invited plenary talk, jointly with Terry Griggs) British Combinatorial Conference, Reading, July 2007.

• Avoidance problems in Steiner triple systems. (Invited talk.) Comenius University, Bratislava, December 2007.

• Avoidance problems in Steiner triple systems. (Seminar talk.) Monash University, Melbourne, May 2008.

• Biembeddings of Latin Squares. (Invited talk.) Reading University, November 2008.

• Rigid Steiner 5-designs. (Invited talk.) University of Queensland, February 2009.

• Steiner triple systems, finite and infinite - sparsity, uniformity and perfection. (Seminar talk.) University of Queensland, February 2011.

• Pasch trades with a negative block. (Contributed talk.) British Combinatorial Conference, University of Exeter, July 2011.

   

Research students

Since joining the OU, I have co-supervised four part-time research students. The first of these, J. P. Murphy, was registered at the University of Central Lancashire and obtained his Ph.D. from there in May 1999. The second, G. K. Bennett, obtained his Ph.D. from the OU in May 2004. The third, A. D. Forbes, obtained his Ph.D. from the OU in December 2006. The fourth, G. J. Lovegrove, obtained his Ph.D. from the OU in March 2009. The details are as follows:

• John Murphy, Steiner triple systems and cycle structure (co-supervised with Terry Griggs)

• Geoff Bennett, Some investigations in Steiner triple systems and related designs (co-supervised with Terry Griggs and Bridget Webb)

• Tony Forbes,  Configurations and colouring problems in block designs (co-supervised with Terry Griggs)

• Graham Lovegrove,  Combinatorial designs and their automorphism groups (co-supervised with Terry Griggs and Kathleen Quinn)

Curriculum connections

M836 Coding Theory

Terry Griggs and I wrote the course notes for this 30 point M.Sc. course. It was presented for the first time in 2002, since when I have been the course team chair and responsible for assessment materials. The course has been very successful, popular with students and having good retention and pass rates.

Generally

Research activity in combinatorics informs our curriculum through courses such as M836 and the undergraduate course MT365 (Graphs, Networks and Design) which is also popular with students and has good retention and pass rates. Our students, who form the majority of part-time mathematics students in the UK at both undergraduate and postgraduate levels would become progressively disadvantaged were this link to be weakened or severed.

Contact: You can email me at: m.j.grannell@open.ac.uk

Publications: You will find details of my publications by following this link.

M. J. Grannell, September 2011.