Dr Graham Clarke

Research

Research Interests

Dr Graham Clarke's research interests are in Algebra, Discrete Mathematics and Mathematics Education. Algebra and Discrete Mathematics have many applications in Computer Science, Communications Engineering and Information Security. He is particularly interested in the applications to network theory, coding and cryptography.

His research activities involve conference organisation, individual and joint research, graduate student supervision, conference talks and research publications.

Conference organisation

In 2008 and 2012 Dr Clarke was the organiser of the Annual Algebra Conference of Victoria held at RMIT. Interstate and Victorian mathematicians attended, and gave a wide variety of talks on Algebra and related topics.

Research

Dr Clarke's individual research has mainly been in Algebra and in Mathematics Education.

His joint research has involved collaboration with Bob Monzo of the United Kingdom. This has resulted in a new topic of research, that of generalised inflations of algebraic structures. Since then, other researchers have also begun to investigate this area of study.

More recently, he has collaborated with Yanfeng Luo and Yifei Hao of Lanzhou University, China, in a study of Cayley Graphs and Completely Simple Semigroups.

Graduate student supervision

Dr Clarke supervised the PhD thesis titled “On E-Pseudovarieties of Finite Regular Semigroups“. This thesis introduced a new algebraic structure known as a generalised existence variety of regular semigroups. RMIT awarded the candidate a University Research Prize for the quality of his Ph.D. thesis. He has also supervised a number of Honours students in Semigroups and related topics, and supervised numerous Masters Degree projects in various areas of Information Security.

Talks

• “Some applications of generalised existence varieties“ (with J.D. Rodgers), Sydney University Conference on Semigroups, 2005. (Proceedings to appear.)
• “Complete congruences on lattices of e-pseudovarieties of finite regular semigroups“ (with J.D. Rodgers), Australian Mathematical Society Conference, Macquarie University, Sydney, 2006.
• “On generalised inflations of algebras“, Joint Australia-New Zealand Mathematics Convention, University of Canterbury, Christchurch, New Zealand, 2008.
• “Distance education with discrete mathematics“, Joint Australia-New Zealand Mathematics Convention, University of Canterbury, Christchurch, New Zealand, 2008.
• “On the Cayley Graphs of Completely Simple Semigroups“, Australian Mathematical Society Annual Conference, University of Queensland, Brisbane, 2010.
• “On Cayley Graphs and Semigroups“, Algebra Conference of Victoria, Monash University, Melbourne, 2010.
• “Universal Cayley Graphs of Semigroups“, Australian Mathematical Society Annual Conference, University of Ballarat, 2012.
• “On Universal Cayley Graphs of Semigroups“, Mini-workshop on Semigroups, University of Tasmania, Hobart, 2012.
• “Extensions of Bisimple Inverse Semigroups“, Algebra Conference of Victoria, RMIT University, Melbourne, 2012.

More information

• Bulletin of the Australian Mathematical Society: referee of submitted papers.
• Semigroup Forum: referee of submitted papers.
• Southeast Asian Bulletin of Mathematics: referee of submitted papers.
• Zentralblatt fur Mathematik / Mathematical Reviews: reviewer.
• Victorian Algebra Group: foundation treasurer; returning officer.
• Accredited Member, Australian Mathematical Society
• Member, American Mathematical Society

Responsibilities

Discrete Mathematics course leadership (RMIT Melbourne, RMIT Vietnam, Open Universities Australia, Taylor’s College Malaysia)

Teaching Activities

• MATH1072/1074 Mathematics for Computing
• MATH1150/2045 Discrete Mathematics
• MATH2041 Mathematics for Advanced Computing
• MATH2148/2172 Algebra for Information Security
• INTE1124/2090 Coding for Reliable Communications

• Bachelor of Arts (Hons), Monash University, 1977
• Ph.D., Monash University, 1982