Semigroup Extensions and their Cayley Graphs
- SPEAKER: Dr Graham Clarke, RMIT University
- Date: Friday 15th September
- Time: 3:00pm–4:00pm (Talk & Q/A)
- Venue: Building 8 Level 9 Room 66 (AGR) , RMIT City campus
The seminar will be followed by snacks and drinks
All students, staff and visitors are welcome
ABSTRACT: Semigroups can be extended in various ways, one of the most useful being by means of ideal extensions. The simplest ideal extensions are null extensions, and from a varietal viewpoint the most useful null extensions are inflations of semigroups. We look at some results on inflations, generalised inflations and null extensions of semigroups, and then turn our attention to Cayley graphs of semigroups and their usefulness in characterising various kinds of extensions of semigroups.
BIO: Graham Clarke obtained his Ph.D. in Semigroups from Monash University. After teaching at Monash and at the Chisholm Institute of Technology, he was appointed as an assistant professor at the University of Arkansas. Upon his return to Australia he became a lecturer at Swinburne Institute of Technology, before taking up his present position at RMIT.
Graham has also been a visiting fellow at James Cook University in far north Queensland, and a visiting lecturer at Xiamen University in southeast China. He has given invited addresses at numerous universities in China: Xiamen University, South China Normal University in Guangzhou, Southwest Normal University in Chongqing, Lanzhou University and Northwest Normal University (both in Lanzhou) and most recently at Beijing Jiaotong University. His main research interests are in Mathematics Education, Algebra and Graph Theory.