Rick Thomas - Recent PhD Students
One of the many enjoyable ways of doing collaborative research is to work with PhD students. Those students with whom I have already published a paper or technical report are listed on the page listing my research collaborators. For completeness, I'm listing all my recent PhD students who have completed their PhDs here. As with my other research collaborators, it's been great fun working with my students and I've been very lucky in being able attract these people to come and work at Leicester.
Duncan Parkes completed his PhD at the end of 2000. He worked on syntactic monoids and also on reduced and irreducible word problems in groups. Amongst other things he proved a conjecture of Haring-Smith about reduced word problems that had been open since 1983 and he answered a question of Madlener and Otto from 1989 about groups with special string-rewriting systems. There are other results on groups with these string-rewriting systems as well. After leaving Leicester Duncan went to work for QinetiQ.
Michael Hoffmann completed his PhD early in 2001 on automatic semigroups. Michael showed that there are various possible different definitions of automaticity and biautomaticity in semigroups and made a systematic study of the differences between them. He also established a geometric condition which is equivalent to automaticity in semigroups and answered several open questions about automatic semigroups (including showing that a finitely generated commutative semigroup need not be automatic). Michael is now a lecturer in Computer Science back here at Leicester having previously been a lecturer in Computer Science at the University of Loughborough.
Steve Lakin completed his thesis on the space complexity of word problems in groups in 2002, with particular emphasis on groups with a context-sensitive word problem. Amongst his results he constructed a group G with deterministic context-sensitive word problem that is not a subgroup of any automatic group. he also studied the conjugacy problem and constructed groups G and H such that H has index 2 in G, G has unsolvable conjugacy problem and H has deterministic context-sensitive conjugacy problem. Steve left here to join the Cogent Computing Group at the University of Coventry, and then on to the University of Glamorgan. He is now at the University of Greenwich.
Tim Hardcastle worked on quasigroups and loops and on the connections between these non-associative structures and group theory. He explored the normal and characteristic structure of quasigroups and loop; he also proved some new results relating the order of a finite multiplication group to the structure of the corresponding loop. After completing his PhD in 2004 Tim left here to work at the Software Technology Research Laboratory at De Montfort University.
Barny Martin was originally supervised by Iain Stewart and I took over as supervisor when Iain moved to Durham (with Iain remaining as an external supervisor). Barny worked on two main topics: firstly various classes of non-deterministic program schemes with while loops, relating these to well-known complexity classes and logics; in particular, he studied classes of structure on which path system logic coincides with polynomial time P. Secondly Barny looked at the complexity of generalisations of non-uniform Boolean constraint satisfaction problems where the inputs may have a bounded number of quantifier alternations. After completing his PhD in 2005 Barny then moved to Durham to work as a research assistant to Stefan Dantchev in the area of Proof Complexity.
Ana Fonseca worked on irreducible word problems of groups. She mainly considered groups with a context-free irreducible word problem and obtained some characterizations in the case where the group is a direct product of a free group and a finite group. She also showed that having a recursive irreducible word problem is equivalent to having a recursive word problem and investigated the case where the irreducible word problem is recursively enumerable. After completing her PhD in 2006, Ana returned to Lisbon.
Graham Oliver worked on FA-presentability of groups and semigroups. He obtained a complete characterization as to which finitely generated groups are FA-presentable and also proved several results about FA-presentable semigroups (focussing on FA-presentability is preserved we combine or disassemble semigroups via standard semigroup constructions). After completing his PhD in 2006, Graham left to work for the Department for Work and Pensions in Sheffield.
Shakeel Arshad was originally supervised by Shengxiang Yang and I took over as supervisor when Shengxiang moved to Brunel (with Shengxiang remaining as an external supervisor). Shakeel worked on memetic algorithms for the static and dynamic Travelling Salesperson problems, producing new and efficient algorithms by refining the local search techniques. At the end of his PhD studies in 2012 Shakeel returned to his position at the University of Malakand.
Sam Jones worked on formal languages and word problems of groups. He looked at natural properties of formal languages which are necessary conditions for a language to be a word problem of a group and then characterized which subsets of these conditions are sufficient for a language satisfying them to be a word problem. He also settled the question of the decidability of these conditions for various classes of languages. After completing his PhD in 2015 Sam moved to the University of Wolverhampton.
Gabriela Asli Rino Nesin considered topics related to word problems of groups. She generalized some results on pairs of groups, which were previously known for context-free pairs only. She then looked at irreducible word problems and showed that a group for which all irreducible word problems are recursively enumerable must necessarily have solvable word problem. Using this she obtained a partial classification of groups for which membership of the irreducible word problem in the class of recursively enumerable languages is not independent of generating set. Lastly, she prove that the groups whose word problem is a terminal Petri net language are precisely the virtually abelian groups After completing her PhD in 2016 Gabriela joined the EPSRC-funded project MathSoMac: the social machine of mathematics headed by Ursula Martin. Gabriela is now at the University of Brighton.
Rick Thomas (email@example.com).