Algorithmic problems in algebra (GRAY_U16SF)
Please note that the job is no longer active!
This PhD project is offered on a self-funding basis. It is open to applicants with funding or those applying to funding sources. Details of tuition fees can be found at http://bit.ly/1NEK5k8.
A bench fee is also payable on top of the tuition fee to cover specialist equipment or laboratory costs required for the research. The amount charged annually will vary considerably depending on the nature of the project and applicants should contact the primary supervisor for further information about the fee associated with the project.
Algorithmic problems in algebra have their origins in work of Thue, Tietze, and Dehn carried out in the beginning of the 20th century. Their work showed how certain problems in logic and topology turned out to be equivalent to corresponding algebraic problems, namely the word problem for finitely presented semigroups and groups, and the isomorphism and conjugacy problems for finitely presented groups. Even though originally motivated by problems in logic and topology, the investigation of algorithmic problems in algebra is now primarily motivated by the internal needs of algebra itself. Algorithmic problems often lie at the heart of difficult and important algebraic problems. Most problems are undecidable in general, and so it becomes important to identify and study classes with good algorithmic properties. This point of view has led to a lot of interesting research on topics including hyperbolic groups, word hyperbolic semigroups, automatic groups and semigroups, one-relator groups, finite complete string rewriting systems, and the study of small overlap conditions. For those problems that are decidable there are also interesting questions about how hard these decision problems are, linking the subject with complexity theory. The PhD project will investigate a range of algorithmic and decision problems in algebra, with a focus on finitely presented semigroups and groups.
Nr of positions available : 1
Early stage researcher or 0-4 yrs (Post graduate)
First Stage Researcher (R1)
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University of East Anglia
University of East Anglia, Norwich Research Park, Norwich
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