The members of this group are interested in a range of topics within algebra and model theory, the latter being a branch of mathematical logic relevant to the study of algebraic structures.
Non-commutative algebras, in particular, various kinds of matrix algebras and their substructures and algebraic properties, as well as polynomial identities in matrix algebras, form Prof Leon van Wyk’s research area.
Dr Karin-Therese Howell works on nearrings and near-vector spaces. She is interested in investigating near-vector spaces and their applications in different branches of mathematics. As a secondary interest she studies functions associated with a given algebraic structure.
Dr Lesley Wessels works on finite Dickson nearfields and their applications and uses graphs to further study their structure. She is also interested in getting reacquainted with Coding theory, and study it as a possible application to Dickson nearfields.
Dr Sophie Marques works on the study of structure of invariant rings and how this is related to ramification, such as freeness, Cohen-Macaulayness, etc. She is also interested in classifying field extensions of low degree and in the inverse Galois problem. She would like to understand ramification better and how it appears in algebra problems. Her interests lie in linear algebra as well, in particular on the non-negative inverse eigenvalue problem.
Dr Gareth Boxall works on topics within pure model theory, especially distality and tame expansions of o-minimal and related structures. He is also interested in model-theoretic aspects of near vector spaces.