Pure Mathematics
Complexity TheoryDr G Davie His research interests are centered on descriptive complexity theory in which the complexity of a binary string is defined as the length of the shortest computer program which outputs the binary string. This algorithmic approach to complexity yields deep insights into probability theory, "randomness", and even the philosophy of science. Other interests are general recursion theory and Topos-theory, a Topos being a special Category which generalizes the concept of a universe of sets. He is also interested in (the relation between) different philosophies of mathematics eg Platonism and Intuitionism. Graph TheoryDr S van AardtVaardsa@unisa.ac.za Tel: +27 12 429 6542 Main Research AreaMy research area is longest paths (detours) in graphs and digraphs. Currently my main aim is to settle the following two conjectures: The Path Partition Conjecture (PPC) for oriented graphs (see [1] below); Prof M Frick Main Research Areas
My current research focuses mainly on the Path Partition Conjecture (PPC) and its directed version. For a summary of results supporting the PPC see [26] below. For the directed version, see [18]. The PPC for oriented graphs led to the Traceabilty Conjecture, which is discussed in [28] and [30]. Functional Analysis and Operator AlgebrasProf LE Labuschagne His main research interest is Functional Analysis and Operator Algebras with a specific focus on the interface of the theory of Composition Operators and C*- and von Neumann algebras, and its potential significance as a rigorous framework for quantum phenomena. Mathematical LogicProf J Heidema The main focus of his research is mathematical logic and related areas, such as model theory, universal algebra, aspects of catgoery theory and deductive databases. Connected to his work are his interests in the philosophy, foundations, history and teaching of mathematics in other fields of study, such as physics and computer science. He has also done research in ring theory, lattice theory and set theory. A joint project with computer scientists comprises the study of semantic information and non-monotonic logics. Mathematics EducationProf J Heidema The aim of the topic is to train specialists in the field of mathematics teaching and some parts of the course-work are given in collaboration with the Department of Further Teacher Education. Full information on this topic is given in a separate brochure "MSc and PhD in Mathematics Education". Matrix TheoryProf JD Botha His research field is matrix theory, with primary focus on factorization of matrices. This programme was originated in 1910 by G. Frobenius. We want to know which matrices can be expressed as a product of symmetric matrices. It it happens then the research can proceed by investigating to what extent the symmetric factors could be further prescribed; say by requiring in addition that the factors have certain prescribed nullities and/or traces, etc. This leads to very interesting problems, the solutions to which are often non-trivial. Pointfree Topology and Nearness spacesProf TA Dube Representation TheoryDr ZE Mpono The focus of research is on finite simple groups, on computational methods in group theory using packages like CAYLEY or MAGMA and GAP, and on the representations and characters of finite groups. Also focus is given to the study of the maximal subgroups of the sporadic simple groups via the Fischer-Clifford theory and the construction of the character tables of these maximal subgroups.
|
Research
