The Cape Town Research Group ''Topology, Algebra and Dynamical Systems'' traces its origins back almost 50 years to the early activities in Categorical Topology at the University of Cape Town.
Under the leadership of Keith Hardie (who died on 19 May 2014) and Guillaume Brümmer, the group established itself as an international centre of research in categorical topology and bi-topology. Further important contributions were made by Japie Vermeulen (who died on 11 February 2001) and Paul Cherenack (who died on 17 January 2002).
A long-time association with Bernhard Banaschewski (McMaster University, Canada) has seen the development of a strong school in frame (locale) theory within the research group. Only recently we celebrated his 90th birthday with a workshop at UCT. We were very lucky to acquire expertise and knowledge in general topology from the seminars of Bernhard Banaschewski for decades (until the 2019). Our usual ''Seminars of the Tuesday'' are an important moment of interaction between young generations of topologists and international experts, who systematically visit us. From the point of view of the theory of the quasi-uniformities, Hans-Peter Kunzi (who died on 08 August 2020) was an international leader, who contributed to place our research group at the highest international levels in the area of the asymmetric topology. His qualities were recognised in various ways: from the position of HOD in the years 2012-2016 in our department, to the organisation of relevant scientific meetings in South Africa, to the presence in prestigious editorial boards of mathematical journals.
Our present research interests cover categorical topology, (asymmetric) analytic topology, frame (locale) theory, theory of locally compact groups, differential geometry, Lie theory and discrete mathematics. More recently we focus on interactions between topology and dynamical systems, investigating topological entropy, Lie groups and random walks.
Our activities often extend to the University of Cape Town, Stellenbosch University and University of the Western Cape, since former members of our research group work in these universities, and, more generally we share some common expertise in topology and its applications.