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AT AIMS Research Group

Launched at the Siyakhula Festival in March 2024, the AT AIMS research group introduces the fundamental mathematical fields of Algebra and Topology to the AIMS Research Centre. Led by Prof. Karin-Therese Howell and Prof. David Holgate, Dean of Natural Sciences at UWC, who holds a joint research position with AIMS and UWC, the group aims to advance these critical areas of mathematics.

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Current Research Topics

The lack of linearity of near-vector spaces allows for encryption techniques that are more secure than their linear counterparts. In particular, the focus of this research group is how traditional linear ciphers can be adapted into a nonlinear setting in the language of near-vector spaces.

Geometry is central to the study of near-vector spaces. Just like every vector space has an associated affine space, every near-vector space has an associated nearaffine space. These nearaffine spaces have been the key to uncovering interesting properties of the algebraic structure of near-vector spaces.

Algebraic Systems Biology (ASB), is an interdisciplinary field that applies algebraic methods to tackle biological problems. Algebra-backed models can help in devising better interventions, without costly simulations. It is also often the case that answering certain biological questions can result in the development of new results in mathematics.

Apart from its combinatorial motivation, graph theory also helps to characterize various algebraic structures. The main goal of studying graphs associated with algebraic structures is to characterize the algebraic structures with graphs and vice versa. In particular, the various graph-theoretic properties of the graphs that we associate with these algebraic structures are of interest; for example, the diameter, girth, clique number, and chromatic number of these graphs. Furthermore, the connections between the algebraic and graph-theoretic properties of the algebraic structures and their associated graphs are investigated.

In 2022 David Holgate was awarded a joint UWC-AIMS Research Chair in Mathematics, under the theme “Topology for Tomorrow (T4T)”. The regular seminars at both UWC and AIMS form part of the AT-AIMS project. We have held annual T4T workshops and other events at AIMS with the main themes being Topological Data Analysis (TDA), point-free and lattice based topology, topological groups and also categorical topology - using category theoretic methods and insights in the study of general topology. We have a group
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Our Students

Researchers
  • Prof Karin-Therese Howell (AIMS & SU)
  • Prof David Holgate (AIMS & UWC)
  • Prof Cang Hui (AIMS & SU)
  • Dr Jacques Rabie (AIMS)
  • Dr Brice Razakarinoro (Postdoctoral Fellow)
PhD
  • Siyabonga Mthimkulu (2024 -) (supervisors: Holgate D., Janelidze Z., Manuell G., Faul P.)
  • Ronald Kerario (2025 -) (supervisor: Janelidze, Z.)
  • Clinton Quee (2026 -) (supervisors: J. Rabie, L. Wessels, K.-T. Howell)
  • Claudia Justus (2025-) (supervisors: Howell K-T, Hui C.)
  • Ruth Abbey (2025-) (supervisors: Howell K-T, Hui C., Rabie J.)
MSc
  • Meva Rakotondratoetra (2024 -) (supervisors: Holgate D., Howell K-T, C. Rathilal (UKZN))

AIMS Structured Master’s Research Projects

  • 2024-25 Clinton Paye Quee, A Study of Graphs Associated with Vector Spaces (supervisor: J. Rabie)
  • 2024-25 Kizito Odizilike, Contributions to the Partitioning of Categorical Data (supervisors: Howell K-T, Hui C., Macauley M.)
  • 2024-25 Ruth Naayi Odankey Abbey, A Study of the Geometric Proof of the Subspace Problem for Near-Vector Spaces (supervisors: J. Rabie, K.-T. Howell)
  • 2024 Ingrid Thandeka Kabinde, Group structures of nonlinear ecological dynamics (supervisors: Howell K-T, Hui C.)
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