Approximate numbers: 15 papers published, 15 papers submitted for publication, 15 postgraduate students, 15 presentations. Below is an overview of the highlights of activities in 2025. Members of the coordinating team are members of editorial boards of 4 international journals in mathematics, of which two are Q1 journals. Most of the members of the coordinating team have NRF ratings, with one B1 rating.
Algebraic Structures
Prof. Goswami furthered collaborations in the Algebraic Structures work package. This included collaboration with Dr. Vaino Shaumbwa from the University of Namibia and Prof. David Blecher from the University of Houston. New fundamental connections and concepts have been explored at the interface of rings, modules, Banach spaces, semirings, quantales, multiplicative lattices and general universal algebras. Prof. Goswami gave his first talk at an international conference on rings and modules in Austria in July, where he was warmly welcomed. 12 papers co-authored by him were published in 2025.
Analytical Structures
“Conference on Ordered Structures with Applications (COSA 2025)” was held at Wits Rural Facility from March 31 to April 4 at Kruger National Park in South Africa and included guest speakers from the FA as well as their collaborators from northern Africa (Tunisia). This conference series brings together researchers working at the interface of analytical and algebraic structures. Dr. Wen-Chi Kuo stepped down from her role of overseing this work package in January 2026 and the role will be offered to newly appointed Deputy Coordinator, Prof. Maggie Aphane.
Categorical Structures
Singificant advances were made in 2025 in the study of higher categorical structures. International collaboration and networking took place with several Italian categories theorists based in Italy and the UK. Prof. Janelidze gave an invited talk at the ItaCa Fest online webinar in April. Several members of the work package presented talks at the International Category Theory Conference held in the Czech Republic in July.
Discrete Structures
A 3-day research and writing retreat was held at Mpekweni in the Eastern Cape in January 24-26.
The participants of the retreat were: Prof. Eric Andriantiana (Rhodes University), Dr Adriana Roux (Stellenbosch University), Dr Valisoa Rakotonarivo (University of Pretoria), and Dr Zekhaya Benard Shozi (University of KwaZulu-Natal). Their work builds on the innovative work in [E.O.D. Andriantiana and Z.B. Shozi, The number of 1-nearly independent vertex subsets, Quaestiones Mathematicae 2024, 47(12): 2353-2373], where a generalised notion of independence in a graph is proposed.
Topological Structures
During March 24-28, Dr. Cerene Rathilal received a visitor, Dr Ana Belèn Avilez Garcia (Chapman University, USA), at the University of KwaZulu-Natal, who joined her in the investigation of connectivity in the context of point-free spaces.
Prof. Dharmanand Baboolal and Dr. Simo Mthethwa are also part of Dr. Rathilal's research group.
Joint Meeting of the London Mathematical Society, the South African Mathematical Society, and the Southern African Mathematical Sciences Association, September 2025
This historic networking event held 1-5 September was co-sponsored with the funds of the focus area. It led to successful collabotaitons and promising future partnerships. The event showcased some of the work on mathematical structures and their applications done in South Africa, Southern Africa and the UK. Several members of the coordinating team of the focus area were invited speakers at this meeting. See https://futuremath.net/imi for more information.
Mathematical Structures Workshop
The purpose of this workshop was engagement with researchers and students at the historically disadvantaged univesity (HDI), Sefako Makgatho Health Sciences University (SMU).
The meeting included presentations by students, a session for identifying mathematical structures studied at SMU for the purpose of future integration of SMU in the focus area.
The meeting also included explorative research sessions, which led to some interesting ideas of how the applications of graphs in chemistry and optimisation could potentially be extended to applications of more nuanced structures: categories. This workshop brought together all of the work packages of the focus area.
Website of the meeting: https://futuremath.net/prmsw
Science Engagement
The activities of the Future Mathematicians Progamme was introduced to the attendees of the Mega Mathematics Festival held in July at the University of the Western Cape, in a dedicated special session held in partnership with the South African Mathematics Foundation and South African Mathematical Society. This programme aims to introduce school learners and university students to abstract mathematical thinking and deductive reasoning.
The third edition of the theatrical, musical, and scientific production Fundamano explored the concept of a biological merger between the human brain and artificial intelligence, confronting audiences with a question of profound societal significance. Through the integration of theatre, music, and scientific imagination, the production created a space for reflection on the ethical, psychological, and social implications of human–AI integration.
https://youtu.be/QSa_cfBAdNQ?si=59yUQIunWJEAiNeA&t=6667
https://youtu.be/UOltCuz-YbM