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Mathematical Structures for Foundations and Innovations: Uncovering Universal Theoretical Principles and Building Integrated Mathematical Capacity to Foster South Africa’s Future Scientific, Technological, and Economic Progress

Coordinator: Prof Zurab Janelidze (Stellenbosch University)

Members

Lead Researchers: Prof. Eric Andriantiana (RU), Dr. Amartya Goswami (UJ), Prof. Zurab Janelidze (SU), Dr. Wen-Chi Kuo (WITS), Dr. Cerene Rathilal (UKZN).

Membership of the Focus Area is open to any South African mathematician or theoretical computer scientist who is a NITheCS Associate and whose research interest touch on mathematical structures. There are currently around 35 members from around 15 South African universities, including 7 HDI’s. To join the Focus Area, please write to the Deputy Coordinator: Dr. Cerene Rathilal (rathilalc@ukzn.ac.za).

Aims

The Focus Area aims to:

  • Advance the study of fundamental mathematical structures by conducting deep, theoretical research into key conceptual frameworks in mathematics.
  • Foster innovation by encouraging researchers to explore new mathematical structures, invariants, and relationships that have not yet been fully understood.
  • Promote interdisciplinary engagement, allowing ideas from diverse areas of mathematics and related fields to inform each other and lead to discoveries.
  • Develop a strong network of mathematical expertise across South Africa, building capacity and enabling collaboration among institutions, while strengthening South Africa’s position in the global research community.
  • Mentor and train postgraduate students and early-career researchers, with a focus on human capital development in mathematics and a strong emphasis on participation from historically disadvantaged institutions (HDIs).
  • Contribute to the global mathematical community by ensuring that the results of the Focus Area are disseminated through high-level academic publications, conferences, and international collaborations.
  • Cultivate structural thinking by developing educational resources, including teaching materials, online lectures, and interactive tools, aimed at introducing structural thinking to school learners and teachers, students and researchers.

Rules

  • Membership of the research programme is open to any NITheCS associate whose work is aligned with the aims of the research programme.
  • Every member of the research programme must include the following as their second address (after their main university address) in all of their publications: National Institute for Theoretical and Computational Sciences (NITheCS), <name of the city of their university>, South Africa.
  • Members of the research programme are generally expected to engage in the academic ecosystem of NITheCS, beyond the activities of the specific research programme (e.g., attend and contribute to NITheCS colloquia).

Almanac

September 2023

  • Research visitor of Bruce Bartlett at Stellenbosch University.
  • Training: online mathematics lesson for school learners by Cerene Rathilal (1 Sep).
  • Training: Cerene Rathilal runs a mathematical exploration olympiad with second-year students at UKZN (4 Sep – 31 Oct).
  • Research visit of Andrew Craig (UJ) at the University of Kwa-Zulu Natal (4-8 September). Host: Cerene Rathilal.
  • Engagement: invited presentation by Zurab Janelidze with the Georgian pop-musician and singer-songwriter, Nugzar Ergemlidze, at his Author’s Music Evening in Batumi, Georgia, on 10 November. The two discussed similarities in the process of creativity in mathematics and in pop music. A movie of the event can be found here.
  • Research: invited talk (Theories of Exactness Properties) by Zurab Janelidze at the Logical & Algebra Seminar (15 Sep), a satellie event to the 108th Peripatetic Seminar on Sheaves and Logic, in Terrasini (Palermo), Sicily (Italy).
  • Research: 13th International Workshop on Non-Classical Models of Automata and Applications (18-19 September, Cyprus): Brink van der Merwe gives two talks, “Formalizing BPE Tokenization” (joint work with Martin Berglund) and “Ordered Context-Free Grammars Revisited”.
  • Training: Heidelberg Laureate Forum (23-29 September): Cerene Rathilal and Vivien Visaya presented a workshop in topological data analysis. Cerene Rathilal hosted a Women in Mathematics session at the same Forum and was a panelist at a panel discussion.

October 2023

  • Research visit of Andrew Craig (UJ) at Chapman University (USA, 28 September – 18 October). Host: Peter Jipsen.
  • Research visit of Cerene Rathilal at University of Pavia (1-6 October). Host: Frank Neumann.
  • Engagement: invited public presentation in the Music Department of Stellenbosch University on the mathematical structure of music (5 October), by Zurab Janelidze, Hans Roosenschoon and their student collaborators.
  • Training: online lessons for school learners: Abstract Algebra (6 and 9 October).
  • Research visit of Nancy Neudauer at Stellenbosch University (6 Oct – 23 Dec). Co-hosts: Bruce Bartlett and Karin-Therese Howell.
  • Training: online lessons for school learners, Mathematics Club at the University of Kwa-Zulu Natal (14 and 21 October).

November 2023

  • Training: talk on “The Evolution of the Number Concept from Natural to Real Numbers” by Charles Nsukukazifani Msipha at the Table Mountain Delta 2023, the 14th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics (26 Nov – 1 Dec)
  • Engagement: presentation by Zurab Janelidze and Cerene Rathilal on this research programme (Mathematical Structures and Modelling) at a NITheCS annual programme review on 24 November.
  • Engagement: invited talk by Zurab Janelidze on Mathematical Structure of Music during a CIMPA School “Blockchain in Theory and Real Applications” at AIMS on 25 November. Zurab Janelidze and Cerene Rathilal championed a Mathematical Exploration Olympiad centered around blockchain on the same day.

December 2023

  •  Engagement: Fundamano 2 production at Drostdy Theatre (1 Dec), featuring musical improvisations based on mathematical structure of music (a project in the research programme).
  • Research: talk by Zurab Janelidze on Nullital Categories at the SAMS Congress (4-7 Dec). Zurab Janelidze and Cerene Rathilal hosted an undergraduate research session at the same congress, featuring research talks by undergraduate participants as well as a plenary talk by Nancy Neudauer on undergraduate research activities in the USA. Such session is organised first time in the history of SAMS Congresses.
  • Training: Workshop for postgraduate students: Topology for Tomorrow (9-11 December) co-organised by Cerene Rathilal, who held there a Mathematical Exploration Olympiad.

Outputs (2022 - 2023)

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Focus Area