Mathematical Structures and Modelling Research Programme
National Institute for Theoretical and Computational Sciences
- Nodes across South Africa
- Home to eight disciplines: astronomy and astrophysics, data science, earth systems and climate change modelling, mathematics, quantitative biology, quantitative finance, statistics, theoretical physics
- Undsciplinary approach: ecosystem for collaboration within, across and beyond disciplines, leading to impactful research
- Hosts weekly (accessible) colloquiums, more technical monthly mini-schools (all available on YouTube) and many other events
- Established as a result of a competitive NITheCS call in 2021
- The goal of the mathematical structures and modelling research programme is to investigate mathematical structures across the traditional boundaries of disciplines within mathematical science (including computer science, mathematical/theoretical physics). The research programme focuses on empowering researchers in advancing their individual discipline-specific research projects and distilling from those projects themes for collaborative interdisciplinary research endeavors.
- Some of the key research themes include: unifying theories of group-like and other algebraic structures, algebraic structures of topology and topological structures of algebra, combinatorial and analytical structures, structure of mathematical creativity and deductive reasoning with applications to automated theorem proving and pedagogy in mathematics, mathematical structure of musical form with applications to musical composition and improvisation
Mathematical Structures and Modelling Research Programme
Future Mathematicians Programme
- A metacurricular approach to developing mathematical exploration skills
- Training of learners and students in contextualized deductive reasoning
- Awareness of mathematics as a profession
- Nurturing affection and love for mathematics by transitioning from the talent philosophy to the passion philosophy
- Symmetries of Connectedness, presented by Bernardus Wessels
- Noetherian forms: a self-dual approach to homomorphism theorems in group theory, presented by Zurab Janelidze
- A discussion on mathematics in South Africa:
- What can we do to address low student numbers in pure mathematics?
- How can we attract more African South African students to pure mathematics?
- How can we support growth of group theory in South Africa?
7th Biannial Conference in Group Theory, 2023, Potchefstroom
Symmetries of Connectedness
Noetherian forms:
- Large-scale structures
- Purpose: unified theory of all group-like structures as far as homomorphism theorems are concerned
- Primitives: composition of group homomorphisms, subgroup inclusion under a homomorphism
