By Prof Roelof Coetzer
In the ever-evolving landscape of academia, certain institutions distinguish themselves not merely by their age or size, but by their unyielding commitment to curiosity and innovation. North-West University (NWU) in South Africa exemplifies this spirit, particularly through its Focus Area for Pure and Applied Analytics (PAA) research entity. This entity is not just pushing the boundaries of mathematical and statistical sciences but is also redefining how these disciplines intersect with real-world applications.
At its core, PAA is dedicated to fundamental research in the foundational principles and paradigms of mathematical and statistical sciences. Their mission is ambitious: to operate at an internationally competitive level, advancing scientific knowledge while fostering an environment where diverse branches of mathematical and statistical sciences converge. This holistic approach encourages the integration of various sub-disciplines, providing a comprehensive understanding of complex research problems.
What sets PAA apart is its mix of, and expertise in various research areas. The group boasts unique expertise in fields such as Applied Linear Algebra and Operator Control Theory, Quantum Field Topology, Quantum Function Spaces, Partial Differential Equations (PDEs) and Dynamical Systems, as well as in Mathematical and Applied Statistics including, but not limited to, Goodness-of-Fit tests, Survival analysis, Non-parametric statistics, Stochastic processes and Statistical Learning. This diverse portfolio enables PAA to tackle a wide array of challenges, from the abstract realms of pure mathematics to tangible, real-world applications.
PAA is committed to staying abreast of new developments in the mathematical and statistical sciences, strategically expanding its skill set to remain at the cutting edge. Therefore, members of PAA are committed to contributing, and being involved in international research initiatives and events, such as the Goodness-fit-Fit and Change Point Workshop (GOFCP) and the CIMPA 3MC Mathematics and Applied Mathematics Workshops. This commitment is not just about keeping up with trends but about setting them, ensuring that their research is visible and remains relevant and impactful in academia and in practice.
Understanding that today's young researchers are tomorrow's pioneers, PAA places a strong emphasis on mentorship and development. By providing an accessible forum for graduate students and emerging researchers, the group fosters an environment where new ideas can flourish. This inclusivity extends to the broader South African mathematical and statistical sciences community, ensuring that the benefits of their research are widely disseminated. Specifically, PAA members are actively involved in the South African Mathematical Society (SAMS) and the South African Statistical
Association (SASA), and significantly contribute to the annual conferences of those societies.
The scope of PAA's research projects is as diverse as it is impressive. In Functional Analysis, Operator Theory, and Applied Linear Algebra, researchers delve into Banach spaces and Operator Algebras. The Algebra, Topology, and Combinatorics team explores areas like Algebraic Combinatorics and Quantum Field Topology. The Mathematical Physics group tackles Noncommutative Analysis and Theoretical Fluid Dynamics. Each project reflects a commitment to exploring new frontiers and applying mathematical principles to solve complex problems.
PAA doesn't just dwell in the theoretical; it actively seeks to apply its research to global challenges. The Modelling team, for instance, engages in Life Science Modelling and Financial Modelling, demonstrating the real-world applicability of their work. Similarly, the Environmental Mathematics group addresses pressing issues like Disease Modelling and Climate Change Linkage, showcasing how mathematical insights can inform and improve our understanding of environmental challenges. In addition, the Applied Mathematics subgroup has specialization in Symmetry Analysis and Theoretical Fluid Dynamics.
The Statistics subgroup offers specialization in the theory of goodness-of-fit tests with about six people actively involved in this research area. Measures of goodness-of-fit are very important in mathematical statistics and is used in, for example, statistical hypothesis testing, to test whether two samples are drawn from the same distribution, or whether outcome frequencies follow a specified distribution. There is also specialization in survival analysis and related topics, which offers great opportunity for theoretical developments and several application areas including, but not limited to, health studies, drug development, reliability and financial and credit risk modelling. PAA also has a research focus group in climate risk and environmental data science, which utilizes topics such as extreme value theory, stochastic processes, time series analysis, harmonic analysis and multivariate data analysis.
For those whose curiosity is piqued by the intricate dance of numbers and mathematics, PAA offers a gateway to a world where mathematics and statistics are not just subjects but tools to decipher the universe's mysteries. Whether you're a budding mathematician seeking a nurturing environment or an industry professional looking for cutting-edge analytical insights and solutions, PAA is ready to engage, collaborate, and innovate.
In a world increasingly driven by big data and complex systems, the research and development being done at PAA is not just relevant, but essential for solving global problems related to industry, government and social challenges, including environmental, climate change and risk, financial risk, urbanization, and others. By leading through curiosity and innovation to explore new ideas, PAA exemplifies the transformative power of mathematical and statistical sciences.
