The “Topology for Tomorrow” workshop, held from 18-19 March 2024, as part of the Siyakhula Festival, brought a forward-looking perspective to the fields of topology and its myriad applications. This two-day event provided a platform for both established and emerging topologists to explore the current global trends, methodologies, and the future direction of topology.

Organised by Prof. David Holgate (University of the Western Cape), Dr Cerene Rathilal (University of Kwazulu-Natal), and Prof. Balázs Szendrői (University of Vienna), the workshop attracted a distinguished roster of speakers, including Prof. Ulrike Tillmann (Cambridge & Oxford) who delivered a keynote on “Seeing Data Through the Eyes of a Topologist.” This session highlighted the intersection of topology with data analysis, showcasing the discipline’s relevance in deciphering complex data structures.

The Commons in Muizenberg served as an informal backdrop for Prof.  Szendrői’s public lecture on “Symmetry and Topology in Islamic Art,” engaging attendees with insights into the topological underpinnings of Islamic artistic expressions. Meanwhile, the hands-on workshop led by Dr Rathilal (UKZN) and Dr Vivien Visaya (University of Johannesburg) on “Topological Data Analysis: Data has shape, and shape has meaning” allowed participants to delve into the practical aspects of topological data analysis , emphasising the ‘shape’ of data in natural sciences.

Additional invited talks from Dr Gillian Grindstaff (Oxford) on “Topological data analysis for natural and social geography” and Prof. Morten Brun (Bergen) on “Density Dependent Persistent Homology” expanded the workshop’s scope, linking topology with geographical and environmental studies. The workshop also featured discussions on the cutting-edge applications of topology in quantum computing by Prof. Bruce Bartlett (Stellenbosch) and the causal structure of spacetime by Prof. Dharms Baboolal (UKZN), further underlining topology’s integral role in contemporary scientific discourse.

The event concluded with a panel discussion moderated by Prof. Szendrői and the panellists included: Prof. Tillman, Prof. Brun, Prof. Loyiso Nongxa, Dr Vasaya and Dr Rathilal. This panel discussion provided a comprehensive overview of the future opportunities in applied topology, drawing from the extensive experience and research interests of its distinguished panellists.

The “Topology for Tomorrow” workshop underscored the dynamic and evolving nature of topology, its relevance to various scientific domains, and its potential to address some of the most pressing questions in contemporary research. Through engaging talks, hands-on sessions, and lively discussions, the workshop illuminated the path for future topological explorations, making a significant contribution to the Siyakhula Festival’s overarching theme of growth and innovation in mathematical sciences.