School of Mathematics, Statistics & Computer Science

Maths PhD Candidate Participates in Prestigious MIT Workshop

Ms Maurine Atieno Songa, a PhD candidate in the School of Mathematics, Statistics and Computer Scienceparticipated in a virtual conference run by the Massachusetts Institute of Technology (MIT) on the topic of Applied Category Theory (ACT).

During Songa’s master’s studies, she became interested in the field of Category Theory, the study of how objects relate to one another, and its real-world applications after her supervisor, Dr Gareth Amery, introduced the idea. In the course of her research, she discovered a thriving community of applied category theorists. Wanting to learn more about the general tools of Category Theory for her research, and explore potential collaborations, Songa applied to MIT’s ACT Conference.

Participating students from around the world prepared for this event from March onwards, as organisers regularly released preliminary papers for participants to read, discuss and present on during biweekly online seminars. The five-day conference in July, intended to be held at MIT but moved to an online event due to the global COVID-19 pandemic, was preceded by a research week in which participants worked together in different areas of ACT to resolve various problems, receiving guidance and advice from ACT experts and teaching assistants (TAs).

‘The research week was highly intense, but I learnt a lot from our advisor, the TA and my three group members,’ said Songa. ‘They were helpful in expanding my understanding as I am new to Category Theory, and we have formed friendships and a great network.’

In the subsequent conference, students and advisors presented what they learnt and new discoveries made, with the goal being for different groups to continue collaborating on various projects. Songa said it was good to meet the larger ACT network.

Songa completed her undergraduate studies at the University of Nairobi in Kenya, followed by a postgraduate diploma at the African Institute for Mathematical Sciences and a master’s at UKZN on the topic of categorical systems biology. She is conducting PhD research exploring the use of causal-set theory to unify notions of gravity and the quantum realm under the supervision of Amery and Professor Dharmanand Baboolal.

Songa said Amery and Baboolal led her to consider how gravity and the quantum realm connect. She chose to continue PhD studies in South Africa, and opted for UKZN’s Discipline of Mathematics because of its welcoming and focused environment.

‘This research has been interesting as it is the perfect blend between topology and quantum gravity, and I hope this project advances the knowledge base of the fundamental Mathematics required to develop the causal set approach to quantum gravity,’ she said.

Songa is applying Category Theory to investigate properties of the category of interval domains that make it an ideal method to describe and understand spacetime. Based on the literature that suggests a strong connection between domain theory, or the study of partially ordered sets, and general relativity, she hopes her research will answer questions concerning the uniqueness of manifolds that approximate causal sets.

Songa also hopes her research will contribute to developing research capacity in the scarce skill areas of pure mathematics and gravitational theories, an important interface given Africa’s increasing investment in observational cosmology and astrophysics.

Songa plans to carve out a career in academia, hoping to use her expertise not only to produce new knowledge, but also to inspire an up-and-coming generation of young researchers in Africa, particularly women, to pursue careers in science, technology, engineering and mathematics.

Words: Christine Cuénod

Photograph: Supplied