Inaugural lecture details innovative mathematical solutions
Professor of Mathematics Oluwatosin Mewomo presented his inaugural lecture on the developing focus of his academic career, which had its beginnings in the realm of notions of amenability in Banach algebras and progressed to fixed point theory.
Mewomo has been at UKZN since early 2015, joining the institution after working at the Federal University of Agriculture, Abeokuta (FUNAAB) in Nigeria for more than 13 years. He attained his undergraduate and honour's degrees in Mathematics from FUNAAB, where he was the top graduating student in his discipline.
His master’s and PhD degrees were obtained from Obafemi Awolowo University in Ile-Ife in Nigeria and at FUNAAB respectively, benefiting from the Ondo State Government Scholarship and Federal Government Scholarship for his MSc, and the African Mathematics Millennium Science Initiative for his PhD.
As an internationally recognised scholar, he has pursued research on functional analysis, an arena of mathematical analysis that deals with vector spaces and the solution of mathematical problems that arise when that space is not finite-dimensional.
He has focused on Banach algebras, fixed point theory and applications to nonlinear and optimisation problems. In Banach algebras, or vector spaces with more analytical structure, he has investigated the notion of amenability and its expressions. His fixed-point theory research investigates fixed-point iterative methods for approximating the fixed point of nonlinear operators, and nonlinear and optimisation problems in Hilbert, Banach and Hadamard spaces.
Deputy Vice-Chancellor of the College of Agriculture, Engineering and Science Professor Albert Modi welcomed guests, colleagues and friends of UKZN to the lecture on behalf of the Vice-Chancellor, saying inaugural lectures – providing official recognition of an individual’s promotion to full professor – showcase to a wider audience the exciting and ground-breaking research and teaching being carried out at UKZN.
Modi noted the diversity of guests who included representatives from other institutions of education Mewomo had worked with, some of whom contributed to his education, and his collaborators and students past and present.
Mewomo began with an introduction to and history of Banach algebras and notions of amenability, demonstrating how these notions originated from measure theoretic problems and moved to abstract harmonic analysis. He discussed characterisations of notions of amenability in Banach algebras and his research team’s contributions, and then introduced notable fixed-point iterative schemes in some important spaces, with applications.
Finding amenability in many cases too restrictive, Mewomo and colleagues had been able to relax some of the constraints in the definition of amenability and introduce various notions of amenability.
He especially focused on how iterative schemes could produce approximate solutions to certain classes of nonlinear problems, fixed points of some nonlinear operators, zero-point problems and his team’s contributions in this area.
Explaining that many problems arising in fields including economics, computer science, engineering and machine learning could be modelled as optimisation problems, Mewomo explained how the fixed-point method was useful for solving these problems.
He provided an example of his team’s work in developing an algorithm to solve a generalised split feasibility problem with applications in image restoration for photographs and medical resonance imaging (MRI). Their method can also be applied to signal processing, particularly recovering sparse signals.
The holder of a C2 rating from South Africa’s National Research Foundation (NRF), Mewomo has also received awards from FUNAAB in recognition of his productivity, and has been among the top 10 of UKZN’s top 30 published researchers for three consecutive years, receiving the Deputy Vice-Chancellor of the College of Agriculture, Engineering and Science Research Award.
He has published over 180 articles in highly-rated peer-reviewed journals, is a reviewer for more than 20 high-impact journals, and also serves on the editorial board of the International Journal of Nonlinear Analysis and Applications.
Mewomo has received several grants and fellowships including from the London Mathematical Society Scheme 5 Fellowship, the National Research Foundation (NRF) Incentive Funding for Rated Research and the International Mathematical Union.
Prioritising building capacity in the field of mathematics, Mewomo has supervised 14 PhD and 22 master’s students, as well as four postdoctoral fellows with a further five doctoral students currently under supervision. He contributes to several panels for South Africa’s Department of Higher Education and Training and has examined theses from across the country and abroad.
He is a member of the American Mathematical Society (AMS) and the Nigerian Mathematical Society, and has reviewed publications and guest edited special journal editions of the former. Mewomo has been an invited speaker at several international conferences and workshops worldwide and has been a visiting researcher at universities in Northern Ireland, Scotland, England, Canada and South Africa as well as at South Africa’s African Institute for Mathematical Science.
Mewomo concluded his lecture by thanking God, his family, advisors, mentors, post-graduate students and post-doctoral mentees, his colleagues, collaborators, hosts, funders, pastors, friends and employers for their invaluable support.
Words: Christine Cuénod