My research theme is dynamic homology. A current project focuses on a procedure for updating a topological summary of a shape as it evolves, when this change can be parameterized by some topological space. Other problems I am thinking about are applying topological data analysis methods to scientific and real-world datasets. See my CV and GitHub page.
My Master’s thesis at the African University of Science and Technology, Abuja, solved an optimization problem: proving an iterative scheme for approximating fixed points of strictly pseudo-contractive maps in a special subtype of Hilbert spaces called Hadamard spaces. Strictly pseudo-contractive maps are a subclass of Lipschitz maps. They are not necessarily continuous, but studying them gives us insight into the study of fixed point theory for non-expansive mappings.
My undergraduate thesis project was a review of R. Ghrists’s paper “Barcodes: the persistent topology of data,” published in the Bulletin of the American Mathematical Society, Volume 45 (2008), pages 61-75.
Here are some snippets from my research trajectory so far (hyperlinks underlined):
- Paper (co-author) “A Topological Approach in Analyzing the Shifts in Air Pollutants’ Dynamics Pre- and Post-COVID-19 Lockdown Era“, published in Springer Nature’s Environmental Monitoring and Assessment (2025).
- Poster presentation for the Institute for Mathematical Sciences and Innovation (IMSI) Geometric Realization of the AATRN Workshop (2025), which I could not attend due to unforeseen circumstances.
- Here is a video on topological “fiber” bundles I made for the AATRN Tutorial 2025 series which never got posted.
- Invited talk at the AMS Eastern Fall Sectional Meeting, SUNY, Albany, NY (2024).
- Invited talk at TDA Seminar in the Department of Computational Mathematics, Science and Engineering, Michigan State University (2024).
- Poster presentation at the Institute for Mathematical Sciences and Innovation (IMSI) Randomness in Topology Workshop (2023).
- Research presentation at Wayne State University Graduate Research Symposium (2023).
- Paper (co-author) “Statistical inference for persistent homology applied to simulated fMRI time series data” published in Volume 5 (2023), Issue 1, of Foundations in Data Science.
- Class presentation on the Snake Lemma (2020).
- Master’s thesis defense presentation on the Proximal Point Algorithm in Hadamard Spaces (2019).
- Conference talk on Topological Persistence In Data Analysis at the Nigerian Women in Mathematics conference (2017).
- Undergraduate thesis: “Topological persistence in data analysis” (a review of Robert Ghrist’s 2008 paper titled “Barcodes: the persistent topology of data”) (2016).
- Poster presentation on undergraduate thesis (2016).
“…the honor of kings is to search out a matter.” (Proverbs 25:2)