My research theme is time-varying homology. I am currently working on an instability problem for a time series of persistent homology summaries and a distance function that serves this project and various other applications in topological data analysis (TDA). My major subject in the Ph.D. program is Algebraic Topology, as examined from chapters 0-3 of Allen Hatcher’s Algebraic Topology text, while my minor subject is Statistics, as taken from chapters 1-8 of Casella and Berger’s Statistical Inference text.
In my Master’s thesis at the African University of Science and Technology, Abuja, I solved an optimization problem: an iterative scheme for approximating fixed points of strictly pseudocontractive maps in a special subtype of Hilbert spaces called Hadamard spaces. Strictly pseudocontractive 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 nonexpansive 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):
- 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)
- Research 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 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)