My current research areas are primarily Topological Data Analysis (TDA) and Low-Dimensional Topology. In addition to these areas, I also find myself looking into areas of Statistics, Machine Learning (specifically Semi-Supervised Machine Learning), Topological Deep Learning (TDL), and Computer Science.
These are my papers that I have written and/or helped write.
B. Appiah, P. Dani, W. Ge, C. Hudson, S. Jain, Y. Lee, M. Lemoine, J. Murphy, A. Pandikkadan, K. Schreve; The algebraic structure of hyperbolic graph braid groups. arXiv:2403.08623 (2024)
"Factors that Relate to Academic Excellence" (completed in May 2022 in compliance with the degree requirements for B.S. in Mathematics at Louisiana Tech University)
Abstract: The American College Testing (ACT) provides university admissions offices a look into a student’s academic ability so that the university can determine admittance and scholarships. The premise of this study is to see whether this is the most effective way to determine academic ability, using the Logistic Regression Model. The data was collected from October 21, 2021 to December 31, 2021 at Louisiana Tech University. Using the Logistic Regression Model, predictions of academic excellence are obtained based on the parameters outlined in this paper. After the parameters for the Logistic Regression Model are calculated, conclusions can be drawn that the ACT is not an effective predictor of academic excellence.
This is a link to papers that I have helped write and been cited as an author. arXiv Link
Given in the LSU Informal Geometry and Topology Seminar:
"The Classification Theorem of Vector Bundles over Compact Spaces" (June 12, 2025)
Abstract: In the summer for the Informal Seminar, we pick a book/paper and we all present over different aspects of the book/paper. In the summer of 2025, we picked a book on K-Theory by Inna Zakharevich.
"Topological Data Analysis and the Persistent Laplacian" (April 16, 2025)
Abstract: In this talk, we will go through some basic information about Topological Data Analysis (TDA) such as Persistent Homology with the goal of getting to the Persistent Laplacian and how these tools are used to analyze data.
"A Brief Introduction to Khovanov Homology through an example" (October 30, 2024)
Abstract: In this talk, we will discuss Khovanov Homology and how to compute this homology using an example with the trefoil knot. We will also discuss the relations between Khovanov Homology and the Jones Polynomial.
Attended:
The Geometric Realization of AATRN (will attend in August 2025)
The 68th Texas Geometry and Topology Conference at Texas A&M University, College Station, TX (November 2024)