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)
M. Lemoine; "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) digitalcommons.latech.edu (2022)
This is a link to papers that I have helped write and been cited as an author. arXiv Link
Louisiana State University Math Department:
"Topological Data Analysis" for the First-year Graduate Student Orientation (August 13, 2025)
Abstract: In this talk, I will outline my research interests and highlight the big pieces in TDA. I will also be in a breakout room for people with questions afterward.
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:
AMS Southeastern Sectional at Tulane University; New Orleans, Louisiana (will attend in October 2025)
Topology of Arrangements with an Eye to Applications at University of Pisa; Pisa, Italy (will attend in September 2025)
The Geometric Realization of AATRN at IMSI; Chicago, Illinois (attended over Zoom, August 2025)
The 68th Texas Geometry and Topology Conference at Texas A&M University; College Station, Texas (November 2024)