Francisco Martinez Figueroa
Postdoctoral Scholar - University of South Florida.
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About Me
I am currently a Postdoctoral researcher at the University of South Florida (USF), working under the mentorship of Professor Natasha Jonoska on discrete and topological models for DNA assembly. Until December 2024, I was also affiliated with the Southeast Center for Mathematics and Biology at Georgia Tech (SCMB) as a junior researcher, collaborating closely with Professor Francesca Storici's genomics group.
I received my PhD in Mathematics from The Ohio State University in 2022 under the supervision of Professor Matthew Kahle. My doctoral work centered on topological and probabilistic methods in graph theory.
Research Interests
Topological combinatorics
Random graphs and probabilistic methods
Chromatic and geometric properties of distance graphs
Computational topology and topological data analysis
Machine learning
Applications to biology
My current research develops topological, combinatorial, and computational tools for studying discrete structures with biological applications. I am especially interested in how topology interacts with randomness, geometry, and high-dimensional data, and in connecting these ideas to problems in genomics and molecular biology. This includes work on tools to analyze DNA RNA-mediated repair mechanisms, and helping interpret experimental datasets related to ribonucleotide incorporation in the Storici Lab. I also develop computational tools to support these analyses and collaborate closely with the experimental team to bridge the gap between mathematical models and biological observations.
My Erdős number is 2.
See my research below and my LinkedIn profile.
Contact me at fmartinezfigueroa at the email domain usf.edu.
Research
Publications
“Generalized Borsuk Graphs.” 2024. Discrete & Computational Geometry 72(4), 1377–1416. arXiv:2110.06453
“Topology and Chromatic Number of Random 𝜖-Distance Graphs on Spheres.” 2023. Geombinatorics 33(1), 14–38. arXiv:2207.13892
with Kahle, M., and Soifer, A. “A Square-Grid Coloring Problem.” 2020. Geombinatorics 29(4), 167–185. arXiv:2004.10192
with Kahle, M. “The Chromatic Number of Random Borsuk Graphs.” 2020. Random Structures & Algorithms 56, 838–850. arXiv:1901.08488
“Gröbner Bases and Their Application to Automated Proofs of Geometry Theorems: A Proof to Pascal’s Hexagram Theorem” [in Spanish]. 2015. Del Valle de Guatemala University, Undergraduate thesis. https://repositorio.uvg.edu.gt/handle/123456789/2333
Preprints
with Jonoska, N., and Saito, M. “The Insertion Chain Complex: A Topological Approach to the Structure of Word Sets.” 2025. (submitted) arXiv:2509.12607
with Kundnani, D. L., Yang, T., Channagiri, T., Xu, P., Lee, Y., Sun, M., et al. “Human Ribomes Reveal DNA-Embedded Ribonucleotides as a New Type of Epigenetic Mark.” 2025. (under revision at Cell). bioRxiv 2025.06.27.661996
with Fadnavis, S., and Kahle, M. “Warmth and Mobility of Random Graphs.” 2021. arXiv:1009.0792
“Optimal Discrete Morse Theory Simplification (Expository Survey).” 2018. arXiv:2111.05774
Computational Tools
InDelsTopo: A Python package for analyzing topological properties of sets of words where insertions and deletions are the main source of variation, using the Insertion Chain Complex framework. This package was developed to study DNA sequences from experiments investigating RNA-mediated repair of DNA following double-strand breaks.
Human ribome Analysis: Computational support and data analysis for human ribonucleotide incorporation, in collaboration with Storici's Lab.
Data Science BootCamp Projects
Comparing World Bank loan impacts across sector.
May 2021, The Erdős Institute Bootcamp. (Top Project)
Teaching
Main Instructor
University of South Florida : (2022 - Present) Main instructor for Linear Algebra and Calculus, responsible for designing syllabi, assignments, and exams, managing grading, leading lectures, and holding office hours.
Teaching Associate
The Erdős Institute : (Fall 2021) Ad honorem Teaching Assistant providing support to participants during live data science problem-solving sessions.
The Ohio State University: (2017-2022) Leading recitation sections and holding office hours for the courses of Precalculus, Calculus I and Calculus II.
Del Valle de Guatemala University: (2012-2014) Teaching assistant for Precalculus, Calculus I and III, Linear Algebra, Discrete Mathematics and Logic.
Directed Reading Program at OSU
Acted as graduate mentor paired with undergraduate students doing a semester-long reading project in mathematics. Spring 2021 (Algorithms and Cryptography), Fall 2019 (Graph Theory).
Online MiniCourse
"Mathematical Software for Teaching: Geogebra and Sage." -Francisco Marroquin University (Guatemala).
Designed and taught a 15 hour online minicourse on using the software of Geogebra and Sage to solve undergraduate level problems in engineering and its implementation in the classroom.
Mathematical Olympiads (in Guatemala)
(2011-2015) Served as an instructor ad honorem training the Guatemalan Team that participated in the International Mathematics Olympiad for high schoolers, teaching Combinatorics and Functional Equations. Participated as team leader for the Guatemalan Team in 2012.
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