About Me
I am a PhD student in mathematics at the University of Florida. My research focuses on computational topology and geometry, with applications to machine learning. My current project focuses on creating efficient algorithms and data structures for working with Bregman divergences, a family of dissimilarity measures used in machine learning and data analysis, and their induced geometries.
My previous project was in computational topology: designing an algorithm for more efficiently computing generators of persistent homology.
I am currently looking to transition into industry after graduation, and am interested in roles in data science, machine learning, and software engineering. You can find more about my qualifications in my resume.
I have previously taught Algebra I for high school and middle school students, and taught and TA’d many college math courses. For a detailed list, please see my CV.
My primary interests lie in computational topology and geometry, information geometry, data science, and machine learning. I am also interested in computer vision, animation, information theory and category theory.
Projects
An efficient extention of Kd-trees to a non-metric setting often used in machine learning.
An extension of the kd-tree data structures for decomposable Bregman divergences. Despite often being assymmetric and never satisfy the triangle inequality, Bregman geometries admit a well-behaved geometry. This allows us to extend the Kd-tree beyond metric spaces and develop efficient algorithms.
This project is in collaboration with Dr. Hubert Wagner, and built off of the ANN package made by Arya and Mount.
Education
PhD in mathematics
University of Florida
2021 -- 2026
Studied computational topology and geometry under the supervision of Dr. Hubert Wagner. My research focuses on the topological and geometric analysis of machine learning models via their outputs or internal representations.
- Dissertation: “Efficient tools for the Geometric and Topological Analysis of Machine Learning Models”
MS in mathematics
Cal Poly, San Luis Obispo
2018 — 2020
Studied pure mathematics and taught precalculus and calculus courses as a graduate teaching assistant. Graduated with honors.
My master’s thesis focused on the theory behind topological data analysis, in particular persistent homology, and explored its applications to time series analysis.
BSc in mathematics; Minor in statistics
Cal Poly, San Luis Obispo
2011 — 2016
Studied applied mathematics with a focus on computer science, with a minor in statistics.
Experience
Topological data analysis seminar organizer
University of Florida
Aug 2024 — Dec 2024
https://tda.math.ufl.edu/fall24/
Organized and led a seminar on topological data analysis for graduate students at the University of Florida. The seminar covers recent advances in theory and applications of topological data analysis.
During my time as seminar organizer, I shifted focus toward applications of TDA and algorithm design.
Taught Algebra I to high school and middle school students at a private school in San Luis Obispo, CA. These courses were hybrid in-person and online due to the COVID-19 pandemic. I created lesson plans, assignments, and assessments for the course.
Was a member of a curriculum development team to adjust the curriculum to have a more gradual flow of concepts and ease the introduction to higher degree polynomials.
Graduate Teaching Assistant
Cal Poly, San Luis Obispo
2018 — 2020
Instructor of Record for Precalculus (MATH 116, 3 courses; MATH 118, 1 course) and Business Calculus (MATH 221, 2 courses) courses.
For these courses, I wrote syllabi, created and graded assignments and exams, held office hours, and taught lectures. During the Spring 2020 quarter, I adapted to online teaching for the COVID-19 pandemic and created online lectures and materials for students.
Publications and Presentations
For a more in depth list of presentations and talks, please refer to my CV. You can find a general overview of my research projects here.
- “Computing Representatives of Persistent Homology Generators with a Double Twist”
P., Wagner- Published and presented at the 25th Canadian Conference on Computational Geometry (CCCG 2023).
- “Fast Kd-Trees for the Kullback—Leibler Divergence and Other Decomposable Bregman Divergences”
P., Wagner- Published and presented at the 19th Algorithms and Data Structures Symposium (WADS 2025).
- “Bregman-Hausdorff divergence: strengthening the connections between computational geometry and machine learning”
P., Dal Poz Kouřimskà, Wagner- Published in Machine Learning and Knowledge Extraction 2025.
More about me
Outside of academia, I enjoy bouldering, lifting, drawing, and cooking.
In addition to English, I am conversationally fluent in Vietnamese and Japanese, and am currently learning Spanish.