My Research

My research focuses on a variety of topics from the fields of computational topology, computational geometry, and network & graph theory. I particularly enjoy extending techniques in topological data analysis, or applying topological & geometric descriptors to machine learning pipelines. Often, I am interested in utilizing these techniques in the context of real world and applied settings.

Keywords: topological machine learning, topological deep learning, topological and geometric descriptors, manifold learning, network theory, topological data analysis,

Selected Projects, Publications, and Preprints

Note that non-alphabetical author listing is denoted with an asterisk.

• Cisewski-Kehe, J., Fasy, B. T., McCleary, A., & Quist, E. (2026). Tensor Computation of Euler Characteristic Functions and Transforms. 42nd International Symposium on Computational Geometry (SoCG 2026), LIPIcs, Vol. 367, pp. 32:1-32:17. doi:10.4230/LIPIcs.SoCG.2026.32
   Keywords: GPU accelerated computation, Euler characteristic transform, topological data analysis


• Andreas, E., Quist, E.*, & Gedeon, T. (2025). Petri Net on Expanded Networks Computes the Dynamics of Finite Multilevel Models. Interface Focus, 15(3), 20240059. https://doi.org/10.1098/rsfs.2024.0059
   Keywords: boolean networks, dynamics, Petri nets, regulatory networks


• Holmgren, B., Quist, E.*, Schupbach, J., Fasy, B. T., & Rieck, B. (2024). The Manifold Density Function: An Intrinsic Method for the Validation of Manifold Learning. preprint: arXiv:2402.09529
   Keywords: manifold learning, algorithm validation, Ripley's K-function, hypersurfaces


• Cisewski-Kehe, J., Fasy, B. T., Giriyan, D., & Quist, E. (2023). The Weighted Euler Characteristic Transform for Image Shape Classification. preprint: arXiv:2307.13940
   Keywords: topological data analysis, persistent homology, image data, shape analysis, classification


• B. McCoy, E. Quist, & A. Schenfisch. (2021). Catching Polygons. 2021 Fall Workshop on Computational Geometry. arXiv:2201.01286
   Keywords: line arrangements, nets, computational geometry, optimization


• Quist, E.* & Millman, D. (2021). A Probabilistic Approach to GPS Art. 2021 AMSA Research Symposium.
   Keywords: Gaussian mixture models, map matching, trajectory clustering

Talks and Activities

• October 4th, 2026 - Scaling Euler Characteristic Functions and Transforms for Modern Machine Learning. Special Session on Artificial Intelligence and Machine Learning Methods in Topological Data Analysis; American Mathematical Society Fall Eastern Sectional Meeting . George Washington University, Washington, DC.
   Abstract
• May 2024 - An Intrinsic Method for the Validation of Manifold Learning. Montana State University Student Research Celebration. Montana State University, Bozeman, MT.
• April 2021 - A Probabilistic Approach to GPS Art. 2021 AMSA Research Symposium.

Awards and Appointments

• MSU School of Computing Outstanding Undergraduate Researcher, May 2024
• Panel Moderator for the Career Discussions Panel at MSU Topology for Data Science (T4DS) Workshop, April 2023
• MSU Nominee, Computing Research Association Outstanding Undergraduate Award, October 2021

Supporting Grants

I have received support (directly or indirectly) from the following grants.

• QuBBD: Collaborative Research: Quantifying Morphologic Phenotypes in Prostate Cancer - Developing Topological Descriptors for Machine Learning Algorithms, National Science Foundation 1664858
• FRG: Collaborative Research: Statistical Approaches to Topological Data Analysis that Address Questions in Complex Data, National Science Foundation 1854336
• CAREER: Topological Descriptors, National Science Foundation 2046730
• Intrinsic Validation of Manifold Learning Techniques, Montana State University Undergraduate Scholars Program, October 2023 - May 2024
• A Probabilistic Approach to GPS Art, Montana State University Undergraduate Scholars Program, May 2021 - December 2021