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

Current Projects

Reach out to learn more about any of the projects I am currently working on.

• Multi-Channel Image Classification using the WECT. The Weighted Euler Characteristic Transform (WECT) is a popular topological representation of image data in classification tasks. Under the direction of Prof. Brittany Fasy, Prof. Jessi Cisewski-Kehe, and Dr. Alex McCleary, I am working on extensions that allow us to use this topological descriptor in more general settings.


• Graphical Network Representations and DSGRN. Under the direction of Prof. Tomas Gedeon and Elizabeth Andreas, I am working on combining the extensive theory of the DSGRN framework with theory in evaluating the dynamics of graphical representations of networks.


• A Geometric Simulation of Prostate Biopsy Slide Images. Topological machine learning algorithms have proven useful in the grading of prostate cancer biopsy images. However, a bottleneck in these processes is access to sufficient volumes of data. We present a geometric and stochastic model for generating synthetic biopsy slide images.

Selected Projects, Publications, and Preprints

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


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


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


• E. Quist, D. Millman. A Probabilistic Approach to GPS Art. 2021 AMSA Research Symposium, 2021 MSU Student Research Celebration.

Awards and Appointments

• MSU School of Computing Outstanding Undergraduate Researcher, May 2024
• Reviewer for La Matematica, March 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

Talks

The following talks were all given in the seminar or book club of the MSU Computational Topology and Geometry Research Group

• Paper Presentation; Demystifying Latschev's Theorem: Manifold Reconstruction from Noisy Data; Majhi, 3/25/24
• Paper Presentation; Isometric Deformation Modelling for Object Recognition; Smeets, Fabry, Hermans, Vandermeulen, and Suetens, 12/5/23
• Research Update; The Weighted Euler Characteristic Transform for Image Shape Classification, 11/1/23
• Paper Presentation; A Concise and Provably Informative Multi-Scale Signature Based on Heat Diffusion; Sun, Ovsjanikov, and Guibas, 10/11/23
• Paper Presentation; A Survey on Shape Correspondence; van Kaick, Zhang, Hamarneh, Cohen-Or, 9/7/23
• Research Update; Intrinsic Validation of Manifold Learning Techniques, 7/18/23
• Paper Presentation; FibeRed: Fiberwise Dimensionality Reduction of Topologically Complex Data with Vector Bundles; Scoccola and Perea, 6/27/23
• Book Club; Oriented Matroids and Linear Programming, 6/22/23
• Book Club; Introduction to Oriented Matroids, 6/8/23
• Paper Presentation; The Christoffel-Darboux Kernel for Topological Data Analysis; Hoefgeest and Slot, 4/24/23 - 5/1/23
• Paper Presentation; Shortest Paths in Portalgons; Löffler, Ophelders, Staals, and Silveira, 2/15/23
• Foundations; Toplogical Spaces, Metric Spaces, and Path Connectedness, 11/30/22
• Foundations; The Interleaving Distance, 10/18/22
• Foundations; The Konigsberg Bridge Problem and Euler Characteristics, 9/7/22
• Foundations; Algorithm Validation and Geodesic Precision/Recall, 4/23/22
• Foundations; Principal Component Analysis and Motivations for Manifold Learning, 2/12/22
• Foundations; The Fréchet Distance, 9/23/21