Halley Fritze

Topological Data Analysis

Most of my research attention is devoted to topological data analysis from an implementation perspective. I am currently interested in generalizing the mapper graph for applications. First I am interested in a spatial generalization for mapper to a higher dimensional simplicial complex, called 2-mapper, and it's stability. I am also investigating encoding mapper for temporal features for dynamical systems, called temporal mapper.

I also have works in algorithm development for inference of coalescent haplotypes in the genomics library tskit under the mentorship of Peter Ralph, as well as experience as a statistician for the Stanford Genome Technology Center under the mentorship of Sharada Kalanidhi.

Check out this interactive graph for 2-mapper!

Papers

• 2-Mapper: Inferring topological structure through higher order mapper. Halley Fritze, Dev Sinha (in progress 2024).
• Identifying orbits in atmostpheric dynamical systems through temporall enriched mapper graphs. Halley Fritze, Dev Sinha, Joshua Dorrington (in progress).
• Neutrophil State-space Modeling: Combining morphology and dynamics. Halley Fritze, Bhagirath Mehta, Alexandra Stavrianidi, Arianna Cao, Ishani Mukherji, Dev Sinha, Ronald Davis, Sharada Kalanidhi (in progress 2024).
• A forest is more than a bunch of trees: haplotypes in inferred ARGs. Halley Fritze, Peter Ralph, Nathaniel Pope, Jerome Kelleher (2024).
  Submitted.
• Embedded Graph Reconstruction Under Hausdorff Noise. Halley Fritze, Sushovan Majhi, Marissa Masden, Atish Mitra, Michael Stickney (2024).
  Extended Abstract for 2024 Fall Conference in Computational Geometry.
• ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain. Submission #48. Halley Fritze, Marissa Masden.Honorable Mention and Highlighted Submission.
  White Paper (Extended paper in progress).

Talks

• A forest is more than its trees: haplotypes and ARGs. TSKIT-dev Seminar, Virtual, April 2025.
• Topological exploration through higher dimensional mapper graphs. AWM Pittsburgh Graduate Seminar, University of Pittsburgh, March 2025.
• Enhanced topological inference through higher dimensional mapper graphs. Joint Mathematics Meetings, AWM Poster Session, January 2025.
• Identifying orbits in atmospheric dynamical systems through mapper graphs. Joint Mathematics Meetings, January 2025.
• Stability of higher-order covers for mapper. Oregon State University, Topology and Geometry Seminar, November 2024.
• Embedded graph reconstruction under Hausdorff Noise. Fall Workshop in Computational Geometry, Tufts University, November 2024.