I am broadly interested in geometric and topological data analysis, an area of mathematics at the intersection of many mathematical fields: geometry, topology, linear algebra, optimization, computing, and machine learning. I am particularly interested in developing and applying tools from computational geometry and topology to a wide variety of data sets from biological aggregations to knowledge networks.
Here are some of my grant projects:
Here are some of my grant projects:
- Co-founder of the Women in Computational Topology (WinCompTop) listserv (join by sending a blank email to: <[email protected]>) and was the PI of the NSF grant to fund the inaugural WinCompTop Workshop at the IMA in August of 2016. For a description of the program, see this write-up in the AWM newsletter.
- PI on the collaborative research project HNDS-R: Stepping out of flatland: Complex networks, topological data analysis, and the progress of science with collaborators Russell Funk and Jason Owen-Smith.
- PI on the collaborative research project CDS&E-MSS: Exact Homological Algebra for Computational Topology (ExHACT) with collaborators Chad Giusti and Gregory Henselman-Petrusek. We are developing the Open Applied Topology software suite.
- PI of the NSF-CBMS grant to fund the regional research conference Topological Data Analysis: Theory and Applications held at Macalester College in June of 2017.
Research Collaborators, supported by NSF WinCompTop grant, IMA, and AIM SQuaRE
Manuscripts
Note: An asterisk denotes an undergraduate student co-author.
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26. Understanding U.S. Racial Segregation Through Persistent Homology
25. A Survey of Simplicial, Relative, and Chain Complex Homology Theories for Hypergraphs (Preprint) 24. U-match Factorization: Sparse Homological Algebra, Lazy Cycle Representatives, and Dualities in Persistent (Co)Homology (Preprint) 23. A Topology Scavenger Hunt to Introduce Topological Data Analysis (Preprint) 22. Image Triangulation Using the Sobel Operator for Vertex Selection 21. Local Versus Global Distances for Zigzag Persistence Modules (Preprint) 20. Capturing Dynamics of Time-Varying Data via Topology (Preprint)
19. Minimal Cycle Representatives in Persistent Homology using Linear Programing: an Empirical Study with User's Guide (Preprint) 18. How to Tutorial-a-thon 17. On Homotopy Types of Vietoris-Rips Complexes of Metric Gluings (Preprint) 16. Topological Data Analysis of Collective Motion 15. The Relationship Between the Intrinsic Cech and Persistence Distortion Distances for Metric Graphs (Preprint) 14. Analyzing Collective Motion with Machine Learning and Topology (Preprint) 13. Assessing Biological Model Validity using Topological Data Analysis (Preprint) 12. Vietoris-Rips and Čech Complexes of Metric Gluings 11. Mind the Gap: A Study in Global Development through Persistent Homology (Preprint) 10. A Complete Characterization of the 1-Dimensional Intrinsic Cech Persistence Diagrams for Metric Graphs (Preprint) 9. Sparse Locally Linear Embedding 8. Stratifying High Dimensional Data Based on Proximity to the Convex Hull Boundary 7. Persistence Images: A Stable Vector Representation of Persistent Homology 6. Persistent Homology on Grassmann Manifolds for Analysis of Hyperspectral Movies (Preprint) 5. Topological Data Analysis of Biological Aggregation Models 4. An Application of Persistent Homology on Grassmann Manifolds for the Detection of Signals in Hyperspectral Imagery (Preprint) 3. Reflections on Math Students' Circles: Two Personal Stories from Colorado 2. Flipped Calculus: A Study of Student Performance and Perceptions 1. On the Strengthening of Topological Signals in Persistent Homology through Vector Bundle Based Maps |
O. Friesen and L. Ziegelmeier
E. Gasparovic, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, and L. Ziegelmeier H. Hang, C. Giusti, L. Ziegelmeier, G. Henselman-Petrusek L. Ziegelmeier O. Laske and L. Ziegelmeier E. Gasparovic, M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, and L. Ziegelmeier L. Xian, H. Adams, C. Topaz, and L. Ziegelmeier L. Li, C. Thompson, G. Henselman-Petrusek, C. Giusti, and L. Ziegelmeier H. Adams, H. Dal Poz Kourimska, T. Heiss, S. Percival, and L. Ziegelmeier M. Adamaszek, H. Adams, E. Gasparovic, M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, and L. Ziegelmeier H. Adams, M-V Ciocanel, C.M. Topaz, and L. Ziegelmeier E. Gasparovic, M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, and L. Ziegelmeier D. Bhaskar, A. Manhart, J. Milzman, J. Nardini, K. Storey, C.M. Topaz, and L. Ziegelmeier M. Ulmer*, L. Ziegelmeier, and C.M. Topaz M. Adamaszek, H. Adams, E. Gasparovic, M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, and L. Ziegelmeier A. Banman* and L. Ziegelmeier E. Gasparovic, M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, and L. Ziegelmeier L. Ziegelmeier, M. Kirby, and C. Peterson L. Ziegelmeier, M. Kirby, and C. Peterson H. Adams, S. Chepushtanova, T. Emerson, E. Hanson, M. Kirby, F. Motta, R. Neville, C. Peterson, P. Shipman, and L. Ziegelmeier S. Chepushtanova, M. Kirby, C. Peterson, and L. Ziegelmeier C.M. Topaz, L. Ziegelmeier, and T. Halverson S. Chepushtanova, M. Kirby, C. Peterson, and L. Ziegelmeier D. White and L. Ziegelmeier L. Ziegelmeier and C.M. Topaz E. Hanson, F. Motta, C. Peterson, and L. Ziegelmeier |
Under Review
Under Review Under Review 2024 2024 2022 2022 2021 2021 2020 2020 2020 2019 2019 2018 2018 2018 2017 2017 2017 2016 2015 2015 2015 2015 2012 |
Sample Talks
- Minimal Cycle Representatives in Persistent Homology using Linear Programming (Slides)
- Presentation to Applied Algebraic Topology Research Network Vietoris Rips Seminar, September 2022
- Using Topology to Measure Dynamics of Time-Varying Systems (Slides)
- Presentation at MBI Workshop "Optimal Transport, Topological Data Analysis and Applications to Shape and Machine Learning" July 2020
- On The Data of Images (Slides)
- Section NExT presentation, Mathematical Association of America North Central Section Spring Meeting, April 2019
- Measuring the Shape of Data (Slides)
- Plenary presentation for the Midwest Undergraduate Mathematics Symposium, April 2018
- Persistence Images: A Stable Vector Representation of Persistent Homology (Slides)
- Presentation to Applied Algebraic Topology Research Network, September 2017
Books Edited
PhD Dissertation
Exploiting Geometry, Topology, and Optimization for Knowledge Discovery in Big Data
My doctoral education was in the Department of Mathematics at Colorado State University. My dissertation was in the area of geometric and topological data analysis with an emphasis on manifold learning, optimization, image analysis, and classification. This work was jointly supervised by my advisors Dr. Michael Kirby and Dr. Chris Peterson. While a graduate student at Colorado State University, I was a member of the Pattern Analysis Lab (PAL), which involves undergraduates, graduate students, post-docs, and professors interacting in an informal setting. This write-up describes a research project that arose from PAL.
My doctoral education was in the Department of Mathematics at Colorado State University. My dissertation was in the area of geometric and topological data analysis with an emphasis on manifold learning, optimization, image analysis, and classification. This work was jointly supervised by my advisors Dr. Michael Kirby and Dr. Chris Peterson. While a graduate student at Colorado State University, I was a member of the Pattern Analysis Lab (PAL), which involves undergraduates, graduate students, post-docs, and professors interacting in an informal setting. This write-up describes a research project that arose from PAL.
