I am a computational mathematician with a deep interest in interdisciplinary applications and data science using topological and geometric techniques. My thesis work focused on constructions and comparisons of weighted directed graphs for representing multidimensional time series data. These constructions use tools from Topological Data Analysis (TDA) and have applications in biological network analysis. Additionally, I work on problems in data visualization by studying representations of high dimensional data as a graph. I have also worked on projects concerning inverse problems in TDA and directed topology.
- Extremal Event Graphs: A (Stable) Tool for Analyzing Noisy Time Series. Published in the Journal of Foundations of Data Science. 2023. This work is joint with Bree Cummins, Brittany Terese Fasy, and Tomas Gedeon.
- Combinatorial Conditions for Directed Collapsing. Published in Research in Computational Topology 2. 2022. This work is joint with Robyn Brooks, Stefania Ebli, Lisbeth Fajstrup, Brittany Terese Fasy, Nicole Sanderson, and Elizabeth Vidaurre.
- Reconstructing Embedded Graphs from Persistence Diagrams. Published in Computational Geometry Theory and Applications (CGTA). 2020. Joint with Brittany Terese Fasy, Rostik Mertz, Samuel Micka, David L. Millman, Daniel Salinas, Anna Schenfisch, Jordan Schupbach, and Lucia Williams.
- Towards Directed Collapsibility. Published in Advances in Mathematical Sciences: AWM Research Symposium. 2020. Joint with Robyn Brooks, Stefania Ebli, Lisbeth Fajstrup, Brittany Terese Fasy, Catherine Ray, Nicole Sanderson, and Elizabeth Vidaurre.
- Learning Simplicial Complexes from Persistence Diagrams. Published in the 2018 proceedings on the Canadian Conference in Computational Geometry (CCCG). Joint with Brittany Terese Fasy, Rostik Mertz, Samuel Micka, David L. Millman, Daniel Salinas, Anna Schenfisch, Jordan Schupbach, and Lucia Williams.
- Loss of TXNIP enhances peritoneal metastasis and can be abrogated by dual TORC1/2 inhibition. Published in Oncotarget. 2018. Joint with Douglas Spaeth-Cook, Mark Burch, Bryce Demoret, Nicholas Grosenbacher, Jason David, Colin Stets, David Cohen, Reena Shakya, John L. Hays, and James L. Chen.
- A shape-context model for matching placental chorionic surface vascular networks. Published in Image Analysis and Stereology. 2018. Joint with Elin Farnell, Shawn Farnell, Jen-Mei Chang, Madison Hoffman, Kathryn Keaty, Sanford Lederman, Carolyn Salafia.
- G-Mapper: Learning a Cover in the Mapper Construction. 2023. This work is joint with Enrique Alvarado, Emily Fischer, Kang-Ju Lee, Sourabh Palande, Sarah Percival, and Emilie Purvine.
- Computing and Comparing Extremal Event DAGs. This code is written and maintained by me, Bree Cummins, and Riley Narem.