Research

My research mainly lies at the intersection of applied algebraic topology, topological data analysis, and topological robotics. A central theme of my work is understanding how the topology of a space changes when several geometric or physical parameters vary simultaneously. I am also interested in directed topology and applied geometry.

Multiparameter persistent homology of restricted configuration spaces of metric graphs

• Persistent Combinatorial Model of the Restricted Second Configuration Space of Metric Star Graphs, with Murad Özaydın.
• Notes on Pointwise Finite-Dimensional 2-Parameter Persistence Modules, with Murad Özaydın.
• Persistent Homology of Configuration Spaces of Trees.

Directed topology

• Gromov–Hausdorff Distance for Directed Spaces, with Lisbeth Fajstrup, Brittany Terese Fasy, Lydia Mezrag, Tatum Rask, Francesca Tombari, and Živa Urbančič.

Applied geometry

• Covariance and Principal Component Analysis on Riemannian Manifolds and Graphs, with Luiz Hartmann and Washington Mio.