My research interests are in geometry, topology, and their applications. In particular, I am focused on inverse problems for topological and geometric invariants, topological optimization and approximation, and the connections between them. I have also been working in the area of data fusion, using techniques from geometry and topology to analyze and synthesize time series data.
- A Fast and Robust Method for Global Topological Functional Optimization (with Alex Wagner and Paul Bendich) [arXiv], in which we propose a new framework for optimizing topological functionals on simplicial complexes that is faster, and produces more robust optima, than prior methods.
- Geometric Fusion via Joint Delay Embeddings (with Paul Bendich) [arXiv], in which we use geometric and topological methods to fuse time series (accepted to Fusion 2020). Won 2nd runner up in the general category of the Fusion 2020 Best Paper Award!
- Intrinsic Topological Transforms via the Distance Kernel Embedding (with Clément Maria, Steve Oudot) [arXiv], in which we use spectral geomety to define a novel topological transform (accepted at SOCG).
- Inverse Problems in Topological Persistence (with Steve Oudot) [arXiv], a survey on inverse problems in applied topology (accepted to Proceedings of Abel Symposium).
- Barcode Embeddings for Metric Graphs (with Steve Oudot) [arXiv], in which we study the inverse problem for the intrinsic persistent homology transform on metric graphs (accepted to Algebraic and Geometric Topology).
- Relaxing the Integral Text: A Challenge for the Advanced Calculus Student (with Paul Carter). [College Mathematics Journal]