Research

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.

Publications

  1. 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.
  2. 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!
  3. 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).
  4. Inverse Problems in Topological Persistence (with Steve Oudot) [arXiv], a survey on inverse problems in applied topology (accepted to Proceedings of Abel Symposium).
  5. 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).
  6. Relaxing the Integral Text: A Challenge for the Advanced Calculus Student (with Paul Carter). [College Mathematics Journal]
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