Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke





.......................

.......................


Research Interests for Paul L Bendich

Research Interests:

I work in computational topology, which for me means adapting and using tools from algebraic topology in order to study noisy and high-dimensional datasets arising from a variety of scientific applications. My thesis research involved the analysis of datasets for which the number of degrees of freedom varies across the parameter space. The main tools are local homology and intersection homology, suitably redefined in this fuzzy multi-scale context. I am also working on building connections between computational topology and various statistical data analysis algorithms, such as clustering or manifold learning, as well as building connections between computational topology and diffusion geometry.

Recent Publications
  1. Solomon, YE; Bendich, P, Convolutional persistence transforms, Journal of Applied and Computational Topology (January, 2024) [doi[abs]
  2. Koplik, G; Borggren, N; Voisin, S; Angeloro, G; Hineman, J; Johnson, T; Bendich, P, Topological Simplification of Signals for Inference and Approximate Reconstruction, IEEE Aerospace Conference Proceedings, vol. 2023-March (January, 2023), ISBN 9781665490320 [doi[abs]
  3. Solomon, E; Wagner, A; Bendich, P, FROM GEOMETRY TO TOPOLOGY: INVERSE THEOREMS FOR DISTRIBUTED PERSISTENCE, Journal of Computational Geometry, vol. 14 no. 2 Special Issue (January, 2023), pp. 172-196 [doi[abs]
  4. Voisin, S; Hineman, J; Polly, JB; Koplik, G; Ball, K; Bendich, P; D‘Addezio, J; Jacobs, GA; Özgökmen, T, Topological Feature Tracking for Submesoscale Eddies, Geophysical Research Letters, vol. 49 no. 20 (October, 2022) [doi[abs]
  5. Solomon, E; Wagner, A; Bendich, P, From Geometry to Topology: Inverse Theorems for Distributed Persistence, Leibniz International Proceedings in Informatics, LIPIcs, vol. 224 (June, 2022), ISBN 9783959772273 [doi[abs]

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320