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Math @ Duke



Paul L. Bendich, Assistant Research Professor

Computational Topology, Intersection Homology and Stratified Spaces, Applications of Algebraic Topology to the Analysis of Scientific Datasets.

Contact Info:
Office Location:  210 Physics
Office Phone:  (919)-660-2811
Email Address: send me a message
Web Page:

Teaching (Fall 2014):

    Physics 235, MWF 12:00 PM-12:50 PM
    (also cross-listed as COMPSCI 434.01)
Office Hours:

Wednesday 12-1
Friday, 3-4

Applied Math
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.

Undergraduate Research Supervised

  • Bingxi Lin (May, 2013 - July, 2013)
    Data RTG REU program on Multi-Scale Topology for Signals and Images 
  • Michael Ogez (May, 2013 - July, 2013)
    Data RTG REU program on Multi-Scale Topology for Signals and Images 
  • Ben Dreyzen (May, 2013 - July, 2013)
    Data RTG REU program on Multi-Scale Topology for Signals and Images 
  • Bryan Jacobson (2012 - 2014)  
Recent Publications   (More Publications)

  1. Paul Bendich, Herbert Edelsbrunner, Dmitriy Morozov, and Amit Patel, Homology and Robustness of Level and Interlevel Sets, edited by Gunnar Carlsson, Homology, Homotopy, and Applications, vol. 15 no. 1 (March, 2013), pp. 51-72  [abs]
  2. Liz Munch, Paul Bendich, Kate Turner, Sayan Mukherjee, Jonathan Mattingly, and John Harer, Probabalistic Frechet Means and Statistics on Vineyards (Submitted, 2013) [6530]  [abs] [author's comments]
  3. with Sergio Cabello and Herbert Edelsbrunner, A Point Calculus for Interlevel Set Homology, Pattern Recognition Letters, vol. 33 no. 11 (August, 2012), pp. 1436-1444  [abs]
  4. with Jacob Harer and John Harer, A Persistent Homology Based Geodesic Distance Estimator (Submitted, 2012)
  5. with Bei Wang and Sayan Mukherjee, Local Homology Transfer and Stratification Learning, Proc. of 24th Sympos. on Discrete Algorithms (2012)
Recent Grant Support

  • Collaborative Research: Statistical inference for stratified spaces and persistent homology, National Science Foundation, DMS-1361208, 2014/07-2017/06.      
Conferences Organized

  • conference, December 2011
ph: 919.660.2800
fax: 919.660.2821

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