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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:  http://www.paulbendich.com

Teaching (Fall 2014):

  • MATH 412.01, TOPOLOGY WITH APPLICATIONS Synopsis
    Physics 235, MWF 12:00 PM-12:50 PM
    (also cross-listed as COMPSCI 434.01)
Teaching (Spring 2015):

  • MATH 212.02, MULTIVARIABLE CALCULUS Synopsis
    Soc/Psych 129, MWF 01:40 PM-02:30 PM
Office Hours:

Monday, 2-3:30
Friday, 9:30-11
Specialties:

Topology
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

  • Marshall Ratliff (2014/08-present)
    Data RTG Topology for Music and Brains Program 
  • Derrick Nowak (2014/08-present)
    Data RTG Topology for Music and Brains Program 
  • Carmen Cox (2014/08-present)
    Data RTG Topology for Music and Brains Program 
  • Alex Pieloch (2014/08-present)
    Data RTG Topology for Music and Brains Program 
  • Aaron Park (2014/08-present)
    co-mentored with Ezra Miller 
  • 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  

 

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

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