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Paul L Bendich, Associate Research Professor of Mathematics and Assistant Director of Curricular Engagement

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.

Contact Info:
Office Location:  121 Physcis Bldg, Durham, NC 27708
Office Phone:  (919) 660-2811
Email Address: send me a message
Web Page:  http://www.paulbendich.com

Teaching (Spring 2020):

  • MATH 238L.001, DATA ANALYSIS AND DECISION SCI Synopsis
    Physics 150, WF 08:30 AM-09:45 AM
    (also cross-listed as EGR 238L.001)
  • MATH 238L.01L, DATA ANALYSIS AND DECISION SCI Synopsis
    Gray 228, Tu 10:05 AM-11:20 AM
    (also cross-listed as EGR 238L.01L)
  • IDS 791.01, DATA SCIENCE DIALOGUES Synopsis
    Gross Hall 103, F 11:45 AM-01:00 PM
  • IDS 791.02, DATA SCIENCE DIALOGUES Synopsis
    SEE INSTRU, F 04:40 PM-05:55 PM
Office Hours:

Monday, 11 AM - Noon, Math 210

Friday, 11:45 - 1 PM Gross Hall 327
Education:

Ph.D.Duke University2008
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, and Research Independent Study (Cover Trees for Jazz Data) 
  • 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. Bendich, P; Bubenik, P; Wagner, A, Stabilizing the unstable output of persistent homology computations, Journal of Applied and Computational Topology (November, 2019), pp. 1-30, SPRINGER  [abs]
  2. Tralie, CJ; Bendich, P; Harer, J, Multi-Scale Geometric Summaries for Similarity-Based Sensor Fusion, Ieee Aerospace Conference Proceedings, vol. 2019-March (March, 2019), ISBN 9781538668542 [doi]  [abs]
  3. Bendich, P, Topology, geometry, and machine-learning for tracking and sensor fusion, Smart Structures and Materials 2005: Active Materials: Behavior and Mechanics, vol. 11017 (January, 2019), pp. lxxxiii-cii, ISBN 9781510627017
  4. Garagić, D; Peskoe, J; Liu, F; Claffey, MS; Bendich, P; Hineman, J; Borggren, N; Harer, J; Zulch, P; Rhodes, BJ, Upstream fusion of multiple sensing modalities using machine learning and topological analysis: An initial exploration, Ieee Aerospace Conference Proceedings, vol. 2018-March (June, 2018), pp. 1-8, IEEE, ISBN 9781538620144 [doi]  [abs]
  5. Tralie, CJ; Smith, A; Borggren, N; Hineman, J; Bendich, P; Zulch, P; Harer, J, Geometric cross-modal comparison of heterogeneous sensor data, Ieee Aerospace Conference Proceedings, vol. 2018-March (June, 2018), pp. 1-10, IEEE, ISBN 9781538620144 [doi]  [abs]
Recent Grant Support

  • Geometric and Topological Methods for Multi-Modal Data Analysis and Fusion, Air Force Office of Scientific Research, FA9550-18-1-0266, 2018/06-2021/06.      
  • BIGDATA: F: DKA: CSD: Topological Data Analysis and Machine-Learning with Community-Accepted Features, National Science Foundation, IIS-1447491, 2014/09-2019/08.      
  • Collaborative Research: Statistical inference for stratified spaces and persistent homology, National Science Foundation, DMS-1361208, 2014/07-2017/06.      
  • Topological Signal Analysis for Multi-Modal Data Analysis, Geometric Data Analytics, Inc., 2016/08-2017/01.      
Conferences Organized

 

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

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