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Paul L Bendich, Assistant 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
Office Phone:  (919) 660-2811
Email Address: send me a message
Web Page:  http://www.paulbendich.com

Teaching (Fall 2018):

  • MATH 465.01, INTRO HIGH DIM DATA ANALYSIS Synopsis
    Gross Hall 318, TuTh 08:30 AM-09:45 AM
  • MATH 765.01, INTRO HIGH DIM DATA ANALYSIS Synopsis
    Gross Hall 318, TuTh 08:30 AM-09:45 AM
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. 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, ISBN 9781538620144 [doi]  [abs]
  2. Tralie, CJ; Smith, A; Borggren, N; Hineman, J; Bendich, P; Zulch, P; Harer, J, Geometric Cross-Modal Comparison of Heterogeneous Sensor Data, Proceedings of the 39th IEEE Aerospace Conference (March, 2018)  [abs]
  3. Bendich, P; Chin, SP; Clark, J; Desena, J; Harer, J; Munch, E; Newman, A; Porter, D; Rouse, D; Strawn, N; Watkins, A, Topological and statistical behavior classifiers for tracking applications, Ieee Transactions on Aerospace and Electronic Systems, vol. 52 no. 6 (December, Accepted, 2016), pp. 2644-2661 [doi]  [abs]
  4. Bendich, P; Gasparovic, E; Harer, J; Tralie, C, Geometric Models for Musical Audio Data, Proceedings of the 32st International Symposium on Computational Geometry (SOCG) (June, 2016)
  5. Bendich, P; Gasparovic, E; Harer, J; Tralie, C, Geometric models for musical audio data, Leibniz International Proceedings in Informatics, Lipics, vol. 51 (June, 2016), pp. 65.1-65.5, ISBN 9783959770095 [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