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Paul L Bendich, Associate Research Professor of Mathematics and Assistant Director of Curricular Engagement of the Information Initiative at Duke

I am a mathematician whose main research focus lies in adapting theory from ostensibly pure areas of mathematics, such as topology, geometry, and abstract algebra, into tools that can be broadly used in many data-centered
applications.
My initial training was in a recently-emerging field called topological data analysis (TDA). I have been
responsible for several essential and widely-used elements of its theoretical toolkit, with a particular
focus on building TDA methodology for use on stratified spaces. Some of this work involves the
creation of efficient algorithms, but much of it centers around theorem-proof mathematics, using proof techniques
not only from algebraic topology, but also from computational geometry, from probability, and from abstract
algebra. Recently, I have done foundational work on TDA applications in several areas, including to neuroscience, to multi-target tracking, to multi-modal data fusion, and to a probabilistic theory of database merging. I am also becoming involved in efforts to integrate TDA within deep learning theory and practice.

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 (Fall 2021):

  • MATH 465.01, INTRO HIGH DIM DATA ANALYSIS Synopsis
    LSRC A247, TuTh 08:30 AM-09:45 AM
    (also cross-listed as COMPSCI 445.01, STA 465.01)
  • MATH 765.01, INTRO HIGH DIM DATA ANALYSIS Synopsis
    LSRC A247, TuTh 08:30 AM-09:45 AM
  • IDS 791.01, DATA SCIENCE DIALOGUES Synopsis
    Online ON, F 11:45 AM-01:00 PM
  • IDS 791.02, DATA SCIENCE DIALOGUES Synopsis
    TBA, -
Teaching (Spring 2022):

  • MATH 238L.001, DATA ANALYSIS AND DECISION SCI Synopsis
    Gross Hall 318, TuTh 08:30 AM-09:45 AM
    (also cross-listed as EGR 238L.001)
  • IDS 791.01, DATA SCIENCE DIALOGUES Synopsis
    Gross Hall 103, F 12:00 PM-01:15 PM
  • IDS 791.02, DATA SCIENCE DIALOGUES Synopsis
    TBA, -
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. Solomon, E; Wagner, A; Bendich, P, A Fast and Robust Method for Global Topological Functional Optimization, 24th International Conference on Artificial Intelligence and Statistics (Aistats), vol. 130 (2021), pp. 109-+
  2. Solomon, E; Bendich, P, Geometric fusion via joint delay embeddings, Proceedings of 2020 23rd International Conference on Information Fusion, Fusion 2020 (July, 2020) [doi]  [abs]
  3. Yao, L; Bendich, P, Graph Spectral Embedding for Parsimonious Transmission of Multivariate Time Series, Ieee Aerospace Conference Proceedings (March, 2020), ISBN 9781728127347 [doi]  [abs]
  4. Blasch, E; Grewe, LL; Waltz, EL; Bendich, P; Pavlovic, V; Kadar, I; Chong, CY, Machine learning in/with information fusion for infrastructure understanding, panel summary, Smart Structures and Materials 2005: Active Materials: Behavior and Mechanics, vol. 11423 (January, 2020), ISBN 9781510636231 [doi]  [abs]
  5. 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]
Recent Grant Support

  • Geometric and Topological Methods for Multi-Modal Data Analysis and Fusion, Air Force Office of Scientific Research, FA9550-18-1-0266, 2018/06-2022/06.      
  • BIGDATA: F: DKA: CSD: Topological Data Analysis and Machine-Learning with Community-Accepted Features, National Science Foundation, IIS-1447491, 2014/09-2019/08.      
Conferences Organized

 

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

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