Paul L Bendich, Associate Research Professor of Mathematics and Assistant Director of Curricular Engagement of the Information Initiative at Duke
I work in computational topology, which for me means adapting and using tools from algebraic topology in order to study noisy and highdimensional 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 multiscale 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) 6602811  Email Address:   Web Page:  http://www.paulbendich.com  Teaching (Fall 2020):
 MATH 465.01, INTRO HIGH DIM DATA ANALYSIS
Synopsis
 LSRC A247, TuTh 08:30 AM09:45 AM
 (also crosslisted as COMPSCI 445.01, STA 465.01)
 MATH 765.01, INTRO HIGH DIM DATA ANALYSIS
Synopsis
 LSRC A247, TuTh 08:30 AM09:45 AM
 IDS 791.01, DATA SCIENCE DIALOGUES
Synopsis
 Gross Hall 103, F 11:45 AM01:00 PM
 IDS 791.02, DATA SCIENCE DIALOGUES
Synopsis
 TBA, F 04:40 PM05:55 PM
 Office Hours:
 Monday, 11 AM  Noon, Math 210
Friday, 11:45  1 PM Gross Hall 327
 Education:
 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 highdimensional 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 multiscale 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 (2014/08present)
Data RTG Topology for Music and Brains Program, and
Research Independent Study (Cover Trees for Jazz Data)  Derrick Nowak (2014/08present)
Data RTG Topology for Music and Brains Program  Carmen Cox (2014/08present)
Data RTG Topology for Music and Brains Program  Alex Pieloch (2014/08present)
Data RTG Topology for Music and Brains Program  Aaron Park (2014/08present)
comentored with Ezra Miller  Bingxi Lin (May, 2013  July, 2013)
Data RTG REU program on MultiScale Topology for Signals and Images  Michael Ogez (May, 2013  July, 2013)
Data RTG REU program on MultiScale Topology for Signals and Images  Ben Dreyzen (May, 2013  July, 2013)
Data RTG REU program on MultiScale Topology for Signals and Images  Bryan Jacobson (2012  2014)
 Recent Publications
(More Publications)
 Bendich, P; Bubenik, P; Wagner, A, Stabilizing the unstable output of persistent homology computations,
Journal of Applied and Computational Topology
(November, 2019),
pp. 130, SPRINGER [abs]
 Tralie, CJ; Bendich, P; Harer, J, MultiScale Geometric Summaries for SimilarityBased Sensor Fusion,
Ieee Aerospace Conference Proceedings, vol. 2019March
(March, 2019), ISBN 9781538668542 [doi] [abs]
 Bendich, P, Topology, geometry, and machinelearning for tracking and sensor fusion,
Smart Structures and Materials 2005: Active Materials: Behavior and Mechanics, vol. 11017
(January, 2019),
pp. lxxxiiicii, ISBN 9781510627017
 GaragiÄ‡, 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. 2018March
(June, 2018),
pp. 18, IEEE, ISBN 9781538620144 [doi] [abs]
 Tralie, CJ; Smith, A; Borggren, N; Hineman, J; Bendich, P; Zulch, P; Harer, J, Geometric crossmodal comparison of heterogeneous sensor data,
Ieee Aerospace Conference Proceedings, vol. 2018March
(June, 2018),
pp. 110, IEEE, ISBN 9781538620144 [doi] [abs]
 Recent Grant Support
 Geometric and Topological Methods for MultiModal Data Analysis and Fusion, Air Force Office of Scientific Research, FA95501810266, 2018/062021/06.
 BIGDATA: F: DKA: CSD: Topological Data Analysis and MachineLearning with CommunityAccepted Features, National Science Foundation, IIS1447491, 2014/092019/08.
 Conferences Organized
