Paul L Bendich, Associate Research Professor
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 datacentered applications. My initial training was in a recentlyemerging field called topological data analysis (TDA). I have been responsible for several essential and widelyused 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 theoremproof 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 multitarget tracking, to multimodal 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) 6602811  Email Address:   Web Page:  http://www.paulbendich.com  Teaching (Fall 2022):
 MATH 412.01, TOPOLOGICAL DATA ANALYSIS
Synopsis
 Gross Hall 318, TuTh 08:30 AM09:45 AM
 (also crosslisted as COMPSCI 434.01)
 MATH 713.01, TOPOLOGICAL DATA ANALYSIS
Synopsis
 Gross Hall 318, TuTh 08:30 AM09:45 AM
 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)
 Solomon, E; Wagner, A; Bendich, P, From Geometry to Topology: Inverse Theorems for Distributed Persistence,
Leibniz International Proceedings in Informatics, Lipics, vol. 224
(June, 2022), ISBN 9783959772273 [doi] [abs]
 Smith, A; Bendich, P; Harer, J, Persistent obstruction theory for a model category of measures with applications to data merging,
Transactions of the American Mathematical Society, Series B, vol. 8 no. 1
(February, 2021),
pp. 138, American Mathematical Society (AMS) [doi] [abs]
 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+
 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]
 Yao, L; Bendich, P, Graph Spectral Embedding for Parsimonious Transmission of Multivariate Time Series,
Ieee Aerospace Conference Proceedings
(March, 2020), ISBN 9781728127347 [doi] [abs]
 Recent Grant Support
 Geometric and Topological Methods for MultiModal Data Analysis and Fusion, Air Force Office of Scientific Research, FA95501810266, 2018/062023/06.
 Conferences Organized
