Paul L. Bendich, Visiting Assistant Professor

Computational Topology, Intersection Homology and Stratified Spaces, Applications of Algebraic Topology to the Analysis of Scientific Datasets.

Contact Info:

Office Location:	210 Physics
Office Phone:	(919)-660-2811
Email Address:
Web Page:	http://www.paulbendich.com

Teaching (Fall 2012):

• MATH 412.01, TOPOLOGY WITH APPLICATIONS Synopsis

  West Duke 08A, TuTh 10:05 AM-11:20 AM

  (also cross-listed as COMPSCI 434.01)

Office Hours:

Tuesday, 12:30=1:30
Wednesday, 1-2

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.

Recent Publications   (More Publications)

1. with Bei Wang and Sayan Mukherjee, Local Homology Transfer and Stratification Learning, Proc. of 24th Sympos. on Discrete Algorithms (Accepted, 2012)
2. with Jacob Harer, PHIsoMap: Intrinsic Distance for Dimension Reduction via Persistent Homology (Submitted, 2011)
3. with Herbert Edelsbrunner, Dmitrity Morozov, and Amit Patel, Homology and Robustness of Level and Interlevel Sets, Homology, Homotopy, and Applications (Accepted, 2011)
4. with Sergio Cabello and Herbert Edelsbrunner, A Point Calculus for Interlevel Set Homology, Pattern Recognition Letters, to appear. (Accepted, 2011)
5. with Taras Galkovskiy and John Harer, Improving Homology Estimates with Random Walk, Inverse Problems, vol. 27 no. 12 (Accepted, 2011)

Conferences Organized

• conference, December 2011