Math @ Duke
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:
Teaching (Fall 2013):
Teaching (Spring 2014):
- MATH 221.01, LINEAR ALGEBRA & APPLICA
- Physics 047, WF 11:45 AM-01:00 PM
- MATH 221.02, LINEAR ALGEBRA & APPLICA
- Physics 259, TuTh 08:30 AM-09:45 AM
- Office Hours:
- Tuesday, 12-1
- 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
- Bryan Jacobson (2012/12-present)
- Recent Publications
- with Jacob Harer and John Harer, A Persistent Homology Based Geodesic Distance Estimator
- with Bei Wang and Sayan Mukherjee, Local Homology Transfer and Stratification Learning,
Proc. of 24th Sympos. on Discrete Algorithms
- with Jacob Harer, PHIsoMap: Intrinsic Distance for Dimension Reduction via Persistent Homology
- with Herbert Edelsbrunner, Dmitrity Morozov, and Amit Patel, Homology and Robustness of Level and Interlevel Sets,
Homology, Homotopy, and Applications
- with Sergio Cabello and Herbert Edelsbrunner, A Point Calculus for Interlevel Set Homology,
Pattern Recognition Letters, to appear.
- Conferences Organized
- conference, December 2011
Duke University, Box 90320
Durham, NC 27708-0320