Research Interests for John J Steenbergen

My attention has been focused on the spectra of the Hodge Laplacians defined on simplicial complexes and how they relate to certain newly-defined isoperimetric constants and random walks. The goal is to generalize the theory of graph expansion to higher dimensions and, ultimately, to analyze the geometry of data via Laplacian eigenvalues.

Areas of Interest:

Applied and Computational Topology/Geometry
Topological/Geometrical Data Analysis
High-dimensional Data Analysis
Dimension Reduction Methods
Clustering
Spectral Graph Theory

Recent Publications

1. J.J. Steenbergen, Caroline Klivans, Sayan Mukherjee., “A Cheeger-Type Inequality on Simplicial Complexes” (Preprint, September, 2012) (Under Review, Advances in Applied Mathematics.) [5091]