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John J Steenbergen, Graduate Student

John J Steenbergen
Contact Info:
Office Location:  274G Physics
Office Phone:  (919) 660-2800
Email Address: send me a message

Typical Courses Taught:

  • MATH 32, INTRODUCTORY CALCULUS II
  • MATH 41L, INTRO CALCULUS II WITH APPLICA
  • MATH 41L, INTRO CALCULUS II WITH APPLICA
  • MATH 32L, LABORATORY CALCULUS II
  • MATH 32L, LABORATORY CALCULUS II
Education:

PhD (Mathematics, Expected)Duke University2013
MS (Mathematics)Duke University2010
BS (Mathematics with honors)Purdue University2008
BS (Statistics)Purdue University2008
Research Interests:

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

Curriculum Vitae
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]
Selected Talks

  1. A Cheeger-Type Inequality for Simplicial Complexes, November 21, 2012, Princeton University IDeAS Seminar [IDeAS-archive]    
  2. A Cheeger-Type Inequality for Simplicial Complexes, November 12, 2012, Duke University Data Seminar [mcal]    
  3. A Cheeger-Type Inequality for Simplicial Complexes, November 03, 2012, The 8th Annual UNCG Regional Mathematics and Statistics Conference [html]    
  4. Dimension Reduction, Laplacians, and Cheeger Numbers, November 05, 2011, The 7th Annual UNCG Regional Mathematics and Statistics Conference [html]    
  5. Dimension Reduction, Laplacians, and Cheeger Numbers, October 13, 2011, Duke University Data Seminar [mcal]    

 

dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320