Josh Thompson
Associate Professor: Northern Michigan University

Research Interests

  • Geometry, topology and their applications
  • Math Education
    •    
  • Visualizing Topology
  • Visualizing Data
  • Geometric and topological data analysis
  • Algorithms on manifolds
  • Anomaly detection algorithms
    •    

    Master's Thesis I've Advised

  • Visualizing Geometric Structures on Topological Surfaces
  • Quandles that are Knot Quandles
  • Plumbing the Depths of the Shallow End: Exploring Persistent Homology Using Small Data

    • Software and Algorithms

  • TDA in R
  • Matrix Algebra in R
  • MASS - Modern Applied Statistics in S

    • Papers and Preprints

  • Collapsing Maps & Quasi-Isometries. with undergraduate Davin Hemmila
  • Computing Geographic Distances. with undergraduate Chase Ashby. Mathematical Spectrum Vol. 48, No. 3, April 2016
  • iMath: Digital Images Modeled with Matrices. International Research in Education Vol. 3 No. 1, March 2015.
  • Evaluating Several Different Web Prediction Algorithms. Proc. of the ISCA 29th Int. Conf. on Computers and Their Applications, CATA 2014.
  • Identity Maps and their extensions on Parameter Spaces: Applications to anomaly detection in video, with K. Wang, M. Kirby and C. Peterson. [Proceedings of the Science and Information Conference (SAI), pp 345-351, 2015 DOI: 10.1109/SAI.2015.7237167 ]

  • Accurate Fault Prediction of BlueGeneP RAS Logs Via Geometric Reduction [.pdf] Proc. of IEEE/IFIP International Conference on DSN, 2010.

    •    MSET on BlueGeneP Figure

  • Graftings of Complex Projective Structures with Schottky Holonomy [.pdf] Geometriae Dedicata: Volume 166, Issue 1 (2013), Page 203-232.
    •   

    Grafting Figure