Research Interests

geometry, topology and their applications

• visualizing topology
• visualizing geometry
  • hyperbolic geometry
  • frenet frames on helix w/code here
  • parallel transport on a torus w/code here
• geometric and topological data analysis
• visualizing data
• math education
  • what if ax=b meant ax=me?
• algorithms on manifolds
• anomaly detection algorithms

undergraduate research

• fun with fourier

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

reading list

• masters thesis ideas
• data & cartan’s moving frames

software and algorithms

• r for matlab users
• tda in r
• matrix algebra in r
• mass - modern applied statistics in s

papers and preprints

• Pseudo Isometric Surgery with Matt Clay, in Topology Proceedings

admissible sequence

• 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