Harri Varpanen (last updated: 29 May 2026)

I work as a Senior Lecturer at the IT institute of Jamk University of Applied Sciences.

I received my Ph.D. training in analysis (p-harmonic functions), but my interest has mostly been in countable Markov chains arising from juggling patterns.

Lately I have been tinkering with some scripting such as a juggling simulator and a go board capturing system.

Preprints (may differ from the published versions):

• On a linearized p-Laplace equation with rapidly oscillating coefficients.
  Illinois Journal of Mathematics 59(2), 499-529, 2016.
  H. Varpanen. (Problem resolved in this preprint.)
• Geometric juggling with q-analogues.
  Discrete Mathematics 338, 1067-1074, 2015.
  A. Engström, L. Leskelä, H. Varpanen.
• Toss and Spin Juggling State Graphs.
  Proceedings of Bridges 2014, pp. 301-308, 2014.
  H. Varpanen. (See also this site.)
• The p-Laplacian with respect to measures.
  Journal of Mathematical Analysis and Applications 400(1), 86-95, 2013.
  A. Tuhola-Kujanpää, H. Varpanen.
• Juggler's exclusion process.
  Journal of Applied Probability 49(1), 266-279, 2012.
  L. Leskelä, H. Varpanen.

Course:

• Math of juggling (Aalto University, spring 2015)
  

Popular math articles (in Finnish):

• The return of the rotating box.
  Arkhimedes 2/2012, p. 21.
  T. Eirola, H. Varpanen.
• Stable and unstable rotation.
  Arkhimedes 5/2009, 10-13.
  H. Varpanen.
• On juggling.
  Solmu 3/2005.
  H. Varpanen.

Theses:

• Gradient estimates and a failure of the mean value principle for p-harmonic functions.
  Ph.D. Thesis, University of Jyväskylä, 2008. (Disclaimer)
• On periodic juggling patterns. (In Finnish)
  M.Sc. Thesis, University of Jyväskylä, 2004.

Videos:

• Varpanen Heureka 2013
• Hacking a Moodle course via its backup file (2020, in Finnish)