Homepage of P. Christopher Staecker: Research

My research is in topological (Nielsen) fixed point theory and some related areas, and the topological theory of digital images. For an introduction to Nielsen fixed point theory for the general mathematical audience, try watching my Youtube videos 85 Years of Nielsen Theory.

My Erdős number is 4: Staecker → Gonçalves → Golasiński → Henriksen → Erdős.

You can download my Curriculum Vitae (74KB PDF) LaTeX source.

Recent Writings and Publications

All of my papers are available at arXiv. The arXiv versions are essentially identical to the published versions. These are also mirrored at Fairfield University's Digital Commons.
Most of my papers eventually get indexed at MathSciNet and Zentralblatt.

Recent Academic Talks and Presentations

• A higher homotopy group for digital images
  A 20 minute research talk given at the Joint Math Meetings, AMS Special Session on Discrete Homotopy Theory. January 5, 2024, in San Francisco. This presents joint work with Gregory Lupton, Oleg Musin, Nicholas Scoville, and Jonathan Treviño-Marroquín.
  
• Video My more accessible talk on the same topic
• Bob Brown's n-valued Nielsen Theory, and a bit more
  A tribute to my PhD advisor Robert F. Brown (1935-2022). This is a 50 minute research talk presented at the conference on Nielsen Theory and Related Topics, in Ostend Belgium, June 5 2023.
  • Video
• Instruments for length and area
  A 40 minute talk given at the Fairfield University Mathematics Colloquium, October 27, 2022. Accessible to anyone.
  • Video
• Gerber's Great Graphical Gizmos
  A 6 minute talk given at Gathering 4 Gardner 14 in Atlanta, April 8 2022. Accessible to anyone.
  • Video
• Nielsen fixed point theory in classical and digital topology
  A series of 3 hour talks given at the Fixed Point Theory Lab, King Mongkut's University of Technology Thonburi, Bangkok Thailand, October 11, 14 & 15, 2019. The first talk requires some basic algebraic topology background, the other two are probably mostly understandable for math undergraduates.
  • Intro to classical Nielsen Theory
  • Fixed points in digital topology
  • Towards a Nielsen theory in digital topology
• Axioms for the fixed point index of an n-valued map
  A 30 minute talk given at the 2019 conference on Nielsen Theory and Related Topics at KU Leuven KULAK, Kortrijk Belgium, June 4 2019.
  • Video
• Rotations on graphs and fractional exponents in groups
  A 50 minute talk given at the Sogang University Mathematics Colloquium, Seoul, South Korea, March 23, 2017.
  The audience was master's-level mathematics graduate students, but anybody can understand the first 15 minutes or so.
  • Video
• The expected difference between N(f) and MF(f)
  A 50 minute research talk given at the 2016 conference on Nielsen Theory and related topics, UNESP Rio Claro, SP, Brazil, July 5 2016.
  
  • Video
  • PDF of slides LaTeX source
• More talks and presentations

Map of talks and jobs

Red are talks, yellow are jobs. Recent things are biggest.

Other stuff

Antique Math Devices

I'm interested in mechanical computation. Here are some pages I made about various old devices. Most go along with my YouTube series.

• Machines