Homepage of P. Christopher Staecker: All Publications and Talks

This page is a full list of my publications, preprints, and academic talks. For my general research interests, see Research.

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.

Academic Talks and Presentations

• 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
• Some digital topology and a Borsuk-Ulam Theorem
  A 50 minute talk given for the Fairfield REU program. Accessible to math undergraduates. Given at Fairfield University, July 23, 2015.
  
  • Video
• Four theorems about the Euler characteristic and some space invaders
  A 45 minute talk given for the Fairfield REU program. Accessible to math students and other mathematically able undergraduates. Given at Fairfield University, June 19, 2014.
  
  • Video
• The rotation number for maps on graphs
  A talk about my paper with Chris Bernhardt: "Generalizing the rotation interval to vertex maps on graphs". Given at the Mathematics Department Colloquium, City College of New York, November 21, 2013. Also at the Mathematics Department Colloquium, Memorial University, Canada, March 27, 2014.
  
  • PDF of my handwritten notes
• Cultivating the gift of awe
  A talk about being small in big empty universe and what it all means for people of faith. At the Huntington lecture series on the life of faith, Huntington United Methodist Church, Shelton CT, October 20, 2013.
  
  • Video
• All kinds of big: Hadwiger's Theorem
  A 30 minute talk given for the Fairfield REU program. Accessible to math students and other mathematically able undergraduates. Given at Fairfield University, July 18, 2013.
  
  • Video
  • PDF of slides LaTeX source
• Axioms for the Lefschetz number as a lattice valuation
  A 30 minute talk given at the Nielsen Theory and Related Topics 2013 conference in Daejeon, Korea, June 28, 2013.
  
  • Video
  • PDF of slides LaTeX source
• 85 years of Nielsen Theory
  A series of 3 one-hour "mini-lectures" giving a general survey of Nielsen Fixed Point, Periodic Point, and Coincidence Point theories. Given at the Nielsen Theory and Related Topics 2013 conference in Daejeon, Korea, June 24-27, 2013.
  
  • Videos: Fixed Points Periodic Points Coincidence Points
  • PDFs of slides: Fixed Points Periodic Points Coincidence Points
    LaTeX source: fixed points periodic points coincidence points
• Voting: How it works, and why it doesn't
  A talk about the unexpectedly crazy mathematics of voting. At the Fairfield University Mathematics & Computer Science Colloquium, November 6 (election day) 2012.
  
  • Video
  • PDF of slides LaTeX source
• The artistry of discovery, and the shocking beauty of God's creation, also known as God loves complexity
  A talk about beauty and complexity in mathematics and what this means to people of faith. At the lecture series on the life of faith, Huntington United Methodist Church, Shelton CT, October 18, 2012.
  • Video
  • PDF of slides LaTeX source
• Dynamics of random selfmaps on surfaces with boundary (PDF), presented at the 2012 Joint Mathematics Meetings, Boston MA, January 7, 2012. LaTeX source
• Nielsen equalizer theory (PDF), presented at the International conference on Nielsen fixed point theory and related topics, Beijing, China, June 24, 2011. LaTeX source
• Elegant ideas, and why you should love them (5MB PDF), the Pi Mu Epsilon Karim Faroud Memorial Lecture, Fairfield University, April 17, 2011. LaTeX source
• Nielsen coincidence theory of iterates (112KB PDF), presented at the AIMS International Conference on Dynamical Systems, Differential Equations and Applications, Dresden, Germany, May 27, 2010. LaTeX source
• Typical elements in free groups are in different doubly-twisted conjugacy classes (125KB PDF), presented at the 2009 conference on Nielsen Theory and Related Topics, St. John's Newfoundland, June 10, 2009. LaTeX source
• Fixed point and coincidence theory on circle bouquets in ten minutes (641KB PDF), a talk for nonmathematicians given for the Messiah College School of Mathematics, Engineering, and Business, March 25, 2009. LaTeX source
• Nielsen fixed point and related theories, presented at the University of Pennsylvania Deformation Theory Seminar, February 25, 2009.
• Generic doubly-twisted conjugacy classes in free groups (83KB PDF), a contributed paper at the AMS Session on Group Theory, at the AMS/MAA Joint Meetings in Washington, DC, January 8, 2009. LaTeX source
• Nielsen fixed point and related theories, presented at the Tetrahedral Geometry/Topology Seminar, November 7, 2008.
• A gentle introduction to fixed point theory, an episode of the Mathematics and Computer Science Chats at Dickinson College, September 30, 2008.
• Teaching mathematics using wikis, presented at the Joint Mathematics Colloquium of Millersville University and Franklin & Marshall College, April 10, 2008.
• A Survey of Nielsen Fixed Point Theory, presented at the Fall Colloquium of the Mathematics Department at the US Naval Academy, Annapolis, August 22, 2007.
• Axioms for a local Reidemeister trace in fixed point and coincidence theory (77KB PDF), presented at a conference on Topological Theory of Fixed and Periodic Points in Będlewo, Poland, July 2007. LaTeX source
• The uniqueness of the coincidence index on orientable differentiable manifolds (116KB PDF), presented at the AMS special session on Fixed Point Theory, Dynamics, and Group Theory, at the AMS/MAA Joint Meetings in New Orleans, LA, January 5, 2007. LaTeX source
• Wiki in the mathematics classroom (355KB PDF), a contributed paper at the MAA Session on Getting Students to Discuss and to Write about Mathematics, at the AMS/MAA Joint Meetings in New Orleans, LA, January 6, 2007. LaTeX source
• Participation and presentation in a meeting of Fixed point theory and related topics in Lewiston, ME, April 25, 2006.
• Computation of Reidemeister classes by nilpotentization (70KB PDF), talk given at the AMS special session on geometric methods in group theory and topology in Durham, NH, April 22, 2006. LaTeX source