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.

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.

*Gerber's Great Graphical Gizmos*

A 6 minute talk given at Gathering 4 Gardner 14 in Atlanta, April 8 2022. Accessible to anyone.*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.*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.*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.*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.

- More talks and presentations

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

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

My research includes techniques for the computation of the Reidemeister trace. These techniques are all encoded for the free open source computational algebra engine GAP.

The easiest way to use these programs is in a web-based implementation:

If you'd prefer, you can download and work with the GAP programs directly yourself. The current release is v2.0, May 2009.

- ntwm2.tar (92 KB)

The package above contains some GAP programs which are of more general interest:

- foxcalc.gap A basic but useful implementation of the Fox Derivative
- dehn.gap Functions for performing Dehn's algorithm for the word problem in finitely presented groups, and some basic functions for verifying small cancellation properties

I have an interest in proof formalization, specifically using the Coq proof assistant, which can produce computer-verifiable proofs of mathematical theorems. You are free to use any of my code subject to the cc-by-sa license.

`listlemmas.v`

A collection of lemmas about lists and sublists.- Browse file: without proofs or with proofs
- Download coq source (.v)

`words.v`

Proof that words in free groups have unique reduced form.- Browse file: without proofs or with proofs
- Download coq source (.v)

PDF icon by David Vignoni from Wikimedia Commons, licenced LGPL