Markus Pfeiffer's homepage
My name is Markus Pfeiffer and I am a PhD research
student at the school of Mathematics and Statistics in
St. Andrews. I am supervised by
Prof. Nik Ruskuc
and
Dr. Max Neunhoeffer
.
My current research deals with word problems of
semigroups, and I am aiming towards a hierarchy of word
problem difficulties together with classification
theorems. My other research interests include but are
not limited to geometric properties of groups,
semigroups and other algebraic structures, automata and
languages and computational algebra.
I am also interested in Category Theory, Programming,
Mathematical Logic and Universal Algebra and Automated
Proof and a lot more and in particular in building
bridges from maths back to applications.
Talks and slides
- Automata and Growth Functions for the Triangle Groups, Conference on Infinite Group Theory, Edinburgh, December 2008, [PDF]
- Semigroups with easily solvable word problem, NBSAN Meeting, St. Andrews, May 2010, [PDF]
- Word Problems for Semigroups, Monoids and Groups, The Burn 2010, [PDF]
- Pure maths is just inventing new numbers isn't it?, CAPOD Postgraduate X-Change, December 2011, [PDF]
- A surprising theorem, talk based on the paper The Kuratowski Closure-Complement-Theorem by B.J. Gardner and M. Jackson.
Teaching
- 2011/2012
- In the academic year 2011/2012 I will try to organise a small research seminar for honours students and PhDs. I am aiming at researching semigroups of small orders for properties connected with formal lanugages. This will be a project that features hands on programming in GAP as well as proving theorems (what some people consider "actual maths"). For details check the detailed page .
- 2010/2011
- In the academic year 2010/2011 I will organise a reading group on the subject of Mathematical Logic. This will mainly be aimed at undergraduate students in maths but we will welcome everyone who is interested. A tentative overview of what I want to cover can be found here
- 2009/2010
- Talk about theory of computation
- Talk about complexity theory
- Talk about foundations of maths
Publications
- 2004
- Fast Nearest Neighbor Search in Medical Image Databases, Aachener Schriften zur Medizinischen Informatik, Vol. 1, Band 8, 2004
- 2008
- Word Acceptors and Growth Functions for the Triangle Groups, Diploma Thesis, [PDF]
- 2011
- Deciding Word Problems using Finite State Automata (with Max Neunhoeffer and Nik Ruskuc), submitted to Theoretical Computer Science preprint [PDF]
- On Baumslag's Proof of Finite Presentability of Wreath Products of Groups, in preparation
- Semigroups with Polyrational Word Problem, in preparation
- 2012
- Word Acceptors and Syntactic Semigroups for the Triangle Groups, in preparation
- Small Syntactic Semigroups, in preparation
Other Work
- I prepared a page with graphical representations of small semigroups and you can find it here
- Small collection of lemmas and theorems about semigroups. [PDF] (With many thanks to Simon Craik)
- An attempt at rephrasing Baumslag's proof when wreath products of finitely presented groups are finitely presented. [PDF]
- Some GAP code to find "syntactic" semigroups in the smallsemi library . This is work done with James Mitchell, Yann Peresse, Jennifer Awang, Bruce Clarke, Rhiannon Dougall, Julius Jonusas, and Michael Torpey for the small semigroups research project . [git]
- Some GAP code to compute some combinatorics on fractals based on the article Symmetry and enumeration of self-similar fractals by Kenneth J. Falconer and John J. O'Connor [git]
Thesis
No, it is not done yet. If you want to have an idea how it is progressing you can watch the word count and various other statistics here
Acknowledgements
- Thanks to Marc Aschmann for the CSS and HTML help with this page.
- Thanks to Edwin Brady for the inspiration for the progress display for my thesis.