# Mathematics

During the period 2005 – 2010, I worked on my PhD in mathematics. I am no longer active in academic research in mathematics, but I would like to write a short summary here.

For the most complete and comprehensive reading with least overlap, I recommend the thesis, the errata and the two articles with Jong Bum Lee and Ku Yong Ha.

## Publications in journals with peer review

It is stardard practice in mathematics to list authors in alphabetical order. I believe this helps to maintain a friendly relationship between the co-authors.

- K. Dekimpe, P. Penninckx,
**On the number of generators of a Bieberbach group**, Comm. Algebra., Vol. 37, No. 12, Dec. 2009, pp. 4332–4345 - K. Dekimpe, B. De Rock, P. Penninckx,
**The R**, Topol. Methods Nonlinear Anal., Vol. 34, No. 2, Dec. 2009, pp. 353–374_{∞}property for infra-nilmanifolds - K. Dekimpe, P. Penninckx,
**Coincidence theory for infra-nilmanifolds**, Topol. Appl., Vol. 157, Issue 10-11, 2010, pp. 1815–1832 - K. Dekimpe, B. De Rock, P. Penninckx,
**The Anosov theorem for infra-nilmanifolds with a 2-perfect holonomy group**, Asian J. Math., Vol. 15, No. 4 (2011), pp. 539–548 - K. Dekimpe, P. Penninckx,
**The finiteness of the Reidemeister number of morphisms between almost-crystallographic groups**, J. Fix. Point Theory A., Volume 9, Number 2(2011), pp. 257–283 - K.Y. Ha, J.B. Lee, P. Penninckx,
**Anosov theorem for coincidences on special solvmanifolds of type (R)**, P. Am. Math. Soc., Vol. 139, No. 6, June 2011, pp. 2239–2248 - K.Y. Ha, J.B. Lee, P. Penninckx,
**Formulas for the Reidemeister, Lefschetz and Nielsen coincidence number of maps between infra-nilmanifolds**, Fixed Point Theory A., 2012:39

# Thesis

- P. Penninckx,
**Fixed point theory and coincidence theory for infra-nilmanifolds**, PhD thesis, K.U.Leuven, 2009 (errata)

Please also see the errata.

# Software

I used a lot of computer experimentation to test hypothesis or find counterexamples. I fixed a bug in CARAT (Crystallographic Algorithms And Tables).

# Signal processing

During the autumn of 2010, I had a position at the K.U.Leuven that allowed me to investigate two tensor-based algorithms for blind signal separation. The contract was for a short period of time (only three months) and I had bad luck with the algorithms (they did not work as well as expected), but I am grateful for this experience because I learned a lot.