Research interestsComputational Topology, Topological Data Analysis
- Python Mapper (with Aravindakshan Babu)
- fastcluster: Fast hierarchical clustering routines for R and Python
- xypdf, PDF output for diagrams in LaTEX with the XY-pic package
- My favorite desktop theme
- Daniel Müllner, Modern hierarchical, agglomerative clustering algorithms, arXiv: 1109.2378
- Elisa Dultz, Harianto Tjong, Elodie Weider, Mareike Herzog, Barry Young, Christiane Brune, Daniel Müllner, Christopher Loewen, Frank Alber, Karsten Weis, Global reorganization of budding yeast chromosome conformation in different physiological conditions, J Cell Biol 212 (2016), no. 3, 321–334
- Daniel Müllner, fastcluster: Fast Hierarchical, Agglomerative Clustering Routines for R and Python, Journal of Statistical Software 53 (2013), no. 9, 1–18
- Daniel Müllner, Orientation reversal of manifolds, Algebr. Geom. Topol. 9 (2009), no. 4, 2361–2390
Dissertation: Orientation reversal of manifoldsAdvisor: Prof. Matthias Kreck
I study the phenomenon of chirality in the context of manifolds. A connected, orientable manifold is called amphicheiral if it admits an orientation-reversing self-map and chiral if it does not. Many familiar manifolds like spheres or orientable surfaces are amphicheiral: they can be embedded mirror-symmetrically into Rn, as the following figure illustrates.
|Reflect at the equator:|
On the other hand, examples of chiral manifolds have been known for many decades, e. g. the complex projective spaces CP2k and some lens spaces in dimensions congruent 3 mod 4. A fundamental question was in which dimensions chiral manifolds exist. While every manifold in dimensions 1 and 2 is amphicheiral, one of my results is that in all other dimensions there exist chiral manifolds.
For more information, read a summary or the dissertation itself:
- Daniel Müllner, Orientation reversal of manifolds, Bonner Mathematische Schriften, vol. 392, Bonn, 2009