Publications (33)
Central Triangulation under Parallel Flip Operations: The CG:SHOP Challenge 2026
Oswin Aichholzer, Joseph Dorfer, Sándor P. Fekete +3
We give an overview of the 2026 Computational Geometry Challenge targeting the problem of finding a Central Triangulation under Parallel Flip Operations in triangulations of point…
Quasicrystals
Uwe Grimm, Peter Kramer
Mathematicians have been interested in non-periodic tilings of space for decades; however, it was the unexpected discovery of non-periodically ordered structures in intermetallic a…
Harmonic polynomials for expanding the fluctuations of the Cosmic Microwave Background: The Poincare and the 3-sphere model
Peter Kramer
Fluctuations of the Cosmic Microwave Background CMB are observed by the WMAP. When expanded into the harmonic eigenmodes of the space part of a cosmological model, they provide ins…
Exact electron states in 1D (quasi-) periodic arrays of delta-potentials
Peter Kramer, Tobias Kramer
Exact one-electron eigenstates in finite parts of 1D periodic and Fibonacci chains of attractive and repulsive delta potentials are computed and analyzed. Bloch and bound state bou…
Tiling theory applied to the surface structure of icosahedral AlPdMn quasicrystals
Peter Kramer, Zorka Papadopolos, Harald Teuscher
Surfaces in i-Al68Pd23Mn9 as observed with STM and LEED experiments show atomic terraces in a Fibonacci spacing. We analyze them in a bulk tiling model due to Elser which incorpora…
Efficiently Reconfiguring a Connected Swarm of Labeled Robots
Sándor P. Fekete, Peter Kramer, Christian Rieck +2
When considering motion planning for a swarm of labeled robots, we need to rearrange a given start configuration into a desired target configuration via a sequence of parallel,…