Faculty of Mathematics
Collaborative Research Centre 701
Spectral Structures and Topological Methods in Mathematics
stripes SFB701

Project B2

Combinatorial and topological structure of aperiodic tilings


Principal Investigator(s) Other Investigators
Michael Baake
Franz Gähler
Jean Bellissard
Tobias Jakobi
Chrizaldy Neil C. Manibo
Eden Delight Provido
Timo Spindeler
Peter Zeiner

Summary:

In this project, we investigate the combinatorial and topological structure of tiling spaces, as well as related lattice problems. Tiling spaces are typically obtained as the hull of one or several tilings under the action of the translation group. In particular, we study the close relations between the combinatorial and geometric properties of the individual tilings, the topological properties of the tiling space, and the properties of the dynamical system under the translation action.

Recent Preprints:

16056 A guide to lifting aperiodic structures PDF | PS.GZ
15075 Determining pure discrete spectrum for some self-affine tilings PDF | PS.GZ
15061 Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examples PDF | PS.GZ
15053 Subgroup Isomorphism Problem for Units of Integral Group Rings PDF | PS.GZ
14076 Radial spacing distributions from planar points sets PDF | PS.GZ
14031 Topology of the Random Fibonacci Tiling Space PDF | PS.GZ
14030 Quotient cohomology of certain 1- and 2-dimensional substitution tiling spaces PDF | PS.GZ
14029 A computer search for planar substitution tilings with n-fold rotational symmetry PDF | PS.GZ
14020 Similar submodules and coincidence site modules PDF | PS.GZ
14005 Tiling Vertices and the Spacing Distribution of their Radial Projection PDF | PS.GZ