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

# Project B2

## Combinatorial and topological structure of aperiodic tilings

Principal Investigator(s) Other Investigators

## 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:

 17027 Geometric properties of a binary non-Pisot inflation and absence of absolutely continuous diffraction PDF | PS.GZ 17024 Lyapunov exponents for binary substitutions of constant length PDF | PS.GZ 16060 What is Aperiodic Order? PDF | PS.GZ 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 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